All puzzles

• analysis/additive.partitionCan the set of positive reals be partitioned into two nonempty sets, both of which are closed under addition? New
• analysis/alternating.seriesGive a concise proof that, asymptotically as n grows, New
• analysis/am.gm.boundGiven real a1, a2, ..., an with arithmetic mean A and geometric mean G, show that New, unsolved
• analysis/bicycleA boy, a girl and a dog go for a 10 mile walk.
• analysis/boy.girl.dogA boy, a girl and a dog are standing together on a long, straight road.
• analysis/bugsFour bugs are placed at the corners of a square.
• analysis/buridanA driver leaves home and drives along a road with a railway crossing, and a train will pass the crossing at some time. New
• analysis/c.infinityWhat function is zero at zero, strictly positive elsewhere, infinitely differentiable at zero and has all...
• analysis/cacheCache and Ferry (How far can a truck go in a desert?) A pick-up truck in the desert gets 10 miles per... Added material
• analysis/calculate.piHow can I calculate many digits of pi? Added material
• analysis/cats.and.ratsIf 6 cats can kill 6 rats in 6 minutes, how many cats does it take to kill one rat in one minute?
• analysis/cauchy.completenessCan the monotone convergence theorem (every bounded monotone sequence of real numbers has a limit) be... New
• analysis/cylinderA right circular cylindrical container with a closed top is to be constructed with a fixed surface area. New
• analysis/derivation.algebrasClassify the vector spaces with an associative product and a nonzero derivation d(ab) = da b + a db. New, unsolved
• analysis/dogA body of soldiers form a 50m-by-50m square ABCD on the parade ground. Added material
• analysis/e.and.piWithout finding their numerical values, which is greater, e^(pi) or (pi)^e?
• analysis/euler.constantIs there a reference for this approximation to Euler's constant, and is there a faster expression? New, unsolved
• analysis/find.the.errorFind the error in each of these two "paradoxes". New, unsolved
• analysis/goatA goat grazes on a circular meadow, its tail is tacked to a stake of the fence - What's the length of the... Added material
• analysis/integralIf f is integrable on (0,inf) and differentiable at 0, and a > 0, and:
• analysis/integral.kernelIf f and g are positive continuous functions on [0,1], k is a positive continuous kernel on [0,1]x[0,1],... New
• analysis/integration.by.partsWhat is wrong with this proof, by integration by parts, that 0 = 1? New, unsolved
• analysis/irrational.stampYou have an ink stamp which is so amazingly precise that, when inked and pressed down on the plane, it...
• analysis/matrix.exponentialHow do you compute the exponential exp(B) of a matrix B? New
• analysis/minimum.timeN people can walk or drive in a two-seater to go from city A to city B.
• analysis/multiple.regressionHow should one compute a multiple linear regression, which amounts to solving a symmetric system of... New
• analysis/nested.square.rootsWhat is the value of x = sqrt( 2 + sqrt( 2 + sqrt( 2 + sqrt( 2 + ...))))? New
• analysis/particleWhat is the longest time that a particle can take in travelling between two points if it never increases...
• analysis/periodWhat is the least possible integral period of the sum of functions of periods 3 and 6?
• analysis/pig.and.farmerA pig runs from one corner of a square pen toward the gate at an adjacent corner while the farmer, starting... New
• analysis/point.nine.repeatingIs 0.999... (nines repeating forever) equal to 1? New
• analysis/quaternionsCan every polynomial with quaternion coefficients be factored into linear factors? New
• analysis/rubberbandA bug walks down a rubber band which is attached to a wall at one end and a car moving away from the wall at the other end. Added material
• analysis/sequenceShow that in the sequence: x, 2x, 3x, ....
• analysis/snowSnow starts falling before noon on a cold December day. Added material
• analysis/step.functionThe function f is defined on the integers in the range 0..100 by the rule: New
• analysis/surreal.numbersWhat are Conway's surreal numbers, and how do they make things such as 1/infinity rigorous? New
• analysis/towerR = N ^ (N ^ (N ^ ...)). Added material
• analysis/two.to.one.functionIs it possible to construct a function f(x) which maps the closed interval [0,1] to [0,1] such that any... New
• analysis/well.orderingSet theory says (using the Axiom of Choice) that every set can be well ordered; how can that be, when the... New
• analysis/functional/distributedFind all f: R -> R, f not identically zero, such that (*) f( (x+y)/(x-y) ) = ( f(x)+f(y) )/( f(x)-f(y) ).
• analysis/functional/half.iterateLet f(x) = (sqrt(2))^x for x > 0; then f^-1(x) = 2 ln(x)/ln(2). New, unsolved
• analysis/functional/linearSuppose f is non-decreasing with f(x+y) = f(x) + f(y) + C for all real x, y.
• analysis/functional/minus.xIdentify a real valued function f(x) which has the property for all real x that f(f(x)) = -x. New
• arithmetic/7-11A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. Added material
• arithmetic/aliquot.sequencesIn an aliquot chain one starts with a number, calculates the sum of its proper divisors, and repeats the process on the result. New
• arithmetic/arithmetic.progressionIs there an arithmetic progression of 20 or more primes?
• arithmetic/birds.in.treesThere is a field. New, unsolved
• arithmetic/cattle.of.the.sunArchimedes' cattle problem has two versions, based on alternate readings of its second paragraph; what are... New, unsolved
• arithmetic/charred.willAfter a fire destroyed the home, the life and the will of a rich aristocrat, a detective found among the... New, unsolved
• arithmetic/coconutsFive sailors collect a pile of coconuts; in the night each in turn divides the pile into five, gives the... New
• arithmetic/collatzStart with any positive integer x; if it is even, replace it by x/2, if odd by 3x+1, and repeat. New
• arithmetic/consecutive.compositesAre there 10,000 consecutive non-prime numbers?
• arithmetic/consecutive.p2qNumbers of the form (p^2)q, p and q different primes, are "special". New
• arithmetic/consecutive.productProve that the product of three or more consecutive positive integers cannot be a perfect square.
• arithmetic/consecutive.sumsFind all series of consecutive positive integers whose sum is exactly 10,000.
• arithmetic/conwayDescribe the sequence a(1)=a(2)=1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n>2. Added material
• arithmetic/count.one.bitsCount the number of ones in a binary number using as few instructions as possible. New
• arithmetic/dogs.meadSolve the cross-number puzzle "Dog's Mead" (also known as "Little Pigley Farm"), in which every entry is a... New, unsolved
• arithmetic/dogs.mice.catsA dog costs $15, four mice cost $1 and a cat costs $1. New
• arithmetic/drawing.pixelsA computer draws a horizontal line 128 pixels long in n seconds with the command "Plot 0,0 128,0 n". New
• arithmetic/egyptian.fractionCan you represent 36/457 as a sum of different fractions with numerator 1? New
• arithmetic/egyptian.fractionsExpress 36/457 as a sum of distinct unit fractions (fractions with numerator 1). New
• arithmetic/element.alphameticEach of the 26 letters has a secret numerical value, and the value of a word is the sum of the values of its letters. New
• arithmetic/factoring.recordWhat is the largest number factored by a general purpose algorithm, and how was it done? New
• arithmetic/fermat.numbersWhat factors are known of the Fermat numbers F_n = 2^(2^n) + 1? New
• arithmetic/feynman.fermatIs there a probabilistic argument that Fermat's Last Theorem is true? New
• arithmetic/five.five.fiveMake the equation 5+5+5=550 true by adding just a single straight line. New
• arithmetic/four.squaresFind integers a, b such that a+45b, a+5b, a+15b and a-3b are all squares. New
• arithmetic/fourth.powersEuler conjectured in 1769 that a^4 + b^4 + c^4 = d^4 has no solutions in positive integers. New
• arithmetic/goldbachWhat is known about Goldbach's conjecture, that every even integer greater than 4 is the sum of two odd... New
• arithmetic/grandpa.sonsWhen Grandpa was over fifty but less than eighty, he told to a friend: "each of my sons has as many sons as... New
• arithmetic/hamming.numbersHamming numbers are defined as numbers whose only prime factors are 2, 3, and 5. New
• arithmetic/highly.compositeWhich numbers n have more divisors than any smaller number, and how large is the number of divisors d(n)... New
• arithmetic/house.numbersA street has between 50 and 500 houses numbered 1, 2, 3, ..., N, and there is a house X such that the sum... New
• arithmetic/integral.rootsWhat is the second smallest integer with integral third, fourth and fifth roots? New
• arithmetic/irrational.powerCan you prove that there is at least one instance where an irrational number raised to an irrational power... New
• arithmetic/knapsacksOn the last day of his vacation, a man goes into a gift shop to buy presents for his grandchildren. New
• arithmetic/largest.non.mersenne.primeWhat is the largest prime integer known to man that is NOT one less than a power of two? New
• arithmetic/lockersThere are 100 closed lockers in a row, numbered 1 to 100, and 100 students. New
• arithmetic/mad.veterinarianA mad veterinarian has created three animal transmogrifying machines. New
• arithmetic/magic.hexagramThe Magic Hexagon New
• arithmetic/magic.squaresAre there large squares, containing only consecutive integers, all of whose rows, columns and diagonals have the same sum? Added material
• arithmetic/max.ageMax discovered that if he subtracted 7 from his age and multiplied it by 7, he got the same answer as... New
• arithmetic/mersenne.primesWhat Mersenne primes 2^p - 1 are known, and when, how and by whom was each one found? New
• arithmetic/negative.baseHow much is 7 in base (-1)? New
• arithmetic/nth.primeThe 1st prime is 2, the 10th prime is 29, the 100th prime is 541, the 1000th prime is 7919, the 10000th... New
• arithmetic/pellFind integer solutions to x^2 - 92y^2 = 1.
• arithmetic/perfect.numbersWhat are all [ Editor: "Can you determine all" in the original ] the "perfect" numbers between 1 and 1,000,000? New
• arithmetic/periodic.recurrenceCan a non-trivial integer sequence in which each element is the sum of the k previous elements be periodic? New
• arithmetic/prime.magic.squareIs there a 3x3 magic square made up of nine different prime numbers? New
• arithmetic/prime.products.setShow that there exists a set A of positive integers with the following property: for every infinite set S... New
• arithmetic/prime.seriesHere is a number series: 41, 43, 47, 53, ... New
• arithmetic/prime.square.sumFind all solutions in integers to a^2 + b^2 + c^2 = d^2, where a, b and d are prime. New
• arithmetic/product.of.powersFind rational numbers a,b,c,d,e,f,g,h,i,j such that: New
• arithmetic/pythagorean.odd.legsIs it possible to construct a right triangle with integer sides having both of the legs odd integers? New
• arithmetic/ratio.64.7The product of some of the numbers 1 to 10 was divided by the product of the remaining numbers. New
• arithmetic/rational.rootsShow that an n-th root of an integer is either an integer or irrational. New
• arithmetic/remainder.one.lessWhat number, if divided by 10, leaves a remainder of 9; then divided by 9 leaves a remainder of 8; divided... New
• arithmetic/repeated.integersCome up with the general formula for the n-th term of the following sequence: New
• arithmetic/seven.unit.fractionsFind seven different unit fractions whose sum is 1. New
• arithmetic/snails.crossingA family of snails takes one hour to cross a lawn, from the time that the first snail puts its 'nose' onto... New
• arithmetic/square.productsProve that for any three positive integers a, b, c such that the product of any two is one less than a square, New
• arithmetic/square.progression.chainIt is not uncommon to find a triple of integers whose squares are in arithmetic progression, e.g. New
• arithmetic/square.root.partitionSplit the square roots of 1, 2, 3, ..., 49, 50 into two groups so that the difference between the sums of... New
• arithmetic/subsetProve that all sets of n integers contain a subset whose sum is divisible by n.
• arithmetic/sum.of.cubesFind two fractions whose cubes total 6.
• arithmetic/sum.of.two.primesIs every even number greater than 2 the sum of two primes? New
• arithmetic/sums.of.powersPartition 1,2,3,...,16 into two equal sets, such that the sums of the numbers in each set are equal, as are...
• arithmetic/taxicabIs 1729 the only number that is the sum of two cubes in two different ways? New
• arithmetic/tenth.root.of.tenWhich is larger, the tenth root of ten or the cube root of two? New
• arithmetic/three.n.plus.oneWhat is a good reference on the 3N+1 problem? New
• arithmetic/titanic.primesWhat are the known titanic primes (primes with at least 1000 decimal digits) that are not Mersenne primes? New
• arithmetic/trampsFour tramps divide 200 hours of work so that each works a different number of hours a day, for as many days as he works hours a day. New
• arithmetic/truncated.multiplicationGiven a function h on {0,1,...,m}, is it a composition of "truncated multiplications" f(x) = floor(x*n)... New
• arithmetic/two.squares.odd.powerHow many solutions are there to a^2 + b^2 = c^5 for integers a, b, c? New
• arithmetic/upside.down.magic.squareUsing the sixteen two-digit numbers made from the digits 1, 6, 8 and 9 (11, 16, 18, 19, 61, 66, 68, 69, 81,... New
• arithmetic/clock/adjacent.ticksAt what times of day is the hour hand of a clock pointing precisely at a minute tick-mark and the minute... New
• arithmetic/clock/christmas.dayProve that the probability that Christmas in a random year will fall on a Wednesday is not 1/7. New
• arithmetic/clock/day.of.weekIt's restful sitting in Tom's cosy den, talking quietly and sipping a glass of his Madeira.
• arithmetic/clock/overlapHow many times per day do a clock's hands overlap?
• arithmetic/clock/palindromicHow many times per day does a digital clock display a palindromic number?
• arithmetic/clock/reversibleHow many times per day can the hour and minute hands on an analog clock switch roles and still signify a...
• arithmetic/clock/right.angleHow many times per day do the hour and minute hands of a clock form a right angle?
• arithmetic/clock/swapped.handsA school clock is showing the wrong time, but the teacher says, "It's wrong now, but it is right 11 times a... New
• arithmetic/clock/thanksgivingHow can you figure out the date of Thanksgiving for any given year? New
• arithmetic/clock/thirdsDo the 3 hands on a clock ever divide the face of the clock into 3 equal segments, i.e.
• arithmetic/digits/6.and.7Does every number which is not divisible by 5 have a multiple whose only digits are 6 and 7?
• arithmetic/digits/abcabcThink of a three-digit number, then form a six-digit number by repeating its three digits (469 becomes 469,469). New
• arithmetic/digits/all.onesProve that some multiple of any integer ending in 3 contains all 1s.
• arithmetic/digits/anomalous.cancellationAmong all 3-digit numbers in which no digit appears more than once, there is one special trait shared by... New
• arithmetic/digits/arabianWhat is the Arabian Nights factorial, the number x such that x!
• arithmetic/digits/armstrong.numbersAre there infinitely many N-digit numbers equal to the sum of the N-th powers of their digits (Armstrong... New
• arithmetic/digits/circularWhat 6 digit number, with 6 different digits, when multiplied by all integers up to 6, circulates its...
• arithmetic/digits/cryptarithmHow do I solve letter substitutions (cryptarithms) like SEND + MORE = MONEY? Added material
• arithmetic/digits/digital.productFor each integer n, write out n in base 10 and let g(n) be the product of the nonzero digits appearing. New
• arithmetic/digits/divisibleFind the least number using 0-9 exactly once that is evenly divisible by each of these digits.
• arithmetic/digits/extreme.productsWhat are the extremal products of three three-digit numbers using digits 1-9?
• arithmetic/digits/hex.multiplesA number has four digits in hexadecimal. New
• arithmetic/digits/kaprekar.6174Take any four-digit number (excluding 1111, 2222, 3333, etc.), sort its digits into descending order, make... New
• arithmetic/digits/labelsYou have an arbitrary number of model kits (which you assemble for fun and profit).
• arithmetic/digits/largest.productUsing all the 9 digits from 1 to 9 and only once, what two numbers multiplied give the largest product? New
• arithmetic/digits/license.plateA mathematics professor complained to the policeman that a student had almost run him down as he attempted to cross the street. New, unsolved
• arithmetic/digits/little.pigleySolve the Little Pigley Farm crossnumber and find the age of Mrs. New, unsolved
• arithmetic/digits/near.integerProve that the decimal expansion of (sqrt(35) + 6)^1995 starts with at least 1000 nines after the decimal... New
• arithmetic/digits/nine.digitsForm a number using 0-9 once with its first n digits divisible by n.
• arithmetic/digits/own.powers3435 = 3^3 + 4^4 + 3^3 + 5^5: it equals the sum of its digits each raised to its own power (taking 0^0 = 0). New
• arithmetic/digits/palindromeDoes the series formed by adding a number to its reversal always end in a palindrome? Added material
• arithmetic/digits/palindrome.differencesWhich integers n can be written as the difference of two palindromes? New
• arithmetic/digits/palindromic.powersWhat are the largest known palindromic squares with a non-palindromic base, palindromic cubes with a... New
• arithmetic/digits/palintiplesFind all numbers that are multiples of their reversals.
• arithmetic/digits/pandigital.prime.factorsThe smallest number whose prime factors, written side by side, use each of the digits 1 through 9 exactly... New, unsolved
• arithmetic/digits/period.of.reciprocalWhat is the length of the repeating period of 1/d written in base r? New
• arithmetic/digits/persistenceThe persistence P(x) of an integer x is the number of times its digits can be multiplied, recursively. New
• arithmetic/digits/power.twoProve that for any 9-digit number (base 10) there is an integral power of 2 whose first 9 digits are that...
• arithmetic/digits/reverseIs there an integer that has its digits reversed after dividing it by 2?
• arithmetic/digits/rotateFind integers where multiplying them by single digits rotates their digits one position, so that the last...
• arithmetic/digits/rotate.temperatureWhen Waldo recently did a conversion of a positive integral Celsius temperature c=275 to its Fahrenheit... New
• arithmetic/digits/sesquiFind the least number where moving the first digit to the end multiplies by 1.5.
• arithmetic/digits/seven.sevensFind the missing digits in this long division problem, where the division has no remainder, and other 7's... New, unsolved
• arithmetic/digits/sevens.long.divisionReconstruct this long division, where most of the digits are represented with asterisks and a few sevens... New, unsolved
• arithmetic/digits/strobogrammaticWhat numerical identities and facts remain true when the page is rotated 180 degrees ("strobogrammatic")? New
• arithmetic/digits/sum.of.digitsFind sod ( sod ( sod (4444 ^ 4444 ) ) ).
• arithmetic/digits/three.digit.sumArrange the digits 1 to 9 to form three 3-digit numbers such that the sum of the two smaller numbers equals the larger. New
• arithmetic/digits/zeros.and.onesDoes every positive integer have a multiple whose decimal representation consists only of 0's and 1's? New
• arithmetic/digits/equations/1234Using the digits 1, 2, 3 and 4 once each, with various sets of allowed operations, how far can you form... New
• arithmetic/digits/equations/123456789In how many ways can "." be replaced with "+", "-", or "" (concatenate) in .1.2.3.4.5.6.7.8.9=1 to form a...
• arithmetic/digits/equations/19921 = -1+9-9+2. Extend this list to 2 through 100 on the left side of the equals sign.
• arithmetic/digits/equations/1994Write as many numbers as possible, from 0 upward, using only the digits 1, 9, 9 and 4, each exactly once... New
• arithmetic/digits/equations/1997Use the four digits 1, 9, 9, 7, in that order, with additions, subtractions, multiplication, division,... New
• arithmetic/digits/equations/24Form an expression that evaluates to 24 that contains two 3's, two 7's, and zero or more of the operators +, -, *, and /, and parentheses.
• arithmetic/digits/equations/383Make 383 out of 1,2,25,50,75,100 using +,-,*,/.
• arithmetic/digits/equations/findWrite a program for finding expressions built out of given numbers and using given operators that evaluate...
• arithmetic/digits/equations/four.4Form expressions equalling each integer from 1 to 112 from four 4's, which may be concatenated to form a... Added material
• arithmetic/digits/equations/make.threeFor each digit from 1 to 9, use that digit three times, with arithmetic operations, to make 3. New
• arithmetic/digits/equations/own.digitsFind all 3-digit numbers that can be formed from their own digits. New
• arithmetic/digits/equations/ten.digits.sum.100Using each of the ten digits 0 through 9 exactly once, and only addition and concatenation (e.g. New
• arithmetic/digits/equations/ten.digits.sum.productUsing the digits 0-9, each only once, construct A+B=C. New, unsolved
• arithmetic/digits/least.significant/factorialWhat is the least significant non-zero digit in the decimal expansion of n!?
• arithmetic/digits/least.significant/factorial.twoWhat are the last two digits of x! New
• arithmetic/digits/least.significant/googolplex.powerIf a googol is 10^100 and a googolplex is 10^googol, what is the digit immediately preceding the last... New
• arithmetic/digits/least.significant/power.of.twoIf G is any integer greater than 1, show that the final digits of 2^(10^G + G + 1) are the same as all the... New, unsolved
• arithmetic/digits/least.significant/tower.of.powerWhat are the least significant digits of 9^(8^(7^(6^(5^(4^(3^(2^1))))))) ?
