Logic

Subcategories

• Invariants3 +2
• Smullyan16 +13
• Weighing15 +9

Puzzles

• 29Three people check into a hotel. Added material
• ages1) Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim.
• aha.puzzlesWhat are some "aha!"-type puzzles, puzzles whose simple solutions are not obvious? New
• answered.not.solvedWhat puzzles can be *answered* without being completely *solved*, e.g. New
• attributeAll the items in the first list share a particular attribute.
• axiom.of.choiceExactly which parts of mathematics would have to be discarded if we threw out the axiom of choice? New
• axiom.of.determinacyIf an arithmetical statement is proved using the Axiom of Determinacy (AD), what must one believe about AD... New
• boodle.phil.moivenGiven these five statements in an unknown language, whom does Phil "moiven"? New, unsolved
• bookwormA bookworm eats from the first page of an encyclopedia to the last page.
• boxesTwo boxes are labeled "A" and "B".
• brain.teasersWhat is the one word in the English language that is always pronounced incorrectly, and other brain teasers? New, unsolved
• calibans.willWhen Caliban's will was opened it was found to contain the following clause: "I leave ten of my books to...
• camelAn Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune.
• centrifugeYou are a biochemist, working with a 12-slot centrifuge.
• 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
• childrenA man walks into a bar, orders a drink, and starts chatting with the bartender.
• condomsWhat is the minimum number of condoms required for safe sex in each case: (a) two men with two women (b)...
• cow.on.islandA boy and his cow arrived at a round lake. New, unsolved
• crossing.wiresCross the wires without crossing the wires: fill the black box with some quantity of NAND gates. New
• crossover[ Editor: What is the minimum number of two-input NAND gates needed to build a crossover circuit, which... New
• dellHow can I solve logic puzzles (e.g., as published by Dell) automatically?
• eat.or.sleepAfter three days without food you die on the spot, and after three days without sleep you die on the spot. New
• elimination97 baseball teams participate in an annual state tournament.
• 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
• finite.axiomatizabilityWhat is the finite axiomatizability theorem of Kleene, Craig and Vaught called, and where was it published? New
• five.coinsYou have three large and two small coins, placed in a row as OxOxO (O large, x small). New
• flipHow can a toss be called over the phone (without requiring trust)? Added material
• flowersHow many flowers do I have if all of them are roses except two, all of them are tulips except two, and all...
• 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
• friendsAny group of 6 or more contains either 3 mutual friends or 3 mutual strangers.
• fusesYou have two one-hour fuses, but the fuses do not burn uniformly.
• gas.stationsGas stations on a circular road hold, in total, just enough gas for one lap. New
• giant.frogA giant frog leaps 5 times as far as a normal frog does. New, unsolved
• goodsteinDo Goodstein sequences grow faster than Ackermann's function? New
• guess.number.one.lieI'm thinking of a number between 1 and 2000. New
• guess.the.numberA teacher thinks of a number between 1 and 15 and three students guess, each time being told "high" or... New
• hats.and.coatsA man has three hats, one red, one white, and one black. New
• heads.pilesTold only how many coins in a stack show heads, how can a man, without looking, split the stack into two... New
• hempel.ravensIf seeing a black raven confirms "all ravens are black", then seeing a white shoe confirms "all non-black... New
• hofstadterIn first-order logic, find a predicate P(x) which means "x is a power of 10."
• hundredThere is a piece of paper with 100 sentences written on: " 1. Added material
• inverterCan a digital logic circuit with two inverters invert N independent inputs?
• josephineThe recent expedition to the lost city of Atlantis discovered scrolls attributted to the great poet, scholar, philosopher Josephine.
• kinshipBrothers and sisters have I none, but that man's father is my father's son. Added material
• lateralWhat are some classic lateral thinking puzzles, and where can I find more?
• latinoSolve this Latino puzzle: fill a 6x6 grid with the numbers 1 to 6 so that each row and column contains one... New
• laura.ageToday is January 1. New
• leadoff.batterThe leadoff batter of a baseball team came up to bat in all nine innings. New
• leadoff.hitterIf the leadoff hitter in the lineup of the visiting team comes up to bat in every inning of a nine-inning... New
• liars.surveyThere are 123 tenants living in an apartment building. New
• locks.and.boxesYou want to send a valuable object to a friend.
• 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
• lunch.specialsThe following conversation between Bob and Jack in a Chinese restaurant was overheard: New
• meeting.trainsGranny Smith, who was leaving London, boarded a train at four minutes past the hour. New
