Digits

Subcategories

• Equations13 +8
• Least significant5 +3
• Most significant2
• Prime5 +1
• Squares6 +2
• Zeros4 +2

Puzzles

• 6.and.7Does every number which is not divisible by 5 have a multiple whose only digits are 6 and 7?
• abcabcThink of a three-digit number, then form a six-digit number by repeating its three digits (469 becomes 469,469). New
• all.onesProve that some multiple of any integer ending in 3 contains all 1s.
• anomalous.cancellationAmong all 3-digit numbers in which no digit appears more than once, there is one special trait shared by... New
• arabianWhat is the Arabian Nights factorial, the number x such that x!
• armstrong.numbersAre there infinitely many N-digit numbers equal to the sum of the N-th powers of their digits (Armstrong... New
• circularWhat 6 digit number, with 6 different digits, when multiplied by all integers up to 6, circulates its...
• cryptarithmHow do I solve letter substitutions (cryptarithms) like SEND + MORE = MONEY? Added material
• digital.productFor each integer n, write out n in base 10 and let g(n) be the product of the nonzero digits appearing. New
• divisibleFind the least number using 0-9 exactly once that is evenly divisible by each of these digits.
• extreme.productsWhat are the extremal products of three three-digit numbers using digits 1-9?
• hex.multiplesA number has four digits in hexadecimal. New
• kaprekar.6174Take any four-digit number (excluding 1111, 2222, 3333, etc.), sort its digits into descending order, make... New
• labelsYou have an arbitrary number of model kits (which you assemble for fun and profit).
• largest.productUsing all the 9 digits from 1 to 9 and only once, what two numbers multiplied give the largest product? New
• 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
• little.pigleySolve the Little Pigley Farm crossnumber and find the age of Mrs. New, unsolved
• near.integerProve that the decimal expansion of (sqrt(35) + 6)^1995 starts with at least 1000 nines after the decimal... New
• nine.digitsForm a number using 0-9 once with its first n digits divisible by n.
• 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
• palindromeDoes the series formed by adding a number to its reversal always end in a palindrome? Added material
• palindrome.differencesWhich integers n can be written as the difference of two palindromes? New
• palindromic.powersWhat are the largest known palindromic squares with a non-palindromic base, palindromic cubes with a... New
• palintiplesFind all numbers that are multiples of their reversals.
• pandigital.prime.factorsThe smallest number whose prime factors, written side by side, use each of the digits 1 through 9 exactly... New, unsolved
• period.of.reciprocalWhat is the length of the repeating period of 1/d written in base r? New
• persistenceThe persistence P(x) of an integer x is the number of times its digits can be multiplied, recursively. New
• power.twoProve that for any 9-digit number (base 10) there is an integral power of 2 whose first 9 digits are that...
• reverseIs there an integer that has its digits reversed after dividing it by 2?
• rotateFind integers where multiplying them by single digits rotates their digits one position, so that the last...
• rotate.temperatureWhen Waldo recently did a conversion of a positive integral Celsius temperature c=275 to its Fahrenheit... New
• sesquiFind the least number where moving the first digit to the end multiplies by 1.5.
• seven.sevensFind the missing digits in this long division problem, where the division has no remainder, and other 7's... New, unsolved
• sevens.long.divisionReconstruct this long division, where most of the digits are represented with asterisks and a few sevens... New, unsolved
• strobogrammaticWhat numerical identities and facts remain true when the page is rotated 180 degrees ("strobogrammatic")? New
• sum.of.digitsFind sod ( sod ( sod (4444 ^ 4444 ) ) ).
• 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
• zeros.and.onesDoes every positive integer have a multiple whose decimal representation consists only of 0's and 1's? New