• arithmetic/digits/most.significant/googolWhat digits does googol!
• arithmetic/digits/most.significant/powersWhat is the probability that 2^N begins with the digits 603245?
• arithmetic/digits/prime/101How many primes are in the sequence 101, 10101, 1010101, ...?
• arithmetic/digits/prime/all.prefixWhat is the longest prime whose every proper prefix is a prime?
• arithmetic/digits/prime/change.oneWhat is the smallest number that cannot be made prime by changing a single digit?
• arithmetic/digits/prime/prefix.one2 is prime, but 12, 22, ..., 92 are not.
• arithmetic/digits/prime/square.difference266117 is a prime number. New
• arithmetic/digits/squares/add.oneIs there an 8-digit square that is still a square when a 1 is written in front of it? New
• arithmetic/digits/squares/change.leadingWhat squares remain squares when their leading digits are incremented?
• arithmetic/digits/squares/length.22Is it possible to form two numbers A and B from 22 digits such that A = B^2? Added material
• arithmetic/digits/squares/length.9Is it possible to make a number and its square, using the digits from 1 through 9 exactly once?
• arithmetic/digits/squares/three.digitsWhat squares consist entirely of three digits (e.g., 1, 4, and 9)?
• arithmetic/digits/squares/twinLet a twin be a number formed by writing the same number twice, for instance, 81708170 or 132132.
• arithmetic/digits/zeros/factorial.givenn is a multiple of 3 and n factorial is equal to: New
• arithmetic/digits/zeros/googolplex.powerTo write a googolplex raised to a googolplex, you write a 1 followed by how many zeros? New
• arithmetic/digits/zeros/millionHow many zeros occur in the numbers from 1 to 1,000,000?
• arithmetic/digits/zeros/trailingHow many trailing zeros are in the decimal expansion of n!?
• arithmetic/tests.for.divisibility/elevenWhat is the test to see if a number is divisible by eleven?
• arithmetic/tests.for.divisibility/nineWhat is the test to see if a number is divisible by nine?
• arithmetic/tests.for.divisibility/sevenWhat is the test to see if a number is divisible by seven? Added material
• arithmetic/tests.for.divisibility/small.divisorsWhat are the tests to see if a number is divisible by 2, 3, 4, ... New
• arithmetic/tests.for.divisibility/threeWhat is the test to see if a number is divisible by three?
• combinatorics/aba.stringsHow many of the strings of ten characters over the alphabet {a,b} contain the substring aba? New
• combinatorics/abracadabraThe word ABRACADABRA is written as a triangle, one letter per row, the first row holding one A, the second... New
• combinatorics/acyclic.digraphsHow many directed acyclic graphs are there on n labelled nodes? New
• combinatorics/alphabet.blocksWhat is the minimum number of dice painted with one letter on all six sides such that all permutations...
• combinatorics/apply.permutationGiven an array A[0..N-1] and a permutation P of 0..N-1 in another array, rearrange A in place so that... New
• combinatorics/bridge.scheduleGiven N teams, how can they play a round-robin tournament, using N-1 prepared games, so that each team... New
• combinatorics/busPutting 33 students in each bus, the teacher has one student left over.
• combinatorics/chlorinated.dioxinsIn the molecule below, chlorine atoms may be attached to any of the 8 outer carbon atoms. New
• combinatorics/colorAn urn contains n balls of different colors.
• combinatorics/counters.beyond.diagonalHow many ways are there to place n counters, diagonal by diagonal, starting from a single counter, so that... New
• combinatorics/covering.recordsTable A lists all 70 combinations of the 8 letters A-H taken 4 at a time; table B lists all 28 combinations taken 6 at a time. New, unsolved
• combinatorics/cube.colouringHow many distinguishable ways are there to paint the faces of a cube using two colours, counting patterns... New
• combinatorics/directed.animalsHow many sets of n squares in the quarter plane contain the corner square and can each be reached from the... New
• combinatorics/disks.on.pegsTwelve disks, each with holes at some of six positions, are to be rotated and stacked so that the pegs pass through them. New
• combinatorics/doors.and.buttonsThere are n doors, and n buttons that control them. New
• combinatorics/euler.circuitsFind a closed formula for the number of Euler circuits on a complete (undirected) graph of n nodes. New
• combinatorics/finite.groupsHow many groups are there of each order up to 16, and what are their multiplication tables? New
• combinatorics/five.sleepersFive people stay overnight in a hotel. New
• combinatorics/fullConsider a string that contains all substrings of length n.
• combinatorics/golf.foursomesSixteen golfers play in foursomes on six different days. New
• combinatorics/golomb.rulerBetween Kroflite and Beeline are five other towns. New
• combinatorics/gossipn people each know a different piece of gossip.
• combinatorics/grid.countingIn an n x n grid of squares, how many squares are there? New
• combinatorics/grid.dissectionHow many (possibly overlapping) squares are in an mxn grid?
• combinatorics/grid.tourA city has 36 locations on a 6x6 grid of roads. New
• combinatorics/happy.cube.pieces"Happy Cube" puzzles each have six square pieces, to be assembled into a hollow cube. New
• combinatorics/josephusYou are one of 1000 captured pirates about to be tied to posts numbered 1 to 1000 arranged in a circle. New
• combinatorics/langfordCan the pattern of 312132 and 23421314 be continued: numbers made of pairs of each digit 1..n, with the two... New, unsolved
• combinatorics/lights.in.circleWe place n lights L_0, L_1, ..., L_{n-1} on a circle. New
• combinatorics/lucky.ticketHow many six-digit tickets (000001 to 999999) have the sum of the first three digits equal to the sum of... New
• combinatorics/multipermutationsIn how many ways can 3n elements be chosen out of an n*n array with exactly 3 in each row and column? New
• combinatorics/no.consecutive.neighborsPut the numbers 1 through 8 into the boxes of this diagram so that no two consecutive numbers are in boxes... New
• combinatorics/np.completeWhat does it mean that a problem is "NP-complete"? New
• combinatorics/odd.permutation.productLet A1, A2, ..., An be any permutation of the numbers 1, 2, ..., n. New
• combinatorics/paths.through.gridHow many distict paths exist from one corner of a rectangular grid to the opposite corner, traveling along...
• combinatorics/permutationCompute the nth permutation of k numbers (or objects).
• combinatorics/phone.dialingHow many telephone numbers can be dialed if each digit is reached from the previous one by a move of a... New
• combinatorics/pizza.toppingsA pizza deal: for one low price you get two pizzas, each with up to 5 toppings chosen from 11. New
• combinatorics/plutarch.numbersPlutarch reports that Hipparchus counted 103,049 compound propositions "on the affirmative side" and... New
• combinatorics/raised.buttonsA 3 x 3 grid of buttons, numbered like a keypad New
• combinatorics/roller.coasterFour people line up for a roller coaster. New
• combinatorics/round.robinSchedule a round robin tournament in which there are N teams, each one playing all the others, in the... New
• combinatorics/same.handshakesProve that if n people attend a party, there will be at least two people who shake the same number of hands. New
• combinatorics/shannon.switching.gameIs there an algorithm for determining whether a given undirected graph has two edge-disjoint spanning trees... New
• combinatorics/shuffling.machineA device which shuffles cards always rearranges them in the same way relative to the order in which they were placed into it. New
• combinatorics/sliding.pairsTake three white poker chips and three red poker chips, line them up thusly: New
• combinatorics/sorting.boundsSorting n keys by binary comparisons needs O(n log n) steps on average; can a sort be faster than O(n log... New
• combinatorics/squarefree.stringsWhat is the longest repetition-free string one can build with {0,1,2}? New
• combinatorics/stamp.foldingIn how many ways can a strip of n blank stamps be folded? New
• combinatorics/subsetsOut of the set of integers 1,...,100 you are given ten different integers.
• combinatorics/sum.distinct.setsConsider an ordered set of n integers, {M(n,i), i=1 to n}. New
• combinatorics/sum.free.groupsArrange the numbers 1...23 into three groups so that in any group the sum of two numbers from that group is not in that group. New
• combinatorics/target.practiceA marksman shoots n cans off a fence, the first anywhere and each later one next to a gap; in how many... New
• combinatorics/teaching.scheduleA teacher at a school with grades 1 through k wants a schedule, repeated every k years, in which she... New
• combinatorics/tictactoe.arrangementsHow many ways are there of arranging 3 crosses and 3 noughts on a 3x3 tictactoe board (excluding rotations... New
• combinatorics/transitionsHow many n-bit binary strings (0/1) have exactly k transitions (an adjacent pair of dissimilar bits, i.e.,...
• combinatorics/true.false.quizHow many answer sheets must you submit to a 10-question true/false quiz to be sure one of them scores at... New
• combinatorics/vassiliev.conjectureIs a certain linear map between two vector spaces of graphs with univalent and oriented trivalent vertices one-to-one? New, unsolved
• combinatorics/coinage/combinationsAssuming you have enough coins of 1, 5, 10, 25 and 50 cents, how many ways are there to make change for a...
• combinatorics/coinage/dimes"Dad wants one-cent, two-cent, three-cent, five-cent, and ten-cent stamps.
• combinatorics/coinage/fourteen.coinsI purchased something for $1.79. New
• combinatorics/coinage/impossibleWhat is the smallest number of coins that you can't make a dollar with?
• combinatorics/coinage/largest.unreachableUsing only 5s and 9s (any number of each), what is the largest total that cannot be made? New
• combinatorics/coinage/mcnuggetsChicken McNuggets come in packs of 6, 9 and 20. New
• combinatorics/coinage/postage.stampsAn envelope holds at most h stamps. New
• combinatorics/coinage/ten.dollarsHow many different ways can ten dollars be made from five dollar bills, one dollar bills, half-dollars, and... New
• competition/contests/enigma.minisampleSolve the puzzles of the National Puzzlers' League's ENIGMA minisample (January 1993), reproduced below. New
• competition/contests/games.magazineWhat are the best answers to various contests run by _Games_ magazine?
• competition/contests/online.competitionsWhat online puzzle competitions are there for advanced solvers? New
• competition/contests/prizeweek.puzzlersOur local newspaper has a contest where you can win money if you correctly fill out the puzzle. New
• competition/contests/riddlerSolve this riddle: New, unsolved
• competition/contests/world.puzzle.1993What puzzles were set at the 2nd Annual World Puzzle Championship (Brno, Czech Republic, 1993), and how did... New
• competition/contests/world.puzzle.championship.1993What were the results of the 2nd World Puzzle Championship, held in Brno in 1993? New
• competition/contests/national.puzzle/npc.1993What are the solutions to the Games magazine 1993 National Puzzle Contest?
• competition/games/15.puzzleHow can I solve Sam Loyd's "15" puzzle, which consists of 15 sliding pieces in a 4 by 4 array, looking like... Added material
• competition/games/alcatrazWhat is the solution to Alcatraz? Added material
• competition/games/backgammonWhat is the minimal number of moves in backgammon such that the initial board configuration is exactly... New
• competition/games/baseball.pitchesWhat is the fewest number of pitches that could be thrown by the winning pitcher in a regulation 9 inning... New
• competition/games/bedlam.cubeHow many solutions does the Bedlam cube puzzle have? New
• competition/games/beggar.your.neighborWhat deal of two-player Beggar Your Neighbor gives the longest game (the most tricks), and can a game go on... New
• competition/games/bridgeAre there any programs for solving double-dummy Bridge?
• competition/games/chinese.ringsHow do you solve the Chinese Rings (also called the Patience Puzzle)? New
• competition/games/chompWhat is a winning strategy for the game "Chomp"? New
• competition/games/cigarettesThe game of cigarettes is played as follows: Two players take turns placing a cigarette on a circular table.
• competition/games/connect.fourIs there a winning strategy for Connect Four? Added material
• competition/games/crapsWhat are the odds in craps?
• competition/games/cribbage.improvementIn cribbage, which four-card hand can gain the most points from the turned-up card? New
• competition/games/cribbage.puzzlesCan a game of cribbage be won 121-0? New
• competition/games/crosswordsAre there programs to make crosswords?
• competition/games/cubeWhat are some games involving cubes? Added material
• competition/games/fibonacci.nimTwo players start with a number of counters. New
• competition/games/fifteen.gameNine cards numbered 1 to 9 lie face up; players alternately take one, and the first to hold three cards... New
• competition/games/freecellWhich deals of the solitaire game FreeCell are impossible to win? New
• competition/games/go-mokuFor a game of k in a row on an n x n board, for what values of k and n is there a win? Added material
• competition/games/gops[ Editor: Two players each hold all the cards of one suit; on each trick both lay a card face down, the... New
• competition/games/hexIs there a known winning strategy for the game of Hex? New
• competition/games/hi-qWhat is the quickest solution of the game Hi-Q (also called Solitaire)? Added material
• competition/games/instant.insanityHow do you solve Instant Insanity: stack four cubes, whose faces are colored red, white, blue and green, so... New
• competition/games/jeopardyWhat are the highest, lowest, and most different scores contestants can achieve during a single game of... Added material
• competition/games/jeopardy.wagerSuppose you are one of two rational players tied with $5000 in two-player Final Jeopardy! New
• competition/games/kites.and.dartsHow do you play the Mabry Dart & Kite game, a two-player game of 3-coloring a Penrose tiling of kites and... New
• competition/games/klondike.lossIn Klondike solitaire, what is the fewest number of cards that can be placed in a beginning setup to... New
• competition/games/life.densityWhat are the densest regular patterns that cover the plane in Conway's game of Life? New
• competition/games/life.dyingWhat is the smallest group of cells in Conway's game of Life that dies completely in one generation, with... New
• competition/games/mastermindWhat algorithms solve MasterMind, and how many guesses do they need? New
• competition/games/monopolyIn Monopoly, you are most likely to land on which property? New
• competition/games/nimPlace 10 piles of 10 $1 bills in a row. Added material
• competition/games/nim.1357How do you win the game of Nim from the standard position of rows of 1, 3, 5 and 7 pieces? New
• competition/games/nim.splittingIn this version of Nim, a move is to cross out any number of consecutive "sticks" in one row. New
• competition/games/nonogramsWhat are some concrete tips for solving nonograms (paint-by-numbers puzzles, like the ones in _Games_ magazine)? New
• competition/games/oskars.cubeWho invented the 3D maze puzzle that involves solving three 2D mazes simultaneously (probably mentioned in... New
• competition/games/othelloHow good are computers at Othello? Added material
• competition/games/peg.solitaireWhat are the solutions for peg solitaire with the following boards?
• competition/games/poker.face.upIn Face-Up Poker, two players each select five cards from a face-up deck, bet, discard and draw.
• competition/games/prime.gameA and B play a game in which they create a six-digit number: 1. New
• competition/games/riskWhat are the odds when tossing dice in Risk?
• competition/games/scrabbleWhat are some exceptional Scrabble Brand Crossword Game (TM) games? Added material
• competition/games/scrabble.bingosWhat are the most common bingos (seven-letter words using a whole rack) in Scrabble? New
• competition/games/scrabble.opening.bingoWhat is the probability that the first seven tiles drawn in Scrabble form a bingo (a seven-letter word... New
• competition/games/scrabble.simulationWhat do computer simulations of many Scrabble games show about scores, bingos, game length, square usage... New
• competition/games/scrabble.word.frequencyWhich words are played most often in Scrabble games on the Internet game servers, and how often are words... New
• competition/games/setWhat is the size of the largest collection of cards from which NO "set" can be selected ? Added material
• competition/games/sliding.blockI am looking for a sliding block puzzle named "the viking game". New
• competition/games/snookerI made the lowest possible winning score for a completed frame of snooker, potting only one ball in the... New
• competition/games/snooker.yellowDuring a normal game of snooker one of the players makes a break of eight points, during which he pots the yellow ball four times. New
• competition/games/somaWhat is the solution to Soma Cubes? Added material
• competition/games/sproutsThe game is played on a piece of paper, initially with a number of points drawn on it, and is a two player turn-taking game. New, unsolved
• competition/games/square-1Does anyone have any hints on how to solve the Square-1 puzzle? Added material
• competition/games/take.away1. There are 2 players and 32 toothpicks. New
• competition/games/think.and.jumpTHINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ARE LEFT WITH ONE PEG!
• competition/games/tictactoeIn random tic-tac-toe, what is the probability that the first mover wins?
• competition/games/tictactoe.machineHow can a tic-tac-toe machine be wired from only a power source, wire, nine toggle switches and eighteen... New
• competition/games/chess/bishop.tourWhat is the smallest number of moves in which a bishop, starting where he chooses, can visit (pass into or... New
• competition/games/chess/consecutive.checksFind the maximum number of consecutive checks from a legal chess position. New
• competition/games/chess/fools.mateWhat is the fastest theoretical way to get checkmate from the opening position? New
• competition/games/chess/impossible.pawnsAdd two black pawns to this position to form an illegal position that becomes legal on the removal of either one of them. New
• competition/games/chess/king.longest.tourWhat is the longest possible closed path of a chess king on the chessboard that does not cross itself? New
• competition/games/chess/knight.controlHow many knights does it take to attack or control the board? Added material
• competition/games/chess/knight.exchangeTwo sets of three knights (one set black, the other white) are placed at opposite ends of a 3x4 board:
• competition/games/chess/knight.mostWhat is the maximum number of knights that can be put on n x n chessboard without threatening each other?
• competition/games/chess/knight.tourFor what size boards are knight tours possible? Added material
• competition/games/chess/knight.tour.any.startA blindfolded performer moves a knight to every square of a chessboard, landing on no square twice,... New, unsolved
• competition/games/chess/modular.queens1. For what integers n>=1 is it possible to place n queens on an nxn chessboard such that every row, every... New, unsolved
• competition/games/chess/mutual.castlingWhite to mate in 2 (A. New
• competition/games/chess/mutual.stalemateWhat's the minimal number of pieces in a legal mutual stalemate? Added material
• competition/games/chess/nonattacking.rooksHow many ways are there to place n rooks on an n x n chessboard so that no rook attacks another? New
• competition/games/chess/queen.controlHow many queens does it take to attack or control the board?
• competition/games/chess/queen.dispositionsHow many different dispositions (up to rotation and reflection of the board) are there of K queens on an N... New
• competition/games/chess/queen.mostHow many non-mutually-attacking queens can be placed on various sized boards?
• competition/games/chess/queen.placementsHow many different ways (not counting rotations and reflections of the board as different) can K queens be... New
• competition/games/chess/queensHow many ways can eight queens be placed so that they control the board? Added material
• competition/games/chess/queens.unattackedHow should N queens be placed on an N x N board to leave the maximum number of unattacked vacant squares? New
• competition/games/chess/rook.pathsHow many non-overlapping paths can a rook take from one corner to the opposite on an MxN chess board? Added material
• competition/games/chess/rooks.3d.mateIn three-dimensional chess, how few rooks are needed to checkmate a lone king? New
• competition/games/chess/shogi.piecesHow many dragons (rook plus king) and how many horses (bishop plus king) can be placed on a 9x9 Shogi board... New
• competition/games/chess/shortest.stalemateWhat are the shortest chess games, from the initial position, that end in stalemate, with captures allowed... New
• competition/games/chess/sixteen.nonattackingIs there any way to place all 16 chess pieces of one color on a board such that none are attacking each other? New
• competition/games/chess/size.of.game.treeHow many different positions are there in the game tree of chess? Added material
• competition/games/chess/stalemate.movesBlack is in a stalemate position. New
• competition/games/chess/underpromotionCan a situation exist in which the only correct move is to move a Pawn to the eighth rank and promote it to a Rook? New
• competition/games/online/omnibusWhere can I find the OMNIBUS puzzles and the SpuZzLes word game on the web? New
• competition/games/online/online.scrabbleHow can I play Scrabble online on the Internet? Added material
• competition/games/online/unlimited.adventuresWhere can I find information about unlimited adventures?
• competition/games/pc/11th.hour.furnitureHow do you solve the furniture sliding-block puzzle in the PC game The 11th Hour? New
• competition/games/pc/The7thGuestWhat are solutions to some of the puzzles in The 7th Guest? Added material
• competition/games/pc/bestWhat are the best PC games? Added material
• competition/games/pc/game.faqsWhich other FAQs about PC games exist? New
• competition/games/pc/reviewsAre reviews of PC games available online? Added material
• competition/games/pc/solutionsWhat are the solutions to various popular PC games? Added material
• competition/games/rubiks/alexanders.starHow do you solve Alexander's Star? New
• competition/games/rubiks/megaminxHow do you solve the Megaminx (the dodecahedral Rubik's-type puzzle with 12 faces of 10 moving pieces each)? New
• competition/games/rubiks/nxnxn.cubesHow do you solve the NxNxN cubes: the Pocket Cube (2x2x2), Rubik's Cube (3x3x3), Rubik's Revenge (4x4x4)... New
• competition/games/rubiks/pyraminxHow do you solve the Pyraminx? New
• competition/games/rubiks/rubiks.clockHow do you quickly solve Rubik's clock?