• mermaidsFrom these nine statements, what, if anything, can we conclude about the connection between seeing a... New
• min.maxIn a rectangular array of people, which will be taller, the tallest of the shortest people in each column,...
• mirror.and.tableYou are in a room. New
• mixingStart with a half cup of tea and a half cup of coffee.
• monty.52Monty and Waldo play a game with N closed boxes.
• mu.puzzleCan you turn MI into MU using the following rules? New
• murder.houseSix people were in a house when a murder was committed in the second bedroom; from their statements, two of... New
• natural.independenceWhich "natural" mathematical statements are known to be independent of the axioms of arithmetic, in the sense of Goedel's theorem? New
• net.book.riddlesSolve the riddles of the net.book.riddles, a 1992-93 collection compiled by Mark Manning from e-mail and... New
• numberMr. S. and Mr. P. Added material
• oil.jarsA merchant was going to market carrying in his cart twelve big clay jars filled with vegetable oil. New
• peano.arithmeticIf Peano Arithmetic cannot prove some true statements about the numbers, is that a defect of PA, and why do... New
• petals.around.the.roseIn the dice game "Petals Around the Rose", what rule gives the answer for each roll of six dice? New
• 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
• pleasant.journeyMy pleasant journey commences when I briefly meet a familiar character marking a pitch in front of a wooden strip. New
• priest.and.ladiesIn the village church, said the priest to the parish clerk: - It is funny to see that those three ladies... New
• pyjamasIf I wear my nightcap, I do not wear the slippers. New
• riddleWho makes it, has no need of it. Added material
• ropesTwo fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart.
• same.streetSally and Sue have a strong desire to date Sam.
• 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
• 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
• self.ref.aptitude.testCan you find the unique solution to Jim Propp's twenty-question Self-Referential Aptitude Test? New
• self.ref.quizCan you score 100% on this ten-question Self-Referential Quiz, and can you prove in a few words why there... New
• self.ref.smallTo each of the following questions, exactly one of the alternatives is true. New, unsolved
• self.ref.testThere is exactly one solution to the following [ Editor: self-referential multiple-choice ] test. New
• self.reproducing.programProve that a program that prints its own source can be written in any programming language whose output... New
• set.theoryWhat are the primitive notions of the standard axiomatizations of set theory (ZF, Goedel-Bernays, Quine's... New
• sheep.on.passThree sheep facing right and three facing left meet on a narrow mountain pass with one empty space between... New
• simple.puzzlesWhat bird comes from an egg, but doesn't lay eggs? New
• situation.puzzles"A man lies dead in a room with fifty-three bicycles in front of him. Added material
• 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
• suitors.hatsA king must choose among four suitors for his daughter's hand, and he wants the most astute of them. New
• supertasksYou have an empty urn, and an infinite number of labeled balls. Added material
• three.casksYou have three casks holding 19, 13 and 7 units. New
• timezoneTwo people are talking long distance on the phone; one is in an East- Coast state of the US, the other is...
• 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
• transoceanic.cableYou laid a transoceanic cable. New
• trick.questionsWhat are some trick questions that seem to pose a hard or impossible question but have a simple answer... New
• tricky.questionsHow many birthdays does the average man have? New
• tulip.bulbsHow can you plant three unidentifiable tulip bulbs (blue, white, red) so that the flowers are sure to show... New
• twelve.and.fifteenOne day in 1980, Jim said, "The day before yesterday I was twelve. New
• twin.birthdaysKerry celebrated her birthday. New
• two.armiesTwo parties who can communicate only by unreliable messages must agree that a transaction (such as an... New
• 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
• two.eggsYou live in a 36-story apartment building, and have access to a window on each floor. New
• two.generalsTwo generals must attack together, but can communicate only by messengers who may be lost; how can they... New
• unexpectedSwedish civil defense authorities announced that a civil defense drill would be held one day the following...
• vergerA very bright and sunny Day The Priest did to the Verger say: "Last Monday met I strangers three None of...
• verse.riddlesSolve these riddles, arranged from simple to difficult. New
• wire.labelsYou are in room A, where you can see the ends of 15 wires, which are labelled 1,2,..
• wrong.labelsThree candle boxes are labeled "white", "red", and "white and red." All three labels are incorrect. Added material
• zebraThere are five houses, each of a different color and inhabited by men of different nationalities, with... New
• zooI took some nephews and nieces to the Zoo, and we halted at a cage marked