• competition/games/rubiks/rubiks.cubeWhat is known about bounds on solving Rubik's cube? Added material
• competition/games/rubiks/rubiks.magicHow do you solve Rubik's Magic? Added material
• competition/games/rubiks/rubiks.tangleWhat is the solution to Rubik's Tangle? Added material
• competition/games/rubiks/skewbHow do you solve the Skewb? New
• competition/games/rubiks/unsolvable.stickeringsIn how many ways can you place the stickers on a Rubik's cube so that the cube is not solvable? New
• competition/games/rubiks/variantsWhat puzzles are there that are similar to Rubik's Cube? New
• competition/tests/analogies/cryptoThe Crypto-Analogies Test by Daryl Inman
• competition/tests/analogies/long1. Host : Guest :: Cynophobia : ?
• competition/tests/analogies/otherComplete these analogies:
• competition/tests/analogies/pairWhat are some analogies with more than one solution?
• competition/tests/analogies/pomfrit1. NATURAL: ARTIFICIAL :: ANKYLOSIS: ?
• competition/tests/analogies/quest1. Mother: Maternal :: Stepmother: ?
• competition/tests/analogies/relationsComplete these analogies: New
• competition/tests/math/derksenHere are some problems by Harm Derksen, who made problems for the Dutch Mathematical Olympiad and the International Mathematical Olympiad. New, unsolved
• competition/tests/math/wilson.problemsSolve these six problems by David Wilson. New
• competition/tests/math/imo/imo.1988What were the problems of the 29th International Mathematical Olympiad (Canberra, 1988)? New
• competition/tests/math/imo/imo.1994What were the problems of the 35th International Mathematical Olympiad (Hong Kong, 1994)? New, unsolved
• competition/tests/math/putnam/putnam.1967In article <5840002@hpesoc1.HP.COM>, nicholso@hpesoc1.HP.COM (Ron Nicholson) writes: > Say that we have a...
• competition/tests/math/putnam/putnam.1987WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION
• competition/tests/math/putnam/putnam.1988Problem A-1: Let R be the region consisting of the points (x,y) of the cartesian plane satisfying both |x| - |y| <= 1 and |y| <= 1.
• competition/tests/math/putnam/putnam.1990Problem A-1 How many primes among the positive integers, written as usual in base 10, are such that their...
• competition/tests/math/putnam/putnam.1992Problem A1
• competition/tests/math/putnam/putnam.1994Problems from the 1994 Putnam exam (December 3, 1994). New
• cryptology/FeynmanWhat are the Feynman ciphers?
• cryptology/VoynichWhat are the Voynich ciphers? Added material
• cryptology/blum.primesWhat are some moderately large primes that leave remainder 3 when divided by 4 ("Blum" primes), for... New
• cryptology/calloway.codeDecode this message: New
• cryptology/coded.message.1818Can you decipher a coded message written on the cover page of a letter dated 20 February 1818? New
• cryptology/codex.seraphinianusIs the invented script of Luigi Serafini's "Codex Seraphinianus" a real (or enciphered) language, and how... New
• cryptology/dorabellaWhat is the Dorabella cipher? New
• cryptology/kryptosWhat is the Kryptos cipher?
• cryptology/marlow.challengeMarlow's job last week took him on an exciting trip. New
• cryptology/opendoor.indexWhat did the National Security Agency's OPENDOOR index of declassified cryptologic documents list? New
• cryptology/phantom.tollboothDecipher the numeric message from the Mathemagician to his brother in Norton Juster's "The Phantom Tollbooth": New, unsolved
• cryptology/swiss.colonyWhat are the 1987 Swiss Colony ciphers?
• cryptology/vcrplusWhat is the code used by VCR+?
• decision/allaisThe Allais Paradox involves the choice between two alternatives: Added material
• decision/burn.gameRose and Colin play the Battle of the Sexes, but Colin may first "burn" 95 utility units in full view of Rose. New
• decision/divide.1000Two persons each divide $1000 into three different amounts and compare highest with highest, middle with... New
• decision/divisionN-Person Fair Division
• decision/dowrySultan's Dowry Added material
• decision/dowry.known.distributionSultan's Dowry with known distribution New
• decision/draw.or.standTwo players each draw a card from a uniform deck of numbers between 0 and 1 and may simultaneously choose... New, unsolved
• decision/ellsbergEllsberg's paradox: why do the common preferences between bets on an urn of known and an urn of unknown... New, unsolved
• decision/envelopeSomeone has prepared two envelopes containing money. Added material
• decision/exchangeAt one time, the Canadian and US dollars were discounted by 10 cents on each side of the border (i.e., a... Added material
• decision/five.piratesFive pirates on an island have one hundred gold coins to split between them. Added material
• decision/guess.weighted.numberA computer generates a number between 1 and 100 (both inclusive), according to a known probability... New
• decision/high.or.lowI pick two numbers, randomly, and tell you one of them. Added material
• decision/ice.cream.vendorsIce-cream vendors arrive one after another at a beach of length 1 and each chooses a spot; customers are... New
• decision/monty.four.doorsIn a four-door Monty Hall game, the contestant guesses door A, Monty opens empty door B, and the contestant switches to C. New
• decision/monty.hallYou are a participant on "Let's Make a Deal." Monty Hall shows you three closed doors. Added material
• decision/newcombNewcomb's Problem Added material
• decision/newcomb.smullyanBox A contains $100 and box B contains either nothing or $1 million. New
• decision/prisonersThree prisoners on death row are told that one of them has been chosen at random for execution the next... Added material
• decision/prisoners.dilemmaWhat is a good strategy for the iterated Prisoner's Dilemma when there is noise, a 5% chance that you... New, unsolved
• decision/proportional.votingHow would you design a voting system that produces the following result: the ratio of meat-eaters to... New
• decision/redI show you a shuffled deck of standard playing cards, one card at a time. Added material
• decision/red.black.bettingYou have $100 to bet on the following game: take a shuffled deck of cards, and deal through it one at a time. New
• decision/rent.divisionN people share a house with N rooms and a fixed total rent; how can the rooms be allocated and priced at... New
• decision/rotating.tableFour glasses are placed in the four corners of a square rotating table (like a lazy susan). Added material
• decision/statistical.inferenceIn what sense is statistical inference inference? New
• decision/stpetersburgWhat should you be willing to pay to play a game in which the payoff is calculated as follows: a coin is...
• decision/switchSwitch? (The Monty Hall Problem) Restored
• decision/three.amountsTwo persons each divide $1000 into three different amounts; whoever has the larger amount in two of the three comparisons wins. New
• decision/travelers.trilemmaTwo travelers who want to meet each come to a crossroad and must go left, right or straight ahead; which... New, unsolved
• decision/truelA, B, and C are to fight a three-cornered pistol duel. Added material
• decision/truel.one.bulletThree people, A, B and C, are each given a gun with one bullet, and all are perfect shots. New
• decision/two.gamblersTwo gamblers, A and B, are about to play a game. New
• decision/zeckhauserWould you pay more to empty both loaded chambers of a six-shooter holding two bullets, or to empty one of... New, unsolved
• decision/crossing/bridge.crossingFour people need to get across a bridge that can only support two at a time. Added material
• decision/crossing/river.crossingHow can various combinations of people, animals, and things get across a river when there are restrictions... Added material
• decision/crossing/tower.pulleyA mother (210 pounds), son (80), daughter (65) and a bowling ball (50) must escape a tower by a pair of... New
• geometry/3d.problemsHere are nine elementary problems in three-dimensional geometry, suitable for advanced high-school students. New, unsolved
• geometry/K3,3Can three houses be connected to three utilities without the pipes crossing? Restored
• geometry/annulus.chordTwo concentric circles are given. New
• geometry/ball.in.cornerA beach ball of radius 1 foot is placed in the corner of a room so it is tangent to the floor and two of the room's walls. New
• geometry/bearIf a hunter goes out his front door, goes 50 miles south, then goes 50 miles west, shoots a bear, goes 50...
• geometry/bear.square.walkA wildlife photographer goes one mile south, one mile east, one mile north and one mile west, and is back... New
• geometry/bisectorProve if two angle bisectors of a triangle are equal, then the triangle is isosceles (more specifically,...
• geometry/calendarBuild a calendar from two sets of cubes.
• geometry/circle.regionsPut n points on a circle and connect each point to every other point by straight lines so as to form the maximum number of regions. New
• geometry/circle.splitting.pointsThere are 2n+3 points in the plane, no three of them collinear and no four of them concyclic. New
• geometry/circles.and.trianglesFind the radius of the inscribed and circumscribed circles for a triangle.
• geometry/circles.through.gridWhat is the smallest number of circles k that pass through all the points of an n x n square grid of points? New
• geometry/coins.to.hexagonArrange 6 coins in two rows of three coins nestled together; what is the minimum number of slide moves to... New
• geometry/coins.trianglePut 10 equal coins on a table to make a filled triangle with a side of 4 coins. New
• geometry/conicsIs there a formula which describes *all* conic sections, which will generate a particular class of same... New
• geometry/cornerA hallway of width A turns through 90 degrees into a hallway of width B.
• geometry/cover.earthA thin membrane covers the surface of the (spherical) earth.
• geometry/cube.cutsA 3x3x3 cube of cheese can be cut into 27 1x1x1 cubes with 6 cuts (2 along every dimension; like a Rubik's Cube). New
• geometry/cycle.polynomialWhat are the cycle polynomials for the Platonic solids?
• geometry/duck.and.foxA duck is swimming about in a circular pond. Added material
• geometry/earth.bandHow much will a band around the equator rise above the surface if it is made one meter longer? Added material
• geometry/fenceA farmer wishes to enclose the maximum possible area with 100 meters of fence.
• geometry/four.peopleAlice, Bob and Carol are standing on a straight line. New
• geometry/grad.school.triangleIn isosceles triangle PQR, angle QPR = 20 degrees and the other two angles are 80 degrees. New
• geometry/grid.linesHow many straight lines do you need to cross every square of a 3x3 board? New
• geometry/half.angle.tangentsFind a triangle with integer sides such that the product of the tangents of its half-angles is (2^8 5^2... New
• geometry/ham.sandwichConsider a ham sandwich, consisting of two pieces of bread and one of ham.
• geometry/hamilton.pathDevise a continuous path that visits each * exactly once: New
• geometry/hexagon.in.triangleStart with an equilateral triangle. New
• geometry/hikeYou are hiking in a half-planar woods, exactly 1 mile from the edge, when you suddenly trip and lose your sense of direction. Added material
• geometry/hole.in.sphereOld Boniface he took his cheer, Then he bored a hole through a solid sphere, Clear through the center,... Added material
• geometry/hypercubeHow many vertices, edges, faces, etc.
• geometry/inscribed.polygonA polygon of 100 sides is inscribed in a circle. New
• geometry/intersecting.cylindersTwo cylinders of unit diameter intersect (100%) at right angles. New
• geometry/intersection.free1,000,000 black points and 1,000,000 white points exist on a planar disk.
• geometry/kissing.numberHow many n-dimensional unit spheres can be packed around one unit sphere?
• geometry/konigsbergCan you draw a line through each edge on the diagram below without crossing any edge twice and without...
• geometry/ladder.and.boxA 3' * 3' packing case is placed against a wall. Added material
• geometry/laddersTwo ladders form a rough X in an alley.
• geometry/lighthouseTwo people walk to the top of a cylindrical lighthouse, one via a straight ladder up the middle and the... New
• geometry/manhole.coverWhy is a manhole cover round? Added material
• geometry/morleyTake any triangle and trisect its internal angles. New
• geometry/mouse.in.penA toy wind-up mouse is put in a circle pen with 1 m radius. New
• geometry/nearest.townTake a map and connect each town shown on it to its nearest (as the crow flies) neighbor by means of a straight line segment. New
• geometry/nine.dotsDraw 4 straight lines in such a way that all the dots of a 3x3 array are touched. New
• geometry/opaque.cubeWhat is the least area surface that can block all lines of sight through a cube? New
• geometry/pentagram.ten.trianglesA regular 5-pointed star is composed of five lines, and has 5 non-overlapping triangles in it. New
• geometry/pentominoArrange pentominos in 3x20, 4x15, 5x12, 6x10, 2x3x10, 2x5x6 and 3x4x5 forms. Added material
• geometry/pentomino.duplicationDivide the 12 pentominoes into two sets of 6 that form two identical shapes (shapes that overlap exactly... New
• geometry/photograph.horizonYou have a photograph of a person in front of a sunset over the sea. New
• geometry/piano.around.cornerWhat is the longest (or largest) object that can be moved along a corridor of width W and around a... New
• geometry/platonic.volumeWhat are the volumes of the regular polyhedra? New
• geometry/point.in.triangleGiven a triangle in the xy plane (specified by its vertices) and a point, find a computationally simple... New
• geometry/points.in.rectangleGiven a rectangle of sides A and B, two points are picked at random, independently and uniformly with respect to area. New
• geometry/points.in.sphereWhat is the expected distance between two random points inside a sphere?
• geometry/points.on.sphereWhat are the odds that n random points on a sphere lie in the same hemisphere? Added material
• geometry/polycubesHow many pentacubes are there really? New
• geometry/polyomino.exclusionGiven a finite family of polyominoes (of any sizes), is the set of the polyominoes that do NOT contain any... New, unsolved
• geometry/polytope.volumeHow can one calculate the hypervolume of a convex n-dimensional polyhedron given the coordinates of its... New
• geometry/puzzle.ringHow can I put together my puzzle rings (where four bands become one)? Added material
• geometry/pyramid.trianglesJoin every pair of the 5 vertices and 8 edge midpoints of a square pyramid. New
• geometry/regular.polyhedraWhy are there only five regular polyhedra, and why is the solid made of two tetrahedra glued face to face... New
• geometry/revolutionsA circle with radius 1 rolls without slipping once around a circle with radius 3.
• geometry/rotating.lineA line of unit length is enclosed within a two-dimensional area. New
• geometry/rotationWhat is the smallest rotation that returns an object to its original state?
• geometry/satellitesYou have a planet that's a perfect sphere. New
• geometry/seven.pointsCan you arrange seven distinct points on a plane, so that of any three taken at random, at least two would... New
• geometry/shephard.pianoWhat's the maximum area shape that will fit around a right-angle corner?
• geometry/shortest.creaseYou have a sheet of paper that is 6 units wide and 25 units long, placed so that the short side is facing you. New
• geometry/six.tangent.circlesStart with a circle O of radius 1 and let a and b be arbitrary real numbers. New
• geometry/smugglerSomewhere on the high sees smuggler S is attempting, without much luck, to outspeed coast guard G, whose boat can go faster than S's.
• geometry/sphere.packingAre face-centred cubic and hexagonal close packing of equal spheres really two different arrangements, or... New
• geometry/spider.and.flyA room is 30 feet long, 12 feet wide and 12 feet high. New
• geometry/spider.on.treeThere is a tree, circumference of which is 4 ft. New
• geometry/spiralHow far must one travel to reach the North Pole if one starts from the equator and always heads northwest? Added material
• geometry/spy.planeA spy plane must see the entire surface of the Earth in one flight; what is the shortest flight, starting... New
• geometry/square.holeIs it possible to drill a square hole? New
• geometry/steiner.treeFour cities stand at the corners of a square. New
• geometry/surveyed.triangleA team of surveyors are given the task of finding the size of an equilateral triangular plot. New
• geometry/table.in.cornerPut a round table into a (perpendicular) corner so that the table top touches both walls and the feet are firmly on the ground.
• geometry/tangent.circlesInside a pipe 3 units in diameter are two pipes, of diameters 2 and 1. New
• geometry/ten.lines.6x6Using ten continuous lines, and not lifting your pencil from the paper, go through all the dots of a 6x6... New, unsolved
• geometry/tetrahedra.in.cubeHow many regular tetrahedrons with edges of length square root of 2 can be packed into a cube with edges of... New, unsolved
• geometry/tetrahedronSuppose you have a sphere of radius R and you have four planes that are all tangent to the sphere such that...
• geometry/three.churchesIn George's small home town there are three churches, equidistant from each other as the crow flies - that... New
• geometry/three.squaresThree squares are placed side by side: New
• geometry/touching.blocksCan six 1x2x4 blocks be arranged so that each block touches n others, for all n?
• geometry/touching.cubesGiven a cube, how many cubes (all identical to the original) can you place around it so they all touch it? New
• geometry/treasure.mapA treasure map locates the treasure using four landmarks, two of which have vanished. New
• geometry/triangle.20.degreesIn isoceles triangle ABC angle A=20, B=80, C=80. Added material
• geometry/triangular.regionsShow that when n lines in general position in the real affine plane (no two parallel, no three concurrent)... New
• geometry/walkA person walks up a hill starting at 8 pm and arrives at the top at midnight.
• geometry/weighted.bisectorsThe perpendicular bisectors of the sides of a triangle meet in a single point. New
• geometry/weird.riverA river flows from town A to town B and has the property that any point on either of its banks is no... New
• geometry/wooden.blockHow was this wooden block made from two pieces, with the joint showing as a dovetail on two adjacent faces? New
• geometry/worm.blanketPerson A has a piece of string exactly one meter long. New
• geometry/wrapping.paperYou have a rectangular solid, A x B x C in dimension, and you want to wrap it with a rectangle of wrapping paper, D x E in size. New
• geometry/coloring/cheese.cubeA cube of cheese is divided into 27 subcubes.
• geometry/coloring/four.color[ Editor: Has the four-color map problem been solved, and what about coloring maps on surfaces of higher genus, such as the torus? New
• geometry/coloring/four.color.proofFind the flaw in this short "proof" of the four color theorem. New, unsolved
• geometry/coloring/kites.and.darts.gameDevise a two-player game based on 3-coloring a tiling of kites and darts. New
• geometry/coloring/painted.cubeA painted wooden cube is cut into n^3 identical smaller cubes; give formulas for how many of the small... New
• geometry/coloring/triominoesThere is a chess board (of course with 64 squares).
• geometry/coloring/two.colored.planeAn infinite plane is colored in red and blue, each spot of color being finite. New
• geometry/coloring/unit.distanceColor every point of the plane with one of N colors so that no two points at distance 1 from one another have the same color. New
• geometry/construction/12.points.5.linesDraw 5 straight line segments through the 12 points below without lifting your pencil, so that each point... New
• geometry/construction/4.triangles.6.linesCan you construct 4 equilateral triangles with 6 toothpicks?
• geometry/construction/5.lines.with.4.pointsArrange 10 points so that they form 5 rows of 4 each. Added material
• geometry/construction/arbelosConstruct a figure equal in area to the region inside a semicircle and outside two smaller semicircles... New
• geometry/construction/artilleryYou are a field officer in the Greek artillery corps. New
• geometry/construction/bisect.with.compassHow do we find the mid-point of a line segment using only a compass? New
• geometry/construction/circle.through.pointGiven a straight line, a point and a circle (on the same side of the line as the point), construct a circle... New
• geometry/construction/h.seven.trianglesDraw three straight lines through a standard capital "H" so that the resulting figure contains seven... New
• geometry/construction/interior.pointGiven three points whose coordinates are known, and a point O inside the triangle they form, how do you... New
• geometry/construction/quadrilateral.to.triangleGiven an arbitrary convex quadrilateral, construct a triangle of equal area using only straight edge and... New
• geometry/construction/square.with.compassConstruct a square with only a compass and a straight edge.
• geometry/construction/tangent.circleGiven a circle C, a line L that doesn't intersect C, and a point P that is not on L and not inside C,... New
• geometry/construction/three.degreesConstruct an angle of 3 degrees with straightedge and compass. New
• geometry/dissections/acute.trianglesCut a square into the fewest number of acute triangles. New
• geometry/dissections/cube.3.4.5.6Dissect a 6x6x6 cube into as few pieces as possible that can be reassembled into three cubes 3x3x3, 4x4x4... New
• geometry/dissections/cubed.cubeShow that a cube of integer side cannot be partitioned into a finite number of smaller cubes of integer sides, all of different sizes. New
• geometry/dissections/diskCan a disk be cut into similar pieces without point symmetry about the midpoint?
• geometry/dissections/hexagonDivide the hexagon into: 1) 3 identical rhombuses.
• geometry/dissections/iced.cakeA rectangular slice of cake ABED is iced along two sides, the icing being the L-shaped region BCGFDE, so... New
• geometry/dissections/isosceles.trianglesWhat is the fewest number of angularly unique isosceles triangles that can be pieced together to form a... New
• geometry/dissections/largest.circleWhat is the largest circle that can be assembled from two semicircles cut from a rectangle with edges a and b?
• geometry/dissections/pizza.cutsHow do you cut a round pizza into 8 pieces with 3 straight cuts? New
• geometry/dissections/planesWhat is the maximum number of parts into which 3-dimensional space can be divided by 5 planes? New
• geometry/dissections/rectangle.to.squareA rectangle with sides x and y is cut with straight cuts into pieces that are reassembled, by rotation and... New
• geometry/dissections/slice.cakeHow do you cut a rectangular cake in half that already has a rectangular piece removed? Added material
• geometry/dissections/square.70Since 1^2 + 2^2 + 3^2 + ...
• geometry/dissections/square.fiveCan you dissect a square into 5 parts of equal area with just a straight edge?
• geometry/dissections/squared.squareGiven a square of n X n proportion, break the square up into smaller squares none of which can be the same dimensions as another. New
• geometry/dissections/tesseractIf you suspend a cube by one corner and slice it in half with a horizontal plane through its centre of...
• geometry/dissections/vanishing.leprechaunHow does the "Vanishing Leprechaun" puzzle work, in which one leprechaun disappears or reappears when the... New
• geometry/dissections/wedding.cakeWith one straight cut, and only the knife as a tool, halve a slice of wedding cake iced on top and on one... New
• geometry/lattice/areaProve that the area of a triangle formed by three lattice points is integer/2.
• geometry/lattice/chessboard.circlesStart with a chessboard and put one marker on each intersection point, including those on the perimeter and... New
• geometry/lattice/equilateralCan an equlateral triangle have vertices at integer lattice points?
• geometry/lattice/ink.stainsThe plane has a dot at every point (x,y) where both x and y are integers. New
• geometry/lattice/madmen.in.forestFive madmen hide in an infinite square grid of trees, each uprooting one tree and standing in its place. New
• geometry/lattice/platonic.solidsFor each of the five Platonic solids, decide whether or not there exists such a solid in R^3 such that each... New
• geometry/lattice/sixteen.geeksPlace 16 people in a 4x4x4 grid of rooms so that the smallest distance between any two of them is as large... New
• geometry/tiling/count.1x2Count the ways to tile an MxN rectangle with 1x2 dominos. Added material
• geometry/tiling/dominoes.two.holesProve that if you remove any two squares of opposite colors from a chessboard, the board can be covered... New
• geometry/tiling/heptomino.boxesIs it possible to pack the 108 heptominoes, with unit thickness, into a 7x9x12 box? New
• geometry/tiling/locate.in.patternThe plane is tiled periodically, without rotation, by copies of a 5x5 square A and a 3x3 square B placed... New
• geometry/tiling/pentacube.contestCan the 29 pentacubes be assembled into the figures set as problems in the German pentacube contests... New
• geometry/tiling/pentomino.cubeFill a 5x5x5 box with 25 identical pieces, each made of five unit cubes: a piece of two units glued to a... New
• geometry/tiling/polycube.boxesWhich polyominoes and polycubes can be packed, all copies alike, into rectangles, boxes and hyperboxes, and... New
• geometry/tiling/rational.sidesA rectangular region R is divided into rectangular areas.
• geometry/tiling/rectangles.with.squaresGiven two sorts of squares, (axa) and (bxb), what rectangles can be tiled? Added material
• geometry/tiling/roman.crossesCover the surface of a cube with five congruent Roman crosses. New
• geometry/tiling/scalingA given rectangle can be entirely covered (i.e.
• geometry/tiling/seven.cubesConsider 7 cubes of equal size arranged as follows.
• geometry/tiling/straight.tetrominoCan a 10x10 square be tiled with 25 1x4 rectangles (straight tetrominoes)? New
• geometry/tiling/t.tetrominoesFrom a 99x99 checkerboard, the middle square of one side is removed. New
• geometry/tiling/triangles.squares.hexagonsOne can fill the surface R^2 with triangles, squares and hexagons as shown below. New
• geometry/topology/complete.graphs.on.torusShow how to draw the complete graphs K6 and K7 on a torus, with no two edges crossing. New
• geometry/topology/euler.formulaA polyhedron with F faces, V vertices and E edges satisfies F + V = E + 2. New
• geometry/topology/fixed.pointA man hikes up a mountain, and starts hiking at 2:00 in the afternoon on a Friday.
• geometry/topology/hairy.ballShow that a "hairy coconut" in an odd number of dimensions cannot be combed: if n is odd, there is no... New
• geometry/topology/horseshoesHow do you get the ring off the wire puzzle called "Horseshoes" or "Handcuffs"? New
• geometry/topology/poincare.conjectureWhat is the exact statement of the Poincare conjecture, and where does it stand (fake R^4s, the case n = 3)? New
• geometry/topology/wobbly.tableCan a four-legged table standing on an uneven (but smooth) floor always be turned so that all four legs... New
• geometry/trigonometry/euclidean.numbersFor what numbers x is sin(x) expressible using only integers, +, -, *, / and square root?
• geometry/trigonometry/inequalityShow that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4.
• group/group.01AEFHIKLMNTVWXYZ BCDGJOPQRSU
• group/group.01a147 0235689
• group/group.02ABEHIKMNOTXZ CDFGJLPQRSUVWY
• group/group.02aABEIKMNOTZ CDFGHJLPQRSUVWXY
• group/group.02bABEHIKMNOPTXYZ CDFGJLQRSUVW
• group/group.03BEJQXYZ DFGHLPRU KSTV CO AIW MN
• group/group.04BDO P ACGIJLMNQRSUVWZ EFTY HKX
• group/group.05CEFGHIJKLMNSTUVWXYZ ADOPQR B
• group/group.06BCEGKMQSW DFHIJLNOPRTUVXYZ
• group/group.07CDEFLOPTZ ABGHIJKMNQRSUVWXY
• group/group.08COS ABDEFGHIJKLMNPQRTUVWXYZ
• group/group.09CDILMVX ABEFGHJKNOPQRSTUWYZ
• group/group.10AHIMOTUVWXY BCDEFGJKLNPQRSZ
• group/group.11BCDIJLMNOPQRSUVWZ AEFGHKTXY
• group/group.12COPSUVWXZ ABDEFGHIJKLMNQRTY
• group/group.13BCDEHIKOX AFGJLMNPQRSTUVWYZ
• group/group.14EHIS MOT ABCDFGJKLNPQRUVWXYZ
• group/group.15HIOX ABCDEFGJKLMNPQRSTUVWYZ
• group/group.16IJ ABCDEFGHKLMNOPQRSTUVWXYZ
• group/group.17J BDFHIKLT GPQY ACEMNORSUVWXZ
• group/group.18AEFHILMNORSUX BCDGJKPQTVWYZ New
• group/group.19BCDEGPTVZ FLMNSX AJK QUW IY H O R New
• group/group.20AR B CLMNSUVWZ DO EFGJTY HIKX P Q New
• induction/fat-men-at-barConsider a bar with N seats arranged in a line.
• induction/handshakeAt a party people shake hands with all the people they do not know.
• induction/hanoiIs there an algorithm for solving the Hanoi tower puzzle for any number of towers? Added material
• induction/integer.polynomialProve that if P is a polynomial of degree k, and P(n) assumes integral values for k+1 consecutive integers... New
• induction/n-sphereWith what odds do three random points on an n-sphere form an acute triangle?
• induction/paradoxIs there a non-trivial property that holds for the first 10,000 positive integers, then fails?
• induction/partyYou're at a party. Added material
• induction/rollAn ordinary die is thrown until the running total of the throws first exceeds 12.
• induction/same.hair.colorWhere is the mistake in this proof by induction that all women have the same hair color? New
• induction/takeoverAfter graduating from college, you have taken an important managing position in the prestigious financial... Added material
• language/close.antonymsWhat words are similar to their antonyms in other langauges? Added material
• language/grandmotherWhat are the words for "grandmother" in various languages? New
• language/international.palindromesList palindromes in English and in other languages. New
• language/multi.lingualWhat words in multiple languages are related in interesting ways? Restored
• language/multi.palindromesList some multi-lingual palindromes.
• language/palindromes.non.englishWhat are some palindromes in languages other than English? New
• language/pi.mnemonicsWhat are some mnemonics for the digits of pi, in English and other languages? New
• language/repeated.wordIn any language, construct a sentence by repeating one word four times.
• language/synonymous.reversalsWhat words are synonymous with their reversals in other languages? Added material
• language/vowels.repeatedIn any language, what word contains the same vowel repeated four times in a row?
• language/dutch/dutch.recordWhat are some Dutch words with unusual properties? Added material
• language/english/double.dactylWrite a double dactyl ("higgledy-piggledy") whose key line is an anagram. New
• language/english/elementThe name of what element ends in "h"? Restored
• language/english/higgledy.piggledyWhat is a higgledy-piggledy (double dactyl), and what are some good ones? New
• language/english/rebusDecode this rebus, said to be posted in a tavern: New
• language/english/unused.word.gameCan you come up with a real word that no one on the Internet has used in a newsgroup in the past few months? New
• language/english/word.odditiesWhat are some interesting word oddities in English: unusual letter combinations, typing curiosities, long... New
• language/english/word.records.introductionHow are the word records of the Taxonomy of Wordplay organized, classified and scored? New
• language/english/crosswords/cryptic/cluesWhat are some clues (indicators) used in cryptics? Restored
• language/english/crosswords/cryptic/doubleEach clue has two solutions, one for each diagram; one of the answers to 1ac. Restored
• language/english/crosswords/cryptic/introWhat are the rules for cluing cryptic crosswords? Restored
• language/english/etymology/acronymWhat acronyms have become common words or are otherwise interesting? Added material
• language/english/etymology/car.acronymsWhat humorous expansions have been made of the names of automobile makes, read as acronyms? New
• language/english/etymology/doubletWhat words have completely different meanings, yet derived from the same word?
• language/english/etymology/doublet.2What are the word records for doublet (completely different words from same root), example of? New
• language/english/etymology/folkWhat words have folk etymologies (e,g., "an apple" from "a napple")?
• language/english/etymology/fossilWhat are some examples of idioms that include obsolete words? Added material
• language/english/etymology/homographsWhat are the word records for Homographs, most? New
• language/english/etymology/lost.positivesWhat happened to words like "tant" (nearby, the opposite of distant) and "cuss" (not talk about, the... New
• language/english/etymology/most.different.etymologiesWhat are the word records for most different etymologies? New
• language/english/etymology/portmanteauWhat are some words formed by combining together parts of other words?
• language/english/etymology/acronyms.anagrams.portmanteaus/acronym.that.has.become.an.uncapitalizedWhat are the word records for acronym that has become an uncapitalized word? New
• language/english/etymology/acronyms.anagrams.portmanteaus/portmanteau.wordWhat are the word records for portmanteau word (word formed by mixing two other words)? New
• language/english/etymology/acronyms.anagrams.portmanteaus/word.formed.as.an.anagramWhat are the word records for word formed as an anagram? New
• language/english/etymology/acronyms.anagrams.portmanteaus/acronym.that.has.become.an.uncapitalized/for.each.letterWhat are the word records for for each letter? New
• language/english/etymology/acronyms.anagrams.portmanteaus/acronym.that.has.become.an.uncapitalized/longestWhat are the word records for longest? New
• language/english/etymology/acronyms.anagrams.portmanteaus/portmanteau.word/for.each.letterWhat are the word records for for each letter? New
• language/english/etymology/acronyms.anagrams.portmanteaus/portmanteau.word/oldestWhat are the word records for oldest? New
• language/english/etymology/acronyms.anagrams.portmanteaus/word.formed.as.an.anagram/for.each.letterWhat are the word records for for each letter? New
• language/english/etymology/words.with.unusual.origins/unknown.originWhat are the word records for unknown origin, shortest? New
• language/english/etymology/words.with.unusual.origins/fossil/for.each.letterWhat are the word records for for each letter? New
• language/english/etymology/words.with.unusual.origins/metanalysis.or.affix.clipping.or.folk/for.each.letterWhat are the word records for for each letter? New
• language/english/etymology/words.with.unusual.origins/trade.names.that.have.become.words/for.each.letterWhat are the word records for for each letter? New
• language/english/meaning/animalFor each animal, give its genus names, collective noun and gate(s), if any (e.g., "horse -> equine, herd,... Added material
• language/english/meaning/animal.proverbsMatch each word or phrase in the first column with the word or phrase in the second column that produces a... New
• language/english/meaning/equationsWhat are the solutions to various letter equations like: 1 = W on a U 3 = BM 4 = Q in a G 5 = D in a ZC 7 =... Added material
• language/english/meaning/free.associationsFill in the blanks with words that complete the free associations, e.g. New
• language/english/meaning/letter.rebusDefine the letters of the alphabet using self-referential common phrases (e.g., "first of all" defines "a").
• language/english/meaning/lost.positivesWhat are some "lost positives", words that exist only in their negative forms, like "disgruntled" without... New
• language/english/meaning/oxymoronsWhat are some oxymorons (phrases whose parts contradict each other, seriously or jokingly)? New
• language/english/meaning/phrasal.verb.gridWhat is the question? New
• language/english/meaning/pleonasmWhat are some redundant terms that occur frequently (like "ABM missile")? Added material
• language/english/meaning/reflexive.verbsFind an English verb whose subject is always a person or persons and whose object is ALWAYS that same... New
• language/english/meaning/shakespeare.titlesWhich Shakespeare plays are clued by WET, DRY, ABORTION, 3", 6" and 9"? New
• language/english/meaning/song.titlesWhat are some song lyrics that involve wordplay?
• language/english/meaning/uk.us.confusionsWhat English words could be confusing or embarrassing because they mean different things in the UK and the US? New
• language/english/meaning/verb.complementsWhat English verb has the most possible complements? New
• language/english/meaning/adjectives.and.adverbs/false.comparativesWhat are the word records for false comparatives? New
• language/english/meaning/ambiguity/different.meanings.or.sensesWhat are the word records for different meanings or senses, most? New
• language/english/meaning/ambiguity/different.parts.of.speechWhat are the word records for different parts of speech, most? New
• language/english/meaning/ambiguous/ambiguousWhat word in the English language is the most ambiguous?
• language/english/meaning/ambiguous/ambiguous.sentencesWhat are some ambiguous sentences, which can be read in two quite different ways? New
• language/english/meaning/ambiguous/potable.colorFind words that are both beverages and colors.
• language/english/meaning/miscellaneous/entire.word/number.nounsWhat are the word records for number nouns? New
• language/english/meaning/miscellaneous/entire.word/one.letter.wordsWhat are the word records for one letter words? New
• language/english/meaning/miscellaneous/sentences/nested.clausesWhat are the word records for nested clauses, most? New
• language/english/meaning/miscellaneous/sentences/repeated.wordsWhat are the word records for repeated words, most? New
• language/english/meaning/miscellaneous/sentences/rhopalism.or.snowball.or.increasing.orWhat are the word records for rhopalism or snowball or increasing or decreasing word length? New
• language/english/meaning/miscellaneous/sentences/self.referentialWhat are the word records for self-referential? New
• language/english/meaning/miscellaneous/word.lists/kangaroo.wordsWhat are the word records for kangaroo words? New
• language/english/meaning/miscellaneous/word.lists/oxymoronsWhat are the word records for oxymorons? New
• language/english/meaning/miscellaneous/word.lists/synonym.chainsWhat are the word records for synonym chains? New
• language/english/meaning/miscellaneous/word.lists/synonym.squaresWhat are the word records for synonym squares? New
• language/english/meaning/nouns/apparently.related.but.unrelated/ending.with.ate.and.itionWhat are the word records for ending with -ate and -ition? New
• language/english/meaning/nouns/unusual.plurals/add.letters.to.beginning.to.makeWhat are the word records for add letters to beginning to make plural, example of? New
• language/english/meaning/nouns/unusual.plurals/colliding.pluralsWhat are the word records for colliding plurals (words with homographic plurals), example of? New
• language/english/meaning/nouns/unusual.plurals/drop.s.to.make.a.pluralWhat are the word records for drop s to make a plural? New
• language/english/meaning/nouns/unusual.plurals/endingWhat are the word records for ending, for each letter? New
• language/english/meaning/nouns/unusual.plurals/internalWhat are the word records for internal? New
• language/english/meaning/nouns/unusual.plurals/mostWhat are the word records for most? New
• language/english/meaning/nouns/unusual.plurals/no.letters.in.common.with.pluralWhat are the word records for no letters in common with plural, longest? New
• language/english/meaning/nouns/unusual.plurals/switching.first.two.letters.to.makeWhat are the word records for switching first two letters to make plural, example of? New
• language/english/meaning/pronouns/ratio.embedded.pronouns.to.length/highestWhat are the word records for highest? New
• language/english/meaning/pronouns/ratio.embedded.pronouns.to.length/highest.including.reversedWhat are the word records for highest including reversed? New
• language/english/meaning/pronouns/ratio.embedded.pronouns.to.length/highest.with.letters.anywhereWhat are the word records for highest with letters anywhere? New
• language/english/meaning/synonyms/anagramList some anagrams (transposals of a word, name or phrase into another with a closely related meaning). Added material
• language/english/meaning/synonyms/antigramList some anagrams (transposals of a word, name or phrase into another with a nearly opposite meaning).
• language/english/meaning/synonyms/antonymWhat words, when a single letter is added, reverse their meanings?
• language/english/meaning/synonyms/antonym.splitThe letters of GASOLINE can be rearranged to spell GAIN and LOSE, which are opposites. New
• language/english/meaning/synonyms/contranymWhat words are their own antonym? Added material
• language/english/meaning/synonyms/double.synonymsWhat words have two different synonymous meanings? Added material
• language/english/meaning/synonyms/kangarooWhat words contain synonyms (and antonyms) within them?
• language/english/meaning/synonyms/pseudantonymList some (near) synonyms that, in form, appear to be antonyms (e.g., "flammable" and "inflammable"). Added material
• language/english/meaning/synonyms/spearlikeAnagram SPEARLIKE ("of the kind befitting or characteristic of a spear") into two words of opposite meaning. New
• language/english/meaning/synonyms/transposalsWhat synonyms are transposals of one another?
• language/english/meaning/synonyms.and.antonyms/double.synonyms.or.words.with.twoWhat are the word records for double synonyms or words with two different synonymous meanings, shortest? New
• language/english/meaning/synonyms.and.antonyms/pseudantonymsWhat are the word records for pseudantonyms (synonyms that appear to be antonyms)? New
• language/english/meaning/synonyms.and.antonyms/contranyms/contranymsWhat are the word records for contranyms, homophonic? New
• language/english/meaning/synonyms.and.antonyms/contranyms/for.each.letterWhat are the word records for for each letter? New
• language/english/meaning/synonyms.and.antonyms/double.duty.antonyms/antonymsWhat are the word records for antonyms, most? New
• language/english/meaning/synonyms.and.antonyms/double.duty.antonyms/for.each.letterWhat are the word records for for each letter? New
• language/english/meaning/synonyms.and.antonyms/synonymic.and.antonymic.reversals.and.transposals/anagramWhat are the word records for anagram (synomymous phrase containing the same letters), longest? New
• language/english/meaning/synonyms.and.antonyms/synonymic.and.antonymic.reversals.and.transposals/antigramWhat are the word records for antigram (antonymous phrase containing the same letters), longest? New
• language/english/meaning/synonyms.and.antonyms/synonymic.and.antonymic.reversals.and.transposals/synonymous.reversalWhat are the word records for synonymous reversal, longest? New
• language/english/meaning/synonyms.and.antonyms/synonymic.and.antonymic.reversals.and.transposals/synonymous.transposalWhat are the word records for synonymous transposal, longest? New
• language/english/pronunciation/autonymWhat is the longest word whose phonetic and normal spellings are the same?
• language/english/pronunciation/breakfastWhat is a word or phrase that starts with the name of each letter of the alphabet? Added material
• language/english/pronunciation/capitalWhat words change pronunciation when capitalized (e.g., polish -> Polish)? Restored
• language/english/pronunciation/ce.as.shThe letters "ce" at the end of a word are usually pronounced like an s, as in race and dance. New
• language/english/pronunciation/chaosWhat poem shows off the chaos of English spelling and pronunciation? New
• language/english/pronunciation/context.pronunciationWhat is the name for a word that is pronounced differently in two different contexts, even though neither... New
• language/english/pronunciation/different.mostWhat are the most ways that the same letter can be pronounced in a single word?
• language/english/pronunciation/echo.verseGive some jokes or riddles whose answers are homophones of part of the question ("ecobursts", "echobursts"... New
• language/english/pronunciation/ghostWhat words sound like they contain letters that they do not? Added material
• language/english/pronunciation/gramogram"XS" is pronounced like "excess." For each starting letter, what is the longest such sequence?
• language/english/pronunciation/ladle.rat.rotten.hutRetell the story "Little Red Riding Hood" with every word replaced by a similar-sounding English word, so... New
• language/english/pronunciation/malapropList some malapropisms (the use of a word sounding somewhat like the one intended). Added material
• language/english/pronunciation/no.shared.phonemesFind two words that differ in spelling by only one letter but share no sounds (phonemes) at all. New
• language/english/pronunciation/oronymList some oronyms (phrases or sentences that can be read in two ways with the same sound). Added material
• language/english/pronunciation/phonetic.lettersWhat does "FUNEX" mean?
• language/english/pronunciation/piglatinWhat words in pig latin also are words?
• language/english/pronunciation/punsWhere can I find a collection of puns? Added material
• language/english/pronunciation/rhymeWhat one and two syllable English words are hard to rhyme? Added material
• language/english/pronunciation/sch.pairsEach pair of clues is answered by a word or name starting with "sch" and a word that sounds like it with... New
• language/english/pronunciation/silent.letterFor each letter, what word contains that letter silent?
• language/english/pronunciation/silent.mostWhat word has the most silent letters in a row? Added material
• language/english/pronunciation/silent.to.soundedA silent letter is sounded by adding a suffix or changing or deleting a letter.
• language/english/pronunciation/spoonerismsList some exceptional spoonerisms.
• language/english/pronunciation/syllableWhat words have an exceptional number of letters per syllable? Added material
• language/english/pronunciation/telegramsSince telegrams cost by the word, phonetically similar messages can be cheaper.
• language/english/pronunciation/tweeze.denied"Tweeze Denied Beef Worker Isthmus", by Ron Hardin of AT&T Bell Labs, retells "'Twas the Night Before... New, unsolved
• language/english/pronunciation/homograph/different.pronunciationWhat sequence of letters has the most different pronunciations?
• language/english/pronunciation/homograph/homographsList some homographs (words spelled the same but pronounced differently).
• language/english/pronunciation/homographs/capitonymWhat are the word records for capitonym (word that changes pronunciation when capitalized)? New
• language/english/pronunciation/homographs/different.pronunciationsWhat are the word records for different pronunciations, most? New
• language/english/pronunciation/homographs/pluralWhat are the word records for plural? New
• language/english/pronunciation/homographs/stress.homographsWhat are the word records for stress homographs? New
• language/english/pronunciation/homophone/homophone.fourCan you name three homophones for "palate" and "censor"?
• language/english/pronunciation/homophone/homophone.longestWhat are long homophones (words spelled differently but pronounced alike)?
• language/english/pronunciation/homophone/homophones.alphabetHomophones can be confusing when used to exemplify a letter.
• language/english/pronunciation/homophone/homophones.disjointWhat words sound alike but have few letters in common?
• language/english/pronunciation/homophone/homophones.letterFor each letter, list homophones that differ by that letter.
• language/english/pronunciation/homophone/homophones.mostWhat words have four or more spellings that sound alike?
• language/english/pronunciation/homophone/trivialConsider the free non-abelian group on the twenty-six letters of the alphabet with all relations of the...
• language/english/pronunciation/homophones/confusing.code.wordsWhat are the word records for confusing code words? New
• language/english/pronunciation/homophones/homophones.with.no.removable.prefix.orWhat are the word records for homophones with no removable prefix or suffix, longest? New
• language/english/pronunciation/homophones/longestWhat are the word records for longest? New
• language/english/pronunciation/homophones/longest.transposalWhat are the word records for longest transposal? New
• language/english/pronunciation/homophones/longest.with.few.letters.in.commonWhat are the word records for longest with few letters in common? New
• language/english/pronunciation/homophones/mostWhat are the word records for most? New
• language/english/pronunciation/homophones/most.letters.in.list.with.noWhat are the word records for most letters in list with no removable prefix or suffix? New
• language/english/pronunciation/miscellaneous/entire.word/all.possible.diphthongsWhat are the word records for all possible diphthongs, shortest? New
• language/english/pronunciation/miscellaneous/entire.word/gramogramsWhat are the word records for gramograms (words that sound like sequences of letters)? New
• language/english/pronunciation/miscellaneous/entire.word/phonetic.spellings.identical.with.regular.spellingWhat are the word records for phonetic spellings identical with regular spelling, longest? New
• language/english/pronunciation/miscellaneous/entire.word/pig.latin.words.that.also.areWhat are the word records for pig latin words that also are words, longest? New
• language/english/pronunciation/miscellaneous/entire.word/variable.pronunciationWhat are the word records for variable pronunciation, most? New
• language/english/pronunciation/miscellaneous/subset.of.word/ghost.lettersWhat are the word records for ghost letters, for each letter? New
• language/english/pronunciation/miscellaneous/subset.of.word/one.letterWhat are the word records for one letter, most phonemes? New
• language/english/pronunciation/miscellaneous/subset.of.word/phonemeWhat are the word records for phoneme, variable spelling, most? New
• language/english/pronunciation/miscellaneous/subset.of.word/rules.for.pronouncing.g.violatedWhat are the word records for rules for pronouncing G violated? New
• language/english/pronunciation/miscellaneous/subset.of.word/silent.lettersWhat are the word records for silent letters? New
• language/english/pronunciation/miscellaneous/subset.of.word/suffixWhat are the word records for suffix, most variable pronunciation? New
• language/english/pronunciation/miscellaneous/subset.of.word/word.with.different.pronunciations.of.sameWhat are the word records for word with different pronunciations of same letter, for each letter? New
• language/english/pronunciation/rhyme/entire.word/refractory.rhymeWhat are the word records for refractory rhyme (word with no common rhyme), example of? New
• language/english/pronunciation/rhyme/subset.of.word/endingsWhat are the word records for endings, most? New
• language/english/pronunciation/syllables/entire.word/add.letters.to.reduce.syllablesWhat are the word records for add letters to reduce syllables, shortest? New
• language/english/pronunciation/syllables/entire.word/add.one.letter.to.add.twoWhat are the word records for add one letter to add two syllables, shortest? New
• language/english/pronunciation/syllables/entire.word/change.one.letter.to.radically.changeWhat are the word records for change one letter to radically change pronunciation? New
• language/english/pronunciation/syllables/entire.word/longestWhat are the word records for longest? New
• language/english/pronunciation/syllables/entire.word/no.known.pronunciationWhat are the word records for no known pronunciation, shortest? New
• language/english/pronunciation/syllables/entire.word/rhopalismWhat are the word records for rhopalism? New
• language/english/pronunciation/syllables/entire.word/shortestWhat are the word records for shortest, for each number of syllables? New
• language/english/sentences/beheadIs there a sentence that remains a sentence when all its words are beheaded?
• language/english/sentences/charadesA ....... surgeon was .......
• language/english/sentences/clerihewsWhat is a clerihew, and what are some good examples? New
• language/english/sentences/contradictory.proverbsWhat are some proverbs that contradict one another?
• language/english/sentences/emphasisList some sentences that change meaning when the emphasis is moved.
• language/english/sentences/garden.pathParse these well formed, grammatically correct English sentences: New
• language/english/sentences/hidden.animalsFind the animal hidden in each sentence. New
• language/english/sentences/idiomsList some idioms that say the opposite of what they mean.
• language/english/sentences/obfuscated.proverbsIdentify these obfuscations of celebrated oracular utterances: New
• language/english/sentences/palindromesWhat are some long palindromes? Added material
• language/english/sentences/pangramA "pangram" is a sentence containing all 26 letters. Added material
• language/english/sentences/parts.of.speechWrite a sentence that uses each of the eight parts of speech (interjection, pronoun, verb, adverb,... New
• language/english/sentences/repeated.wordsWhat is a sentence with the same word several times repeated? Added material
• language/english/sentences/reversed.clichesCan anyone add to this list of cliches with word reversals to create clever sayings? New
• language/english/sentences/scrabble.tilesTell a story using exactly the 100 tiles of a Scrabble set (the two blanks may stand for any letters). New
• language/english/sentences/sentenceFind a sentence with words beginning with the letters of the alphabet, in order.
• language/english/sentences/snowballConstruct the longest coherent sentence you can such that the nth word is n letters long.
• language/english/sentences/supersentenceWhat is the shortest sentence containing all four phrases and three subordinate clauses identified in...
• language/english/sentences/two.consonant.sentenceCreate a sentence using only two consonants and as many vowels as you want; each letter may be used more... New, unsolved
• language/english/sentences/upside.down.palindromesFind a palindrome that is also unchanged when read upside down. New
• language/english/sentences/weirdMake a sentence containing only words that violate the "i before e" rule.
• language/english/sentences/word.boundariesList some sentences that can be radically altered by changing word boundaries and punctuation. Added material
• language/english/sentences/self.ref/self.ref.lettersConstruct a true sentence of the form: "This sentence contains _ a's, _ b's, _ c's, ...," where the numbers... Added material
• language/english/sentences/self.ref/self.ref.numbersWhat true sentence has the form: "There are _ 0's, _ 1's, _ 2's, ..., in this sentence"?
• language/english/sentences/self.ref/self.ref.sentencesWhat are some self-referential sentences? New
• language/english/sentences/self.ref/self.ref.wordsWhat sentence describes its own word, syllable and letter count?
• language/english/spelling/adverb.endingsFor each letter of the alphabet, find an adverb that ends in that letter, preferably one that is not also... New
• language/english/spelling/alphabetical.numbersIf the positive integers up to a million are ordered alphabetically (spelled out in English), at what... New
• language/english/spelling/american.ourWhat common British words containing "our" are spelled the same in America?
• language/english/spelling/ate.to.itionFind English verbs ending in -ATE whose related noun ends in -ITION (as "micturate" and "micturition"). New
• language/english/spelling/aunt.tillyAunt Tilly likes butter and jelly, but not peanuts or jam. New
• language/english/spelling/body.partsName 28 parts of the body which are spelled with 4 letters. New
• language/english/spelling/frequencyIn the English language, what are the most frequently appearing: 1) letters overall?
• language/english/spelling/gryFind three completely different words ending in "gry." Added material
• language/english/spelling/hidden.ruleWhat are some puzzles, like Aunt Sally's Green Door, in which players must discover the hidden rule... New
• language/english/spelling/j.endingWhat words and names end in j?
• language/english/spelling/kstWhat 8-letter word has the letters KST in the middle, in the beginning, and at the end? New
• language/english/spelling/letter.countWhat are some exceptional isograms, polygrams, pyramid words, etc.? Restored
• language/english/spelling/letter.orderWhat words have letters in various unusual orders (alphabetical, etc.)? Restored
• language/english/spelling/lipogramsWhat books have been written without specific letters, vowels, etc.? Added material
• language/english/spelling/longestWhat is the longest word in the English language? Added material
• language/english/spelling/mirror.nameName a famous person in thirteen letters whose name, written vertically in capital letters, reads the same... New, unsolved
• language/english/spelling/mostWhat word has the most variant spellings?
• language/english/spelling/near.palindromeWhat are some long near palindromes, i.e., words that except for one letter would be palindromes?
• language/english/spelling/new.doorRearrange the letters of NEW DOOR to form one word. New
• language/english/spelling/number.setsSet A contains 0, 4, 5, 9, 11, 12, 13, 14, 19, ..., 20, 24, 25, ... New
• language/english/spelling/numeric.pangramWhat's special about the number 1,001,000,000,001,000,001,001,002,568? New
• language/english/spelling/nymList some words ending in -nym.
• language/english/spelling/rare.endingsFind common words with these endings, in the manner of the "gry" puzzle. New, unsolved
• language/english/spelling/rare.trigraphsWhat trigraphs (three-letter combinations) occur in only one word? Added material
• language/english/spelling/relations.to.other.wordsWhat are the word records for Relations to Other Words? New
• language/english/spelling/shion.endingFind three English words ending in "shion". New
• language/english/spelling/single.wordsWhat words have exceptional lengths, patterns, etc.? Added material
• language/english/spelling/statesWhat long words have all bigrams either a postal state code or its reverse? Restored
• language/english/spelling/superdemonsWhat words are extremely hard to spell?
• language/english/spelling/ten.preceptsAn old inscription carved on the back of a pew fooled the congregation for many years. New
• language/english/spelling/twenty.nineWhat is unique about the number 29? New
• language/english/spelling/vowelsWhat words contain each vowel once, for each possible order? Added material
• language/english/spelling/alphabetical.order/entire.word/balance.pointsWhat are the word records for balance points? New
• language/english/spelling/alphabetical.order/entire.word/base.26.wordsWhat are the word records for base 26 words? New
• language/english/spelling/alphabetical.order/entire.word/difference.pairWhat are the word records for difference pair (subtracting adjacent letters forms another word)? New
• language/english/spelling/alphabetical.order/entire.word/digital.wordWhat are the word records for digital word (letters replaced by their alphabetical positions as decimal... New
• language/english/spelling/alphabetical.order/entire.word/equidistant.wordWhat are the word records for equidistant word (nth letter same distance from A as nth letter from end is... New
• language/english/spelling/alphabetical.order/entire.word/last.in.reverse.alphabetical.orderWhat are the word records for last in reverse alphabetical order, for each letter? New
• language/english/spelling/alphabetical.order/entire.word/letter.productWhat are the word records for letter product (multiply together positions of letters in alphabet)? New
• language/english/spelling/alphabetical.order/entire.word/letter.shift.pairWhat are the word records for letter-shift pair (shift letters to new letters in the alphabet to form... New
• language/english/spelling/alphabetical.order/entire.word/letter.sum.of.equal.sized.piecesWhat are the word records for letter sum of equal-sized pieces equal? New
• language/english/spelling/alphabetical.order/entire.word/letter.sumsWhat are the word records for letter sums (add together positions of letters in alphabet)? New
• language/english/spelling/alphabetical.order/entire.word/letters.in.alphabetical.orderWhat are the word records for letters in alphabetical order? New
• language/english/spelling/alphabetical.order/entire.word/letters.in.order.minus.notWhat are the word records for letters in order minus not, longest? New
• language/english/spelling/alphabetical.order/entire.word/letters.in.reverse.alphabetical.orderWhat are the word records for letters in reverse alphabetical order? New
• language/english/spelling/alphabetical.order/entire.word/letters.restricted.to.mathematical.sequencesWhat are the word records for letters restricted to mathematical sequences? New
• language/english/spelling/alphabetical.order/entire.word/lipogramWhat are the word records for lipogram (word missing certain letters)? New
• language/english/spelling/alphabetical.order/entire.word/number.namesWhat are the word records for number names? New
• language/english/spelling/alphabetical.order/entire.word/roller.coasterWhat are the word records for roller-coaster (word with letters that alternate between going forward and... New
• language/english/spelling/alphabetical.order/entire.word/sum.pairWhat are the word records for sum pair (adding adjacent letters forms another word)? New
• language/english/spelling/alphabetical.order/entire.word/total.disorderWhat are the word records for total disorder (no letter in its alphabetic place), longest? New
• language/english/spelling/alphabetical.order/entire.word/vicinalWhat are the word records for vicinal (each letter has an alphabetic neighbor in the word), longest? New
• language/english/spelling/alphabetical.order/subset.of.word/consecutive.letters.in.alphabetWhat are the word records for consecutive letters in alphabet? New
• language/english/spelling/alphabetical.order/subset.of.word/last.letter.next.in.alphabet.afterWhat are the word records for last letter next in alphabet after first letter? New
• language/english/spelling/alphabetical.order/subset.of.word/letters.in.alphabetical.place.or.alphabetWhat are the word records for letters in alphabetical place or alphabet crashes? New
• language/english/spelling/consonants/entire.word/all.consonantsWhat are the word records for all consonants, longest? New
• language/english/spelling/consonants/subset.of.word/biconsonantWhat are the word records for biconsonant, for each, longest? New
• language/english/spelling/consonants/subset.of.word/consonant.stringWhat are the word records for consonant string, longest? New
• language/english/spelling/consonants/subset.of.word/containing.five.consonantsWhat are the word records for containing five consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.five.types.of.consonantsWhat are the word records for containing five types of consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.four.consonantsWhat are the word records for containing four consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.four.types.of.consonantsWhat are the word records for containing four types of consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.one.consonantWhat are the word records for containing one consonant, longest? New
• language/english/spelling/consonants/subset.of.word/containing.three.consonantsWhat are the word records for containing three consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.three.types.of.consonantsWhat are the word records for containing three types of consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.two.consonantsWhat are the word records for containing two consonants, longest? New
• language/english/spelling/consonants/subset.of.word/containing.two.types.of.consonantsWhat are the word records for containing two types of consonants, longest? New
• language/english/spelling/consonants/subset.of.word/monoconsonant.or.containing.one.type.ofWhat are the word records for monoconsonant or containing one type of consonant? New
• language/english/spelling/consonants/subset.of.word/n.gramsWhat are the word records for n-grams? New
• language/english/spelling/frequency.order/entire.word/lipogramWhat are the word records for lipogram? New
• language/english/spelling/frequency.order/entire.word/sumwordWhat are the word records for sumword (word converted to the sum of the frequency of its letters per... New
• language/english/spelling/frequency.order/subset.of.word/rare.lettersWhat are the word records for rare letters? New
• language/english/spelling/letter.appearance/entire.word/rotation.or.reflection.symmetryWhat are the word records for rotation or reflection symmetry? New
• language/english/spelling/letter.appearance/entire.word/spelled.with.letters.with.ascenders.bdfhijkltWhat are the word records for spelled with letters with ascenders = bdfhijklt, longest? New
• language/english/spelling/letter.appearance/entire.word/spelled.with.letters.with.descenders.gjpqyWhat are the word records for spelled with letters with descenders = gjpqy, longest? New
• language/english/spelling/letter.appearance/entire.word/spelled.with.short.lowercase.letters.acemnorsuvwxzWhat are the word records for spelled with short lowercase letters = acemnorsuvwxz, longest? New
• language/english/spelling/letter.appearance/entire.word/spelled.with.tall.lowercase.letters.bdfghijklpqtyWhat are the word records for spelled with tall lowercase letters = bdfghijklpqty, longest? New
• language/english/spelling/letter.appearance/entire.word/unusual.punctuationWhat are the word records for unusual punctuation? New
• language/english/spelling/letter.appearance/subset.of.word/ratio.dotted.to.undotted.lettersWhat are the word records for ratio dotted to undotted letters, highest? New
• language/english/spelling/letter.appearance/subset.of.word/ratio.letters.with.ascenders.to.thoseWhat are the word records for ratio letters with ascenders to those without, highest? New
• language/english/spelling/letter.appearance/subset.of.word/ratio.letters.with.descenders.to.thoseWhat are the word records for ratio letters with descenders to those without, highest? New
• language/english/spelling/letter.choices/consonantsWhat are some words containing consonants in unusual ways? Restored
• language/english/spelling/letter.choices/letter.dimensionWhat are some words containing all narrow, tall, short, etc. Restored
• language/english/spelling/letter.choices/lipogramWhat are some exceptional lipograms? Restored
• language/english/spelling/letter.choices/morseWhat are some words that have unusual properties in Morse code? Restored
• language/english/spelling/letter.choices/puzzle.wordWhat are some words formed from chemical symbols, state abbreviations, etc.? Restored
• language/english/spelling/letter.choices/typewriterWhat are some words that are typed in unusual ways? Restored
• language/english/spelling/letter.pattern/entire.wordWhat are some exceptional palindromes, tautonyms, head'n'tail words? Restored
• language/english/spelling/letter.pattern/equidistant.wordsAn equidistant word is one in which the first and last, second and second to last, third and third to last, etc. New
• language/english/spelling/letter.pattern/subset.of.wordWhat are some exceptional words containing doubled and repeated letters, etc.? Restored
• language/english/spelling/letters.selected.from.given.set/entire.word/isosephyWhat are the word records for isosephy? New
• language/english/spelling/letters.selected.from.given.set/entire.word/monthsWhat are the word records for months, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/morse.codeWhat are the word records for Morse code? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.amino.acid.abbreviationsWhat are the word records for spelled with amino acid abbreviations, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.chemical.symbolsWhat are the word records for spelled with chemical symbols, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.overlapping.amino.acid.abbreviationsWhat are the word records for spelled with overlapping amino acid abbreviations, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.overlapping.chemical.symbolsWhat are the word records for spelled with overlapping chemical symbols, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.overlapping.two.letter.uWhat are the word records for spelled with overlapping two-letter U.S. New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.piano.notesWhat are the word records for spelled with piano notes, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.roman.numeralsWhat are the word records for spelled with Roman numerals, longest? New
• language/english/spelling/letters.selected.from.given.set/entire.word/spelled.with.two.letter.u.sWhat are the word records for spelled with two-letter U.S. New
• language/english/spelling/letters.selected.from.given.set/entire.word/telephone.keypadWhat are the word records for Telephone keypad? New
• language/english/spelling/letters.selected.from.given.set/entire.word/zodiacal.signsWhat are the word records for zodiacal signs, longest? New
• language/english/spelling/letters.selected.from.given.set/subset.of.word/telephone.keypadWhat are the word records for Telephone keypad? New
• language/english/spelling/operations.on.words/ate.itionFind a verb ending in "ate" whose associated noun is obtained by replacing the "ate" with "ition." Is... New
• language/english/spelling/operations.on.words/category.anagramRearrange the 32 letters a,a,a,a,a,c,c,d,d,d,e,e,e,e,h,h,h,i,l,l,m,m,n,n, o,o,r,s,s,s,t,u into four words:... New, unsolved
• language/english/spelling/operations.on.words/deletionWhat exceptional words turn into other words by deletion of letters? Added material
• language/english/spelling/operations.on.words/er.estFind words that form other words when both -r (or -er) and -st (or -est) are added, e.g. New
• language/english/spelling/operations.on.words/er.reversedIn general, a [blank]er is someone who [blank]s. New
• language/english/spelling/operations.on.words/insertionWhat exceptional words turn into other words by insertion of letters?
• language/english/spelling/operations.on.words/insertion.and.deletionWhat exceptional words turn into other words by both insertion and deletion of letters?
• language/english/spelling/operations.on.words/less.nessFind a word that forms two other words, unrelated in meaning, when "less" and "ness" are added.
• language/english/spelling/operations.on.words/movementWhat exceptional words turn into other words by movement of letters?
• language/english/spelling/operations.on.words/number.letter.changeNINE contains the letter N twice; change both N's to P's and you get PIPE. New, unsolved
• language/english/spelling/operations.on.words/s.s.wordsWhat words besides EXINES can take an S at the beginning and end, but only both together? New
• language/english/spelling/operations.on.words/sign.anagramRearrange the letters of the roadside sign "Don't pretend to be what you don't intend to be" into an... New, unsolved
• language/english/spelling/operations.on.words/substitutionWhat exceptional words turn into other words by substitution of letters?
• language/english/spelling/operations.on.words/substitution.and.transpositionWhat exceptional words turn into other words by substitution and transposition of letters?
• language/english/spelling/operations.on.words/transpositionWhat exceptional words turn into other words by transposition of letters? Added material
• language/english/spelling/operations.on.words/words.within.wordsWhat exceptional words contain other words?
• language/english/spelling/plurals/collisionTwo words, spelled and pronounced differently, have plurals spelled the same but pronounced differently.
• language/english/spelling/plurals/doubtful.numberA little word of doubtful number, a foe to rest and peaceful slumber.
• language/english/spelling/plurals/drop.sDrop an "s" and singular becomes plural, feminine becomes masculine. Restored
• language/english/spelling/plurals/drop.terminalWhat words have their plurals formed by dropping the final letter?
• language/english/spelling/plurals/endingsList a plural ending with each letter of the alphabet.
• language/english/spelling/plurals/frenchWhat English word, when spelled backwards, is its French plural? Restored
• language/english/spelling/plurals/manWords ending with "man" make their plurals by adding "s".
• language/english/spelling/plurals/odd.pluralWhat are some oddly formed plurals?
• language/english/spelling/plurals/plural.of.pluralWhat word has a plural that itself takes a plural (a "pluralses")? New
• language/english/spelling/plurals/switch.firstWhat plural is formed by switching the first two letters?
• language/english/spelling/relations.to.other.words/cryptarithmetic.word.setsWhat are the word records for cryptarithmetic word sets? New
• language/english/spelling/relations.to.other.words/overlapping.wordsWhat are the word records for overlapping words? New
• language/english/spelling/relations.to.other.words/pangramWhat are the word records for pangram (list of words containing all the letters of the alphabet)? New
• language/english/spelling/relations.to.other.words/subtransposal.listWhat are the word records for subtransposal list, longest? New
• language/english/spelling/relations.to.other.words/word.girdersWhat are the word records for word girders, longest? New
• language/english/spelling/relations.to.other.words/word.groupsWhat are the word records for word groups? New
• language/english/spelling/relations.to.other.words/word.squaresWhat are the word records for word squares? New
• language/english/spelling/relations.to.other.words/entire.word/bi.logogramWhat are the word records for bi-logogram (word whose letters can be regrouped and/or reversed to form... New
• language/english/spelling/relations.to.other.words/entire.word/deletionWhat are the word records for deletion? New
• language/english/spelling/relations.to.other.words/entire.word/deletion.and.insertionWhat are the word records for deletion and insertion? New
• language/english/spelling/relations.to.other.words/entire.word/insertionWhat are the word records for insertion? New
• language/english/spelling/relations.to.other.words/entire.word/letter.bankWhat are the word records for letter bank (words formed from letters selected from a set)? New
• language/english/spelling/relations.to.other.words/entire.word/logogramWhat are the word records for logogram (word whose letters can be regrouped to form smaller words), longest... New
• language/english/spelling/relations.to.other.words/entire.word/movementWhat are the word records for movement? New
• language/english/spelling/relations.to.other.words/entire.word/reversal.pairWhat are the word records for reversal pair (reverse the letters in a word to form another word)? New
• language/english/spelling/relations.to.other.words/entire.word/substitutionWhat are the word records for substitution? New
• language/english/spelling/relations.to.other.words/entire.word/transadditionWhat are the word records for transaddition (add one letter and rearrange to form another word)? New
• language/english/spelling/relations.to.other.words/entire.word/transdeletionWhat are the word records for transdeletion (delete one letter and rearrange to form another word)? New
• language/english/spelling/relations.to.other.words/entire.word/transpositionWhat are the word records for transposition (rearrange letters to form another word)? New
• language/english/spelling/relations.to.other.words/entire.word/transubstitutionWhat are the word records for transubstitution (substitute one letter and rearrange to form another word)? New
• language/english/spelling/relations.to.other.words/entire.word/words.within.wordsWhat are the word records for words within words? New
• language/english/spelling/relations.to.other.words/subset.of.word/complete.permutationsWhat are the word records for complete permutations? New
• language/english/spelling/relations.to.other.words/subset.of.word/compound.parts.of.speechWhat are the word records for compound parts-of-speech? New
• language/english/spelling/relations.to.other.words/subset.of.word/gamesWhat are the word records for games? New
• language/english/spelling/sets.of.words/garble.groupsDesign a combination lock with *letters* instead of digits, with the added restriction that each... New
• language/english/spelling/sets.of.words/ladderFind the shortest word ladders stretching between the following pairs: hit - ace pig - sty four - five play... Added material
• language/english/spelling/sets.of.words/noncrashingFind as large a set as possible of six-letter words, no two of which have the same letter in the same... New
• language/english/spelling/sets.of.words/nots.and.crossesWhat is the most number of letters that can be fit into a three by three grid of words, such that no letter...
• language/english/spelling/sets.of.words/perfect.ladderA "perfect" ladder comprises five-letter words where every letter is the new letter once, no position is...
• language/english/spelling/sets.of.words/squaresWhat are some exceptional word squares (square crosswords with no blanks)? Added material
• language/english/spelling/sets.of.words/threepeatersForm the shortest list of six-letter words in which each word in the list has as its second, fourth, and...
• language/english/spelling/sets.of.words/transposal.squaresWhat are the largest known regular transposal squares and double transposal rectangles? New
• language/english/spelling/sets.of.words/variogramWhat is the largest known variogram (word square where repeated letters count as one square)?
• language/english/spelling/sets.of.words/word.tortureWhat is the longest word all of whose contiguous subsequences are words?
• language/english/spelling/structure/entire.word/head.n.tail.wordWhat are the word records for head 'n' tail word (word formed by repeating a sequence of letters with one... New
• language/english/spelling/structure/entire.word/isomorph.or.matching.letter.patternWhat are the word records for isomorph or matching letter pattern (words that repeat letters in the same... New
• language/english/spelling/structure/entire.word/number.of.different.lettersWhat are the word records for number of different letters? New
• language/english/spelling/structure/entire.word/palindromeWhat are the word records for palindrome (same word when letters are reversed)? New
• language/english/spelling/structure/entire.word/sesquipedalian.wordWhat are the word records for sesquipedalian word (long word), longest? New
• language/english/spelling/structure/entire.word/spelling.graphsWhat are the word records for spelling graphs (draw line from letter to letter looping back for repeated... New
• language/english/spelling/structure/entire.word/start.and.endWhat are the word records for start and end (starting and ending letters of word are identical)? New
• language/english/spelling/structure/entire.word/switch.wordWhat are the word records for switch word (letters like train cars can be switched to a siding), longest? New
• language/english/spelling/structure/entire.word/tautonymWhat are the word records for tautonym (word formed by repeating a sequence of letters)? New
• language/english/spelling/structure/subset.of.word/all.letter.orders.in.wordWhat are the word records for all letter orders in word? New
• language/english/spelling/structure/subset.of.word/alternatingWhat are the word records for alternating? New
• language/english/spelling/structure/subset.of.word/bigrams.or.digramsWhat are the word records for bigrams or digrams? New
• language/english/spelling/structure/subset.of.word/ending.gryWhat are the word records for ending -gry? New
• language/english/spelling/structure/subset.of.word/identical.lettersWhat are the word records for identical letters? New
• language/english/spelling/structure/subset.of.word/internal.structureWhat are the word records for internal structure? New
• language/english/spelling/structure/subset.of.word/repeated.lettersWhat are the word records for repeated letters, most? New
• language/english/spelling/structure/subset.of.word/repeated.prefixWhat are the word records for repeated prefix, longest? New
• language/english/spelling/structure/subset.of.word/tetragram.setsWhat are the word records for tetragram sets, all 23751 possible? New
• language/english/spelling/structure/subset.of.word/trigramsWhat are the word records for trigrams, all 17576 possible? New
• language/english/spelling/structure/subset.of.word/unusual.spellingWhat are the word records for unusual spelling? New
• language/english/spelling/typewriter.order/entire.word/spelled.in.left.to.right.typewriterWhat are the word records for spelled in left-to-right typewriter order, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.in.right.to.left.typewriterWhat are the word records for spelled in right-to-left typewriter order, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.adjacent.keys.on.typewriterWhat are the word records for spelled with adjacent keys on typewriter, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.alternating.hands.on.typewriterWhat are the word records for spelled with alternating hands on typewriter, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.keys.in.groupsWhat are the word records for spelled with keys in groups, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.letters.from.typewriter.bottomWhat are the word records for spelled with letters from typewriter bottom row, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.letters.from.typewriter.middleWhat are the word records for spelled with letters from typewriter middle row, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.letters.from.typewriter.topWhat are the word records for spelled with letters from typewriter top row, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.one.finger.on.typewriterWhat are the word records for spelled with one finger on typewriter? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.typewriter.letters.from.leftWhat are the word records for spelled with typewriter letters from left hand, longest? New
• language/english/spelling/typewriter.order/entire.word/spelled.with.typewriter.letters.from.rightWhat are the word records for spelled with typewriter letters from right hand, longest? New
• language/english/spelling/typewriter.order/entire.word/typewriter.shiftwordWhat are the word records for typewriter shiftword (shift hand position on typewriter to form another word)? New
• language/english/spelling/typewriter.order/subset.of.word/spelled.using.all.typewriter.fingersWhat are the word records for spelled using all typewriter fingers, shortest? New
• language/english/spelling/typewriter.order/subset.of.word/spelled.using.all.typewriter.fingers.inWhat are the word records for spelled using all typewriter fingers in order, shortest? New
• language/english/spelling/typewriter.order/subset.of.word/spelled.using.all.typewriter.fingers.in.2What are the word records for spelled using all typewriter fingers in reverse order, shortest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/alternating.vowel.consonantWhat are the word records for alternating vowel/consonant? New
• language/english/spelling/vowel.consonant.patterns/entire.word/consonants.minus.vowelsWhat are the word records for consonants minus vowels, highest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/consonymWhat are the word records for consonym (words with same consonant pattern), longest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/consonym.listWhat are the word records for consonym list, longest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/eight.letterWhat are the word records for eight letter? New
• language/english/spelling/vowel.consonant.patterns/entire.word/no.matching.vowel.patternWhat are the word records for no matching vowel pattern, shortest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/ratio.consonants.to.vowelsWhat are the word records for ratio consonants to vowels, highest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/ratio.vowels.to.consonantsWhat are the word records for ratio vowels to consonants, highest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/seven.letterWhat are the word records for seven letter, all 128 possible? New
• language/english/spelling/vowel.consonant.patterns/entire.word/vowels.minus.consonantsWhat are the word records for vowels minus consonants, highest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/well.mixed.consonymsWhat are the word records for well-mixed consonyms, longest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/well.mixed.words.with.same.consonantWhat are the word records for well-mixed words with same consonant-vowel pattern, longest? New
• language/english/spelling/vowel.consonant.patterns/entire.word/words.with.the.same.consonantsWhat are the word records for words with the same consonants? New
• language/english/spelling/vowels/entire.word/all.vowel.hawaiian.wordsWhat are the word records for all-vowel Hawaiian words? New
• language/english/spelling/vowels/entire.word/all.vowelsWhat are the word records for all vowels, longest? New
• language/english/spelling/vowels/entire.word/no.vowelsWhat English words have no vowels? New
• language/english/spelling/vowels/entire.word/three.letter.wordsWhat are the word records for three letter words, all 216 possible? New
• language/english/spelling/vowels/subset.of.word/all.120.possible.ordersWhat are the word records for all 120 possible orders? New
• language/english/spelling/vowels/subset.of.word/each.onceWhat are the word records for each once? New
• language/english/spelling/vowels/subset.of.word/each.once.in.orderWhat are the word records for each once in order? New
• language/english/spelling/vowels/subset.of.word/restricted.numbers.of.vowelsWhat are the word records for restricted numbers of vowels? New
• language/english/spelling/vowels/subset.of.word/restricted.vowel.typesWhat are the word records for restricted vowel types? New
• language/english/spelling/vowels/subset.of.word/tetragramsWhat are the word records for tetragrams, all 625 possible? New
• language/english/spelling/vowels/subset.of.word/trigramsWhat are the word records for trigrams, all 216 possible? New
• language/english/spelling/vowels/subset.of.word/vowel.stringWhat are the word records for vowel string, longest? New
• language/finnish/finnish.pluralWhat Finnish word is the anagram of its plural? Restored
• language/finnish/finnish.recordWhat are some Finnish words with unusual properties? Added material
• language/french/english.french.sentencesWhat is the longest reasonable sentence in English that is also a sentence in French? New
• language/french/french.palindromesList some French palindromes. Added material
• language/french/french.recordWhat are some French words with unusual properties?
• language/french/mots.d.heuresThis French verse, read aloud, sounds like an English nursery rhyme; which one? New, unsolved
• language/german/german.palindromesList some German palindromes. Added material
• language/german/german.recordWhat are some German words with unusual properties? Added material
• language/german/longest.wordWhat is the longest word in German? New
• language/italian/italian.recordWhat are some Italian words with unusual properties? Added material
• language/norwegian/norwegian.recordWhat are some Norwegian words with unusual properties?
• language/spanish/spanish.palindromesWhat are some palindromes in Spanish (and Galician and Catalan)? New
• language/swedish/swedish.recordWhat are some Swedish words with unusual properties? Added material
• logic/29Three people check into a hotel. Added material
• logic/ages1) Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim.
• logic/aha.puzzlesWhat are some "aha!"-type puzzles, puzzles whose simple solutions are not obvious? New
• logic/answered.not.solvedWhat puzzles can be *answered* without being completely *solved*, e.g. New
• logic/attributeAll the items in the first list share a particular attribute.
• logic/axiom.of.choiceExactly which parts of mathematics would have to be discarded if we threw out the axiom of choice? New
• logic/axiom.of.determinacyIf an arithmetical statement is proved using the Axiom of Determinacy (AD), what must one believe about AD... New
• logic/boodle.phil.moivenGiven these five statements in an unknown language, whom does Phil "moiven"? New, unsolved
• logic/bookwormA bookworm eats from the first page of an encyclopedia to the last page.
• logic/boxesTwo boxes are labeled "A" and "B".
• logic/brain.teasersWhat is the one word in the English language that is always pronounced incorrectly, and other brain teasers? New, unsolved
• logic/calibans.willWhen Caliban's will was opened it was found to contain the following clause: "I leave ten of my books to...
• logic/camelAn Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune.
• logic/centrifugeYou are a biochemist, working with a 12-slot centrifuge.
• logic/chainWhat is the least number of links you can cut in a chain of 21 links to be able to give someone all... Added material
• logic/childrenA man walks into a bar, orders a drink, and starts chatting with the bartender.
• logic/condomsWhat is the minimum number of condoms required for safe sex in each case: (a) two men with two women (b)...
• logic/cow.on.islandA boy and his cow arrived at a round lake. New, unsolved
• logic/crossing.wiresCross the wires without crossing the wires: fill the black box with some quantity of NAND gates. New
• logic/crossover[ Editor: What is the minimum number of two-input NAND gates needed to build a crossover circuit, which... New
• logic/dellHow can I solve logic puzzles (e.g., as published by Dell) automatically?
• logic/eat.or.sleepAfter three days without food you die on the spot, and after three days without sleep you die on the spot. New
• logic/elimination97 baseball teams participate in an annual state tournament.
• logic/faulty.chipsA professor has n VLSI chips that can be placed on a test bed 2 at a time, where they test each other. New
• logic/finite.axiomatizabilityWhat is the finite axiomatizability theorem of Kleene, Craig and Vaught called, and where was it published? New
• logic/five.coinsYou have three large and two small coins, placed in a row as OxOxO (O large, x small). New
• logic/flipHow can a toss be called over the phone (without requiring trust)? Added material
• logic/flowersHow many flowers do I have if all of them are roses except two, all of them are tulips except two, and all...
• logic/four.envelopesFour envelopes show 7, A, 2 and H; which must you turn over to test the rule "If the envelope has an A on... New
• logic/friendsAny group of 6 or more contains either 3 mutual friends or 3 mutual strangers.
• logic/fusesYou have two one-hour fuses, but the fuses do not burn uniformly.
• logic/gas.stationsGas stations on a circular road hold, in total, just enough gas for one lap. New
• logic/giant.frogA giant frog leaps 5 times as far as a normal frog does. New, unsolved
• logic/goodsteinDo Goodstein sequences grow faster than Ackermann's function? New
• logic/guess.number.one.lieI'm thinking of a number between 1 and 2000. New
• logic/guess.the.numberA teacher thinks of a number between 1 and 15 and three students guess, each time being told "high" or... New
• logic/hats.and.coatsA man has three hats, one red, one white, and one black. New
• logic/heads.pilesTold only how many coins in a stack show heads, how can a man, without looking, split the stack into two... New
• logic/hempel.ravensIf seeing a black raven confirms "all ravens are black", then seeing a white shoe confirms "all non-black... New
• logic/hofstadterIn first-order logic, find a predicate P(x) which means "x is a power of 10."
• logic/hundredThere is a piece of paper with 100 sentences written on: " 1. Added material
• logic/inverterCan a digital logic circuit with two inverters invert N independent inputs?
• logic/josephineThe recent expedition to the lost city of Atlantis discovered scrolls attributted to the great poet, scholar, philosopher Josephine.
• logic/kinshipBrothers and sisters have I none, but that man's father is my father's son. Added material
• logic/lateralWhat are some classic lateral thinking puzzles, and where can I find more?
• logic/latinoSolve this Latino puzzle: fill a 6x6 grid with the numbers 1 to 6 so that each row and column contains one... New
• logic/laura.ageToday is January 1. New
• logic/leadoff.batterThe leadoff batter of a baseball team came up to bat in all nine innings. New
• logic/leadoff.hitterIf the leadoff hitter in the lineup of the visiting team comes up to bat in every inning of a nine-inning... New
• logic/liars.surveyThere are 123 tenants living in an apartment building. New
• logic/locks.and.boxesYou want to send a valuable object to a friend.
• logic/lost.in.woodsYou are lost in the forest with eight campers, two of whom sometimes lie; how do you find the one path of... New
• logic/lunch.specialsThe following conversation between Bob and Jack in a Chinese restaurant was overheard: New
• logic/meeting.trainsGranny Smith, who was leaving London, boarded a train at four minutes past the hour. New
• logic/mermaidsFrom these nine statements, what, if anything, can we conclude about the connection between seeing a... New
• logic/min.maxIn a rectangular array of people, which will be taller, the tallest of the shortest people in each column,...
• logic/mirror.and.tableYou are in a room. New
• logic/mixingStart with a half cup of tea and a half cup of coffee.
• logic/monty.52Monty and Waldo play a game with N closed boxes.
• logic/mu.puzzleCan you turn MI into MU using the following rules? New
• logic/murder.houseSix people were in a house when a murder was committed in the second bedroom; from their statements, two of... New
• logic/natural.independenceWhich "natural" mathematical statements are known to be independent of the axioms of arithmetic, in the sense of Goedel's theorem? New
• logic/net.book.riddlesSolve the riddles of the net.book.riddles, a 1992-93 collection compiled by Mark Manning from e-mail and... New
• logic/numberMr. S. and Mr. P. Added material
• logic/oil.jarsA merchant was going to market carrying in his cart twelve big clay jars filled with vegetable oil. New
• logic/peano.arithmeticIf Peano Arithmetic cannot prove some true statements about the numbers, is that a defect of PA, and why do... New
• logic/petals.around.the.roseIn the dice game "Petals Around the Rose", what rule gives the answer for each roll of six dice? New
• logic/phone.number.questionA girl says, "I'm 12 plus half my age," and "I can't give you my phone number, but I'll answer yes or no to... New
• logic/pleasant.journeyMy pleasant journey commences when I briefly meet a familiar character marking a pitch in front of a wooden strip. New
• logic/priest.and.ladiesIn the village church, said the priest to the parish clerk: - It is funny to see that those three ladies... New
• logic/pyjamasIf I wear my nightcap, I do not wear the slippers. New
• logic/riddleWho makes it, has no need of it. Added material
• logic/ropesTwo fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart.
• logic/same.streetSally and Sue have a strong desire to date Sam.
• logic/sand.timersHow can you time cooking a sauce for exactly 9 minutes using only a 4-minute sand timer and a 7-minute sand... New
• logic/self.refFind a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of... Added material
• logic/self.ref.aptitude.testCan you find the unique solution to Jim Propp's twenty-question Self-Referential Aptitude Test? New
• logic/self.ref.quizCan you score 100% on this ten-question Self-Referential Quiz, and can you prove in a few words why there... New
• logic/self.ref.smallTo each of the following questions, exactly one of the alternatives is true. New, unsolved
• logic/self.ref.testThere is exactly one solution to the following [ Editor: self-referential multiple-choice ] test. New
• logic/self.reproducing.programProve that a program that prints its own source can be written in any programming language whose output... New
• logic/set.theoryWhat are the primitive notions of the standard axiomatizations of set theory (ZF, Goedel-Bernays, Quine's... New
• logic/sheep.on.passThree sheep facing right and three facing left meet on a narrow mountain pass with one empty space between... New
• logic/simple.puzzlesWhat bird comes from an egg, but doesn't lay eggs? New
• logic/situation.puzzles"A man lies dead in a room with fifty-three bicycles in front of him. Added material
• logic/situation.puzzles.outtakesThe following puzzles have been removed from my situation puzzles list, or never made it onto the list in the first place. Restored
• logic/suitors.hatsA king must choose among four suitors for his daughter's hand, and he wants the most astute of them. New
• logic/supertasksYou have an empty urn, and an infinite number of labeled balls. Added material
• logic/three.casksYou have three casks holding 19, 13 and 7 units. New
• logic/timezoneTwo people are talking long distance on the phone; one is in an East- Coast state of the US, the other is...
• logic/train.shuntingAn engine kept at a depot must exchange two cars: car A at station A and car B at station B, on a track... New
• logic/transoceanic.cableYou laid a transoceanic cable. New
• logic/trick.questionsWhat are some trick questions that seem to pose a hard or impossible question but have a simple answer... New
• logic/tricky.questionsHow many birthdays does the average man have? New
• logic/tulip.bulbsHow can you plant three unidentifiable tulip bulbs (blue, white, red) so that the flowers are sure to show... New
• logic/twelve.and.fifteenOne day in 1980, Jim said, "The day before yesterday I was twelve. New
• logic/twin.birthdaysKerry celebrated her birthday. New
• logic/two.armiesTwo parties who can communicate only by unreliable messages must agree that a transaction (such as an... New
• logic/two.black.pebblesA maiden must draw one of two pebbles from a bag, said to be one white and one black, to win her freedom... New
• logic/two.eggsYou live in a 36-story apartment building, and have access to a window on each floor. New
• logic/two.generalsTwo generals must attack together, but can communicate only by messengers who may be lost; how can they... New
• logic/unexpectedSwedish civil defense authorities announced that a civil defense drill would be held one day the following...
• logic/vergerA very bright and sunny Day The Priest did to the Verger say: "Last Monday met I strangers three None of...
• logic/verse.riddlesSolve these riddles, arranged from simple to difficult. New
• logic/wire.labelsYou are in room A, where you can see the ends of 15 wires, which are labelled 1,2,..
• logic/wrong.labelsThree candle boxes are labeled "white", "red", and "white and red." All three labels are incorrect. Added material
• logic/zebraThere are five houses, each of a different color and inhabited by men of different nationalities, with... New
• logic/zooI took some nephews and nieces to the Zoo, and we halted at a cage marked
• logic/invariants/djikstras.urnAn urn contains an unknown number of white and black balls (but more than one).
• logic/invariants/infected.checkerboardShow that fewer than N black cells can never turn a whole NxN grid black when each cell with at least 2... New
• logic/invariants/odd.handshakesn people (n >= 2) attend a party, and each person shakes hands with some of the others. New
• logic/smullyan/black.hatThree logicians, A, B, and C, are wearing hats, which they know are either black or white but not all white.
• logic/smullyan/cannot.tellA knight always tells the truth, and a knave always lies. New
• logic/smullyan/electionA Meta-Puzzle: who was the Mathematician, who the Philosopher, who was Normal, and in what order did they... New
• logic/smullyan/equivocatorOn the way to Heaven you meet a person who sometimes tells the truth and sometimes lies. New
• logic/smullyan/fork.three.menThree men stand at a fork in the road. Added material
• logic/smullyan/fork.two.menTwo men stand at a fork in the road. Added material
• logic/smullyan/integersTwo logicians place cards on their foreheads so that what is written on the card is visible only to the other logician.
• logic/smullyan/kings.daughterOn an island of knights (who always tell the truth), knaves (who always lie) and normals (who may do... New
• logic/smullyan/liars.et.alOf a group of n men, some always lie, some never lie, and the rest sometimes lie. Restored
• logic/smullyan/marry.non.normalYou wish to marry the daughter of the king of the Island of Knights, Knaves, and Normals. New
• logic/smullyan/painted.headsWhile three logicians were sleeping under a tree, a malicious child painted their heads red.
• logic/smullyan/priestIn a small town there are N married couples in which one of the pair has committed adultery. Added material
• logic/smullyan/rattlePuzzle 61 in R. Smullyan's _What is the Name of This Book?_ is about Tweedledum and Tweedledee. New, unsolved
• logic/smullyan/stampsThe moderator takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two... Added material
• logic/smullyan/three.menOf three men, one always lies, only never lies, and one sometimes lies. Restored
• logic/smullyan/two.fifths.truthfulOn a certain island, everyone is either a truth-teller or a liar. New
• logic/weighing/balanceYou are given 12 identical-looking coins, one of which is counterfeit and weighs slightly more or less (you...
• logic/weighing/boxYou have ten boxes; each contains nine balls.
• logic/weighing/easter.eggsYou are presented with six chocolate Easter eggs of which you are to choose three. New
• logic/weighing/find.medianWhat is the least number of pairwise comparisons needed to find the median of 2n+1 distinct real numbers?
• logic/weighing/five.sacksYou have 5 sacks of gold and a normal scale. New, unsolved
• logic/weighing/good.coinYou have 11 coins, fewer than half of them bogus, and a balance scale; can you find for sure a good coin in... New
• logic/weighing/gummy.bearsReal gummy drop bears have a mass of 10 grams, while imitation gummy drop bears have a mass of 9 grams.
• logic/weighing/optimal.weightsWhat is the smallest set of weights that allow you to weigh on a balance scale every integer number of...
• logic/weighing/postage.scaleWith a postage scale that compares a load against a whole number of ounces, how many weighings find which... New
• logic/weighing/rank.fiveHow many weighings with a beam balance are required to rank five different weights from lightest to heaviest? New
• logic/weighing/scale.five.sacksYou have 5 sacks of gold and a normal scale (one that gives a total weight, like a bathroom scale, not a pan balance). New
• logic/weighing/six.cubesYou are given 6 cubes (A, B, C, D, E and F). New
• logic/weighing/ten.coins.two.weightsYou have 10 coins; maybe they all weigh the same, maybe they don't. New
• logic/weighing/uneven.armsYou have a balance scale, with one arm twice the length of the other. New
• logic/weighing/weighingsSome of the supervisors of Scandalvania's n mints are producing bogus coins.
• magic/hook.and.rubber.bandHow does the "impossible" tube puzzle work in which a hook-piece, pushed into a tube that has a rubber band... New
• magic/snapping.gameIn the Snapping Game, player 1 is told a name by a spectator and communicates it to player 2 by snapping... New
• magic/trip.gameSomeone thinks of a famous person and tells player 1, but not player 2. New
• magic/card/alternating.colorsHow must a deck of red and black cards be ordered so that, dealing the top card face up and putting the... New
• magic/card/guess.1.of.5There are two magicians, A and B. Added material
• magic/card/guessing.over.phoneYou are at a party and announce that you have a friend who is such a great psychic that he can tell what...
• physics/actual.infinityGive one valid counter-example to "everything is finite": a piece of evidence that the infinite is actually... New
• physics/airplane.liftIs Bernoulli's principle the explanation of how an airplane wing generates lift? New
• physics/balloonA helium-filled balloon is tied to the floor of a car that makes a sharp right turn.
• physics/barometerHow would you find out the height of a building using a barometer? New
• physics/bicycle.balanceWhen you ride your bike at constant velocity (say 5 m/s) you tend to keep your balance far easier than when... New
• physics/black.boxA black box with three terminals contains three equal resistors of unknown value, connected either as a delta or as a wye. New
• physics/bomb.testerSome bombs are good and some are duds; a good bomb has a sensor that sets it off if a single photon hits it. New
• physics/brickWhat is the maximum overhang you can create with an infinite supply of bricks?
• physics/bubblesIn a universe with the same physical laws, but which is mostly water with little bubbles in it, do the... Added material
• physics/cannonballA person in a boat drops a cannonball overboard; does the water level change?
• physics/charges.in.sphereEight equally charged particles inside a sphere repel each other and come to rest; what figure do they form? New, unsolved
• physics/charges.on.sphereEight equally charged particles repel each other inside a sphere and come to rest; what figure do they form? New
• physics/coriolisHow large is the Coriolis effect on water flowing down a sink drain, and on an artillery shell? New
• physics/delta.wyeHow can you tell whether sealed black boxes contain three identical resistors connected in Delta or in Wye? New
• physics/doughnutDoes the inner dimension of an iron doughnut increase or [Editor: "of" in the original] decrease when the... New
• physics/duffing.equationWhat exactly is Duffing's equation, and how does the strange attractor associated with it emerge? New
• physics/ehrenfest.paradoxA rigid disk spinning near the speed of light has its rim Lorentz contracted but not its radius; is the... New
• physics/electron.driftHow fast do electrons travel through a wire, and if they are slow, why does the light come on almost the... New
• physics/electrons.on.sphereHow should 8 electrons be placed on a sphere to minimize their energy? New
• physics/fall.into.sunSuppose the Earth suddenly stopped in its orbit. New
• physics/faucetSomeone didn't leave the faucet turned off all the way, so there is a slow but steady leak (i.e. New
• physics/feynman.sprinklerAn S-shaped lawn sprinkler spins one way when water is pumped out of it. New
• physics/floating.cubeIn what position does a floating wooden cube come to rest: flat on a face, on an edge, or with a corner up? New
• physics/fly.and.trainA fly flying towards an oncoming steam train hits its front and is carried along with it. New
• physics/fly.in.bottleA fly is trapped in a bottle which in turn is in a bucket of water. New
• physics/free.fall.throwYou are falling from 1000 feet holding a 30 lb child. New
• physics/gold.and.leadA thief swaps an 18 ounce gold bar for an 18 ounce lead weight on a pressure plate, and the alarm goes off. New
• physics/hair.dryerIf you block the air-inlet for a hair-dryer, the tone of the motor of that hair-dryer seems to rise ... New
• physics/hat.in.riverThe Harvard bridge and the Longfellow bridge are 1 mile apart. New
• physics/heated.ringA metal ring is heated. New
• physics/heavy.electronAn electron is accelerated so close to the speed of light that its (relativistic) mass is 1 kilogram. New
• physics/inclined.treadmillA motorcycle rides on a flat treadmill moving at 40 mph, so that it stays stationary relative to an observer beside it. New
• physics/isotopes.heaviestWhat is the heaviest isotope? New
• physics/juggling.bridgeA woman who weighs 100 lb carries two gold balls, 10 lb each. New
• physics/left.right.aliensExplain which direction is left, and which direction is right, to an English-speaking alien from Alpha... New
• physics/magnetsYou have two bars of iron.
• physics/milk.and.coffeeYou are just served a hot cup of coffee and want it to be as hot as possible later. Added material
• physics/mirrorWhy does a mirror appear to invert the left-right directions, but not up-down? Added material
• physics/monkeyHanging over a pulley there is a rope, with a weight at one end. Added material
• physics/n.switchesWire n switches, a power source and a lamp so that switching any one of the switches changes the state of... New
• physics/pigeonsA 1000-kg truck carrying 500 kg of live pigeons in a sealed cargo compartment pulls up to a weighing... New
• physics/pole.in.barnAccelerate a pole of length l to a constant speed of 90% of the speed of light (.9c).
• physics/primary.colorsWhy are red, yellow and blue the primary colours for paint, but red, green and blue for light, and how does... New
• physics/resistorsWhat is the resistance between various pairs of vertices on a lattice of unit resistors in the shape of a 1. Added material
• physics/return.currentWhy does the return current in the ground plane of a circuit board follow the path directly beneath the... New
• physics/sailA sailor is in a sailboat on a river. Added material
• physics/shoot.sunIf you are standing at the equator at sunrise, where must you point a laser cannon to hit the Sun dead center?
• physics/skidWhat is the fastest way to make a 90 degree turn on a slippery road?
• physics/small.mirrorLooking in a small mirror, do you actually see a larger portion of your face when you hold the mirror farther away? New
• physics/spheresTwo spheres are the same size and weight, but one is hollow.
• physics/spherical.cavityIf all space is filled with rock except a spherical cavity, what is the effect of gravity inside the cavity? New
• physics/spinning.universeI am sitting on a swivel-stool and I push myself so that I start spinning around, and I get dizzy. New
• physics/submerged.balloonA balloon filled with air is completely submerged under water, a weight attached to it. New
• physics/thermal.inversionHow can heat exchange alone (no mixing) bring cold blue water at 1 degree up to 99 degrees using an equal... New
• physics/three.way.switchesHow can three three-way switches (single-pole, double-throw) be wired so that each of them can switch a... New
• physics/time.travel.paradoxIf you went back in time to before you were born to kill your parents, what would happen? New
• physics/train.backwardWhat part of a train is always moving in the opposite direction relative to the rest of the train? New
• physics/train.wheelsThe left and right wheels on a train car are welded to the axle to make one solid wheel-axle-wheel combination. New
• physics/two.boxes.two.lampsHere's a puzzle that requires a slight knowledge of electronics, and some verbal skills: New
• physics/windIs a round-trip by airplane longer or shorter if there is wind blowing?
• physics/yotHow do you get the silver dollar out of the yot, a metal puzzle that looks like a top with a silver dollar... New
• pickover/pickover.01Title: Cliff Puzzle 1: Can you beat the numbers game?
• pickover/pickover.02Title: Cliff Puzzle 2: Grid of the Gods From: cliff@watson.ibm.com
• pickover/pickover.03Title: Cliff Puzzle 3: Too many 3's From: cliff@watson.ibm.com
• pickover/pickover.04Title: Cliff Puzzle 4: Time in a Bottle From: cliff@watson.ibm.com
• pickover/pickover.05Title: Cliff Puzzle 5: Mystery Sequence From: cliff@watson.ibm.com
• pickover/pickover.06Title: Cliff Puzzle 6: Star Chambers From: cliff@watson.ibm.com
• pickover/pickover.07Title: Cliff Puzzle 7: 3x3 Recursion From: cliff@watson.ibm.com
• pickover/pickover.08Title: Cliff Puzzle 8: Squares and Squares and Squares ....
• pickover/pickover.09Title: Cliff Puzzle 9: 3-Atoms and Growth From: cliff@watson.ibm.com
• pickover/pickover.10Title: Cliff Puzzle 10: The Ark Series From: cliff@watson.ibm.com
• pickover/pickover.11Title: Cliff Puzzle 11: The Leviathan Number From: cliff@watson.ibm.com
• pickover/pickover.12Title: Cliff Puzzle 12: Slides in Hell From: cliff@watson.ibm.com
• pickover/pickover.13Title: Cliff Puzzle 13: Ladders to Heaven From: cliff@watson.ibm.com
• pickover/pickover.14Title: Cliff Puzzle 14: Geography Genuflection From: cliff@watson.ibm.com
• pickover/pickover.15Title: Cliff Puzzle 15: Cherries in Wine Glasses From: cliff@watson.ibm.com Added material
• pickover/pickover.16Title: Cliff Puzzle 16: Undulating Squares From: cliff@watson.ibm.com Added material
• pickover/pickover.17Title: Cliff Puzzle 17: Weird Recursive Sequence From: cliff@watson.ibm.com
• pickover/pickover.18Title: Cliff Puzzle 18: Difficult Nested Roots From: cliff@watson.ibm.com
• pickover/pickover.22Are there factorions (numbers equal to the sum of the factorials of their digits) larger than 40,585? New
• probability/acute.triangleWhat are the odds for a random triangle to have only acute angles? New
• probability/amoebaA jar begins with one amoeba.
• probability/aprioriAn urn contains one hundred white and black balls.
• probability/base.rateAn AIDS test shows the right result 99% of the time. New
• probability/bayesOne urn contains black marbles, and the other contains white or black marbles with even odds.
• probability/bus.packsI often shop downtown in the afternoon, leave at a random time, and take the bus home. New
• probability/cabA cab was involved in a hit and run accident at night. Added material
• probability/cancellationA semi popular system to beat the roulette table is called the cancellation system. New
• probability/chip.gameSue and Bob are playing a game in which Sue starts with A chips, Bob starts with B chips, and they play... New
• probability/chutes.and.laddersWhat is the expected number of moves it takes a single player to win Chutes and Ladders? New
• probability/consecutiveYou have a cube with two sides painted red.
• probability/coprimeWhat's the probability that two positive integers chosen at random will be coprime? New
• probability/couponThere is a free gift in my breakfast cereal. Added material
• probability/dartsPeter throws two darts at a dartboard, aiming for the center.
• probability/derangement12 men leave their hats with the hat check. Added material
• probability/dice.totalsLet f[n,s](x) be the probability of rolling the total x on n fair s-sided dice. New
• probability/die.shuffleYou have just won $6,000,000 at a casino. New, unsolved
• probability/disease.testA rare dread disease strikes one out of a million people at random. New
• probability/distinct.digitsWhat is the expected number of different digits in a random 9-digit string, such as a U.S. New
• probability/dna.matchThe probability that an innocent man would match the DNA found at a crime scene is about one in a million. New
• probability/fair.gameIn this coin game between A and B, who is favored? New
• probability/fair.russian.rouletteHow can you play Russian Roulette with each person having a 50/50 chance of losing?
• probability/familySuppose that it is equally likely for a pregnancy to deliver a baby boy as it is to deliver a baby girl.
• probability/fly.on.clockA fly lands on the face of a clock whose minute hand extends to the edge of the face and whose hour hand is... New
• probability/four.ballsYou have four balls in a bag. New
• probability/friday.13thWhat is the chance of a Friday being the 13th of the month? New
• probability/gerrymanderYou have two urns and 100 marbles, 50 white and 50 black.
• probability/gold.coins.drawersWe have three drawers with coins in them, and we know which drawers have which coins: New
• probability/headlightsAt dusk you want to turn on your headlights when half of the oncoming drivers have theirs on, judging only... New, unsolved
• probability/hit.targetCharlie hits the target 80 times in 100 shots. New
• probability/hospitalA town has two hospitals, one big and one small.
• probability/icosThe "house" rolls two 20-sided dice and the "player" rolls one 20-sided die.
• probability/intervalsGiven two random points x and y on the interval 0..1, what is the average size of the smallest of the three...
• probability/killers.and.pacifistsYou enter a town that has K killers and P pacifists.
• probability/knight.returnA knight starts on square A1 of a chessboard and makes random moves (each legal move equally likely) until it is again on A1. New
• probability/leading.digitWhat is the probability that the ratio of two random reals starts with a 1?
• probability/lightsWaldo and Basil are exactly m blocks west and n blocks north from Central Park, and always go with the...
• probability/lost.in.planeA starship lost 100 light-millennia from Sol knows only its distance from Sol, not the direction; jumping... New
• probability/lotteryThere are n tickets in the lottery, k winners and m allowing you to pick another ticket.
• probability/lottery.consecutiveIn a lottery drawing 6 numbers from 1 to 50, what is the probability that the drawing contains at least one... New
• probability/marble.gameYou start with a box holding one black and one white marble, and sample twice with replacement. New
• probability/marbles.ten.moreIn a vase are 10 more black marbles than white marbles. New, unsolved
• probability/martingaleIn roulette, if you begin by betting one dollar on red, then double your bet if you lose, and double again... Added material
• probability/menagesYou have a dinner-party, with a big, round table in the center of the room. New
• probability/nearest.neighborYou are one of many birds arranged at random along an infinitely long telephone wire. New
• probability/nesting.cupsA two year old has 8 plastic cups of different sizes that can be put inside each other. New
• probability/nine.black.marblesI have a bag that initially held 10 marbles. New
• probability/no.two.meetN people agree to meet between 2:00 and 3:00 P.M. New
• probability/normal.tailHow can one calculate the probability of large random deviates (Z scores), such as 15 sigma from the expected mean? New
• probability/oldest.girlYou meet a stranger on the street, and ask how many children he has. Added material
• probability/ones.in.windowIn a linear string of N elements, each element independently takes the value 1 with probability p and 0 with probability 1-p. New
• probability/particle.in.boxA particle is bouncing randomly in a two-dimensional box.
• probability/pebbles.in.pondYou throw N pebbles into a round pond, uniformly distributed. New
• probability/phone.numbersMy sister was assigned a new 7-digit phone number that differs from mine only in the first and last digits. New
• probability/piAre the digits of pi random (i.e., can you make money betting on them)?
• probability/pi.ninesWhat is the probability that the decimal expansion of pi contains a sequence of exactly one million nines... New
• probability/prefix.overlapConsider an alphabetized list of words which has been compressed by replacing the characters repeated... New
• probability/random.chordA long straw is tossed at random onto a circle; given that it falls so that it intersects the circle, what... New
• probability/random.polygon.centerPoints are chosen uniformly at random on a circle until their convex hull contains the center. New
• probability/random.walkWaldo has lost his car keys!
• probability/randomness.vs.chaosCan one tell true randomness apart from the output of a deterministic (chaotic) system? New
• probability/reactorThere is a reactor in which a reaction is to take place.
• probability/rouletteYou are in a game of Russian roulette, but this time the gun (a 6 shooter revolver) has three bullets... Added material
• probability/same.color.halfA bag holds white and black marbles, with 10 more white than black. New
• probability/set.card.guessDraw a Set card from the deck. New, unsolved
• probability/sex.ratioIs the sex of a baby a fair coin toss, independent from one birth to the next, or can some parents be more... New
• probability/shooting.roomYou are led into a room where everyone will be shot if two dice come up double sixes, but a sign says at... New
• probability/singular.binary.matrixWhat is the probability that a randomly written n x n binary matrix (all elements 1 or 0) is singular? New
• probability/sock.drawerFrom a pile of 25 different pairs of socks, how many socks must you pull out on average before you get a... New
• probability/t.distributionGiven a value t of Student's t statistic, is there an approximation or a fairly straightforward way to... New
• probability/taxisYou are looking for a taxi in a town where all taxis are individually numbered 1,2,3,... New
• probability/tennis.meetingN players are entered in a singles tennis tournament. New
• probability/tennis.serveYou hear on the radio that your favorite tennis player won her latest match 6-4 6-4 without ever having her serve broken. New
• probability/tetragonsPick 4 random points A, B, C, D in a plane (in a rectangle, say) and draw the tetragon A-B-C-D-A. New
• probability/three.antsThree ants are at different corners of a triangle.
• probability/three.boxesThree boxes each contain two coins: two gold (gg), two silver (ss), and one silver, one gold (sg). New
• probability/three.sided.coinIf you toss a coin, it rarely lands on its edge. New
• probability/transitivityCan you number dice so that on average die A beats die B beats die C beats A?
• probability/two.cuts.yield.triangleIf a line is cut in two independent random places, what are the odds that the pieces can form a triangle? Added material
• probability/two.wins.in.a.rowTo win a prize you must win two games of chess in a row out of three, alternating between a strong player... New
• probability/up.down.sequenceAssume all random numbers come from the uniform distribution on the unit interval. New
• probability/updating.meanHow can estimates of the mean and standard deviation of a series of observations be updated in a... New, unsolved
• probability/wine.labelsYou are given 9 unlabeled bottles of wine, all different, and the 9 labels that belong on them, but you don't know which is which. New
• probability/wrong.seat100 passengers board a plane with 100 seats; the first, a crazy old lady, takes a wrong seat, and each... New
• probability/birthday/lineAt a movie theater, the manager announces that they will give a free ticket to the first person in line...
• probability/birthday/same.dayHow many people must be at a party before you have even odds or better of two having the same bithday (not... Added material
• probability/birthday/ubuIn the town of Ubu (population 365), leap years, weekends, and all traditional holidays have been abolished by mayoral edict. New
• probability/card/counting.matchShuffle a deck of cards, then deal one card at a time, counting off "Ace, deuce, ... New
• probability/card/die.shuffleA dealer shuffles six cards, numbered 1 to 6 in order, by rolling a die six times: on the i-th roll, the... New
• probability/card/flushWhich set contains proportionately more flushes than the set of all possible poker hands?
• probability/card/glimpsed.aceA slightly less-than-honest bridge player (south) caught a glimpse of a card dealt to her opponent on the... New
• probability/card/guess.suitFrom a standard (52-card, well-shuffled) deck of cards, the player is dealt seven cards, face down. New
• probability/card/last.diamondCards are dealt to five players until the deck is exhausted.
• probability/card/more.acesGiven that a bridge hand contains an ace, or given that it contains the ace of spades, in which case are... Added material
• probability/card/poker.handsFrom a 52 card deck it is possible to deal 2,598,960 different five-card poker hands. New
• probability/card/red.aceA bridge player glimpses a red ace in West's hand; West then leads the ace of diamonds. New
• probability/card/shuffling.algorithmWhat is wrong with this card shuffling algorithm, and how can a bridge deal be stored in 12 bytes so that... New
• probability/card/two.of.each.suitIf a standard 52-card pack is dealt out at random to four players, what is the probability that each player... New
• probability/flips/arbitrary.probabilityUsing only the toss of a fair coin, devise an experiment whose probability of success is 1/3. New
• probability/flips/at.least.y.in.a.rowIf the probability of an individual event occurring (heads on a coin, 3 on a die, an error in a received... New
• probability/flips/gamblers.ruinTom has 2 quarters and Jerry 3; they flip fairly, loser paying winner a quarter, until one is broke. New
• probability/flips/once.in.runWhat are the odds that a run of one H or T (i.e., THT or HTH) will occur in n flips of a fair coin?
• probability/flips/optimal.unfair.coinWhich unfair coin best simulates a fair coin, when you know p? New
• probability/flips/reflected.sequenceTwo players alternately flip coins into a row; the first player wins as soon as the whole row is a reflected sequence (a palindrome). New
• probability/flips/twice.in.runWhat is the probability in n flips of a fair coin that there will be two heads in a row?
• probability/flips/unfairGenerate even odds from an unfair coin. Added material
• probability/flips/unfair.three.choicesFind 'p' for an unfair coin [Editor: "as above" in the original], so that the coin can be used to choose... New
• probability/flips/waiting.timeCompute the expected waiting time for a sequence of coin flips, or the probabilty that one sequence of coin... Added material
• real-life/balance.nailsYou are given a small block of wood with a nail hammered partially into it, and 6 more nails of the same size. New
• real-life/brightest.time"See my clock, Dad? New
• real-life/corkHow do you get a cork out of a wine bottle without a corkscrew? New
• real-life/five.times.a.yearI did something recently that I do *exactly* 5 times a year, every year. New
• real-life/ice.traysA friend of mine turns some of the ice trays in his freezer upside-down when he goes on vacation. New
• real-life/icecubesYou have an old-fashioned refrigerator with a small freezer compartment which could hold seven ice cube...
• real-life/lost.nutsWhile changing a flat tire, all five of the tire lugs roll into a storm drain, out of reach.
• real-life/microwaveEvery morning when I warm my milk for breakfast, I put one cup of milk in the microwave (which is in working order) for exactly 84 seconds.
• real-life/painted.linesWhy would white lines be painted on the streets at manholes, and why would it be done in November? New
• real-life/three.switchesA lightbulb is turned on by one of three switches, but you cannot see the bulb from the switches. Added material
• real-life/timing.traffic.lightHow long was the red light, if you had no clock with a second hand but could work it out later at home? New
• real-life/train.fireA train that can do only 50 mph is being overtaken by a fire moving at 70 mph along a straight track with... New, unsolved
• real-life/truck.under.bridgeA truck doesn't quite fit under a bridge and becomes stuck.
• real-life/tunnel.crashHere is a puzzle that may save your life someday. New
• references/faqWhere should I look if I can't find the answer here?
• references/flexagonsWhere can I find technical information on hexaflexagons and other flexagons? New
• references/magazinesWhat magazines and journals contain puzzles? Added material
• references/mailing.listsWhat e-mail mailing lists on recreational mathematics and puzzles are there? New
• references/mechanical.puzzlesWhere can I buy mechanical puzzles (burrs, wire puzzles, interlocking puzzles), and which ones are worth... New
• references/online.referencesWhat dictionaries, thesauri and other reference works can a puzzle solver search on line? New
• references/organizationsWhat organizations exist for puzzle lovers? Added material
• references/polyformsWhere can I find polyomino, polyhex, polyiamond and other polyform puzzles (arranging a fixed set of shapes... New
• references/productsWhere can I buy puzzles and puzzle games or software? New
• references/puzzle.classificationHow can puzzles and games be classified? New
• references/quotationsWhere can I find the source for a quotation?
• references/rec.puzzles.faqWhich puzzles are asked most often on rec.puzzles, and what should one do before posting a puzzle there? New
• references/web.sitesWhat World Wide Web sites have puzzles? New
• references/books/bloopersWhat are some errors made in puzzle books? Added material
• references/books/calculus.problem.solvingWhat are some good books on calculus and on mathematical problem solving? New
• references/books/chess.bibliographyIs there a bibliography of mathematical chess problems, retrograde analysis and other unusual chess puzzles? New
• references/books/continued.fractionsWhat are some good books on continued fractions? New
• references/books/crossword.historyWhat books tell the history of the crossword puzzle? New
• references/books/geometryWhat are some good books on geometry for the recreational reader? New
• references/books/logic.bibliographyWhat are some good books on logic and set theory? New
• references/books/markov.chainsWhat books and papers describe "real-world" applications of Markov chains? New
• references/books/math.booksWhat are some good introductory books on number theory, combinatorics and algebra? New
• references/books/number.theoryWhat are some good introductory books on number theory, combinatorics and algebra? New
• references/books/sparse.matricesWhat are good references for sparse-matrix methods? New
• references/books/waveletsWhat are good references for learning wavelet theory? New
• references/software/crossword.printingIs there a PostScript program that prints a crossword puzzle diagram, with automatic numbering, from a... New
• references/software/logic.gridWhat software is there for constructing or solving logic puzzles of the kind that come with a grid to aid... New
• references/software/scrabble.move.serverIs there a network server that plays Scrabble-like word games against programs, for word-game programmers... New
• references/software/word.search[ Editor: What software is there for making word search puzzles? New
• series/decimal.hex.reversalComplete the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 53, 371, ... New
• series/doubled.digitsWhat's the next number? New
• series/factorial.towersFind the next number in this series: New
• series/lcd.displayWhat is the next symbol in the following sequence? New
• series/lcd.patternsWhat pattern comes next in this sequence of four patterns? New
• series/led.segmentsWhat would the next symbol in this series look like? New
• series/letter.count.convergenceCan anyone spot the logic behind this sequence? New
• series/number.name.lengthsWhat number comes next? New
• series/paper.sizesFind the missing number: New
• series/polygonsWhat is next in this series? New
• series/primorial.fibonacciWhat are the next few terms, and why? New, unsolved
• series/race.distancesIdentify this very simple number series. New
• series/reduced.fractionsWhat is this sequence? New
• series/roman.numeral.lettersWhich of the words avail, oval, valid, mail continues the sequence dig, minim, militia, sieve, ave? New
• series/series.00How can I find the next number in this series? Added material
• series/series.01M, N, B, D, P ?
• series/series.02H, H, L, B, B, C, N, O, F ?
• series/series.03W, A, J, M, M, A, J?
• series/series.03aG, J, T, J, J, J, A, M, W, J, J, Z, M, F, J, ?
• series/series.03bA, J, B, C, G, T, C, V, J, T, D, F, K, B, H, ?
• series/series.03cM, A, M, D, E, L, R, H, ?
• series/series.04A, E, H, I, K, L, ?
• series/series.05A B C D E F G H?
• series/series.06Z, O, T, T, F, F, S, S, E, N?
• series/series.06aF, S, T, F, F, S, ?
• series/series.071, 1 1, 2 1, 1 2 1 1, ... Added material
• series/series.08aG, L, M, B, C, L, M, C, F, S, ?
• series/series.08bA, V, R, R, C, C, L, L, L, E, ?
• series/series.09aS, M, S, S, S, C, P, P, P, ?
• series/series.09bM, S, C, P, P, P, S, S, S, ?
• series/series.10D, P, N, G, C, M, M, S, ?
• series/series.11R O Y G B ?
• series/series.12A, T, G, C, L, ?
• series/series.13M, V, E, M, J, S, ?
• series/series.14A, B, D, O, P, ?
• series/series.14aA, B, D, E, G, O, P, ?
• series/series.15A, E, F, H, I, ?
• series/series.16A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, X, Y?
• series/series.17T, P, O, F, O, F, N, T, S, F, T, F, E, N, S, N?
• series/series.1810, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ___ , 100, 121, 10000
• series/series.190 01 01011 0101101011011 0101101011011010110101101101011011 etc.
• series/series.201 2 5 16 64 312 1812 12288
• series/series.215, 6, 5, 6, 5, 5, 7, 6, ?
• series/series.223 1 1 0 3 7 5 5 2 ?
• series/series.2322 22 30 13 13 16 16 28 28 11 ?
• series/series.24What is the next letter in the sequence: W, I, T, N, L, I, T?
• series/series.251 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ?
• series/series.261 3 2 6 7 5 4 12 13 15 14 10 11 9 8 24 25 27 26 ?
• series/series.270 1 1 2 1 2 1 3 2 2 1 3 1 2 2 4 1 3 1 3 2 2 1 4 2 ?
• series/series.280 2 3 4 5 5 7 6 6 7 11 7 13 9 8 8 17 8 19 9 10 13 23 9 10 ?
• series/series.291 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 4 3 4 ?
• series/series.30I I T Y W I M W Y B M A D
• series/series.316 2 5 5 4 5 6 3 7
• series/series.320 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1
• series/series.332 12 360 75600
• series/series.343 5 4 4 3 5 5 4 3
• series/series.351 2 3 2 1 2 3 4 2 1 2 3 4 2 2 3
• series/series.36ETIANMSURWDKGO
• series/series.3710^3 10^9 10^27 10^2 0 4 8 3
• series/series.38?, ?, ?, T, W, H, R, F, U, I, ?, ?, ...
• series/series.39M, E, P, B, P, ?
• series/seven.nine.eightFill in the blank: New
• series/subway.stopsWhat is the missing term and what does the series represent? New
• series/titan.sequencesDetermine X in each of the following sequences (two from the Titan test, which appeared in Omni magazine,... New
• series/united.states.letters1. What letter comes next in this sequence? New
• series/word.lengthsAnd what are the next two numbers in this sequence? New
• treasure/BealeWhat are the Beale ciphers? Added material
• treasure/alchemyWhat was the treasure hunt in _Alchemy_, the illustrated book by Graeme Whittle, and was it solved? New
• treasure/amaranthWhat is the solution to _The Amaranth_? New
• treasure/conundrumWhat is the solution to _Conundrum_ by Don Shaw? New
• treasure/egyptian.jukeboxHow do you solve the drawers in _The Egyptian Jukebox_ by Nick Bantock? New
• treasure/golden.keyWhat became of "The Golden Key", Don Shaw's 1982 treasure-hunt book? New
• treasure/helium.dreamWhat is the solution to _Helium Dream and the Lost Heart_ by Dan James? New
• treasure/henry.hookWhere was the phone number hidden in Henry Hook's trivia challenge book? New
• treasure/key.to.the.kingdomWhat is the solution to _The Key to the Kingdom_ by Tony Meeuwissen? New
• treasure/lost.railway.engineWere the answers to the armchair treasure hunt "Search for the Lost Railway Engine" by Steve and Pauline... New
• treasure/masqueradeWhat is the solution to _Masquerade_ by Kit Williams? Added material
• treasure/mazeWhat is the solution to _Maze_ by Christopher Manson? Added material
• treasure/rubyWhat was the hidden registration number of the car in the treasure-hunt book _Ruby_? New
• treasure/treasureWhat is the solution to _Treasure_ by Dr. Added material
• treasure/treasure.biblioList books on treasure hunting or that contain armchair treasure hunts. Added material
• treasure/treasure.questWhat was the answer to Treasure Quest, the 1996 computer game from Sirius Publishing that offered a $1... New
• treasure/unnamedWhat is the solution to the unnamed book by Kit Williams?
• trivia/area.codesWhen looking at a map of the distribution of telephone area codes for North America, it appears that they are randomly distributed. Added material
• trivia/basketball.jerseysWhy do you never see numbers with a digit greater than 5 on basketball players' jerseys? New
• trivia/blue.moonWhat is a "blue moon," and where does the phrase "once in a blue moon" come from? New
• trivia/coincidenceName some amazing coincidences. Added material
• trivia/college.teamsWhich college teams (basketball or football) have team names that do not end with an "s"? New
• trivia/disconnected.statesWhich U.S. states are completely disconnected, so that some part of the state cannot be reached without... New
• trivia/easter.dateHow is the date of Easter calculated, and might the method change after 2001? New
• trivia/eskimo.snowHow many words do the Eskimo have for snow? Added material
• trivia/extreme.states1. Which state (in the United States of America) is the Southern most state? New
• trivia/fact.or.fictionPopular trivia - fact or fiction? New
• trivia/federal.reserveWhat is the pattern to this list: Boston, MA New York, NY Philadelphia, PA Cleveland, OH Richmond, VA...
• trivia/first.baseCan you name the 8 different ways that a major league baseball player can find himself safe at first base... New
• trivia/groupsEach question lists some members of a group and some things that are NOT members of it. New
• trivia/jokes.collection[ Editor: A collection of jokes, humorous lists and parodies from a 1997 web page, "Joeks, Jokes, Jokes!"... New
• trivia/jokes.self-referentialWhat are some self-referential jokes? Added material
• trivia/leap.secondsHow many extra (leap) seconds have we found it needful to put in over the years? New
• trivia/left.handedWhat do the following people have in common? New
• trivia/memory.tricksWhat's 3 + 7? What's 4 + 6? Added material
• trivia/mileWhy does a mile have 5280 feet in it?
• trivia/misnomersHow many gallons does a ten-gallon hat hold? New
• trivia/most.common.city.nameWhat is the most common city name (in the United States)? New
• trivia/mr.nobodyWho is the funny little man, as quiet as a mouse, who does the mischief that is done in everybody's house? New
• trivia/name.stringsWho can come up with the best name string, a chain of names in which each person's surname is the next... New
• trivia/no.birthdayA certain person lived for many years to a ripe old age, but [ Editor: ". New
• trivia/nugry.treasuryWhat is in the Nugrys' Treasury of Puzzles, the rec.puzzles parody of its own most frequently asked questions? New
• trivia/one.border.countriesName a country that borders exactly one other country, disregarding water borders. New
• trivia/peace.signHow was the peace sign (an upside-down Y inside a circle) created, and by whom? New
• trivia/people.ever.livedHow many people have ever lived? New
• trivia/punctuated.place.namesName a place whose name cannot be written with letters and hyphens only. New
• trivia/quarterback.ratingCan anyone tell me what this formula represents? New
• trivia/rec.puzzles.humorWhat are some examples of the humour found in rec.puzzles threads? New
• trivia/roman.clockWhy do so many Roman-numeral clock faces use "IIII" for 4 rather than "IV"? New
• trivia/shaggy.dogWhat is a shaggy dog story, and what are some examples? New
• trivia/smileyWhat are some ways to make a smliey?
• trivia/stonehengeAre there any interesting mathematical things one can say about Stonehenge? New
• trivia/sun.riseDoes the sun always rise (on Earth) in the east?
• trivia/twenty.four.hoursWhy are there 24 hours in a day, and 60 minutes in an hour and 60 seconds in a minute? New
• trivia/vostok.call.signsThe following are the last five entries in a list relating to travel / exploration. New
• trivia/winners.backwardsWhat games or sporting events can you name where the winners are going backwards? New
• trivia/three.letters/animal.soundName ten common, non-slang three-letter words for animal sounds.
• trivia/three.letters/body.partsName ten common, non-slang three-letter words for body parts.
• trivia/three.letters/farm.animalsName ten common, non-slang three-letter words for farm animals.
• trivia/three.letters/liquid.containersName ten common, non-slang three-letter words for containers of liquid.
• trivia/three.letters/transportName ten common, non-slang three-letter words for vehicles. Added material
• trivia/three.letters/unit.of.measureName ten common, non-slang three-letter words for scientific units of measure.
• trivia/two.letters/prepositionName ten common, non-slang two-letter prepositions.
• trivia/two.letters/pronounName five common, non-slang two-letter pronouns.