Monthly Archives: September 2014

My collection of #Mensa puzzles

  (1) If James purchased:   sweater,   encyclopedia,   mug,   aftershave,   and a jacket. Who purchased:   notebook,   anorak,   socks,   underwear,   and sandles? (2) What number should replace the question mark? (3) The … Continue reading

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Puzzle | Palindromes with exactly 6 distinct prime factors

  The first few palindromes with exactly 6 distinct prime factors: 222222, 282282, 474474, 555555, 606606, 646646, 969969, 2040402, 2065602, 2206022, 2417142, 2646462, 2673762, 2875782, 3262623, 3309033, 4179714, 4192914, 4356534, 4585854, 4912194, 5021205, 5169615, 5174715, 5578755, …   I call … Continue reading

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Puzzle | Palindromes with exactly 5 distinct prime factors

  The first few palindromes with exactly 5 distinct prime factors: 6006, 8778, 20202, 28182, 41514, 43134, 50505, 68586, 87978, 111111, 141141, 168861, 202202, 204402, 209902, 246642, 249942, 262262, 266662, 303303, 323323, 393393, 399993, 438834, 454454, 505505, 507705, 515515, 516615, … Continue reading

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Equation| (a^3 – b^3)(c^3 – d^3) = (x^3 + y^3)^3

      Find more solutions.   David found :                                    

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Puzzle| Palindromes with exactly 4 distinct prime factors

  The first few palindromes with exactly 4 distinct prime factors: 858, 2002, 2442, 3003, 4774, 5005, 5115, 6666, 10101, 15351, 17871, 22422, 22722, 24242, 26562, 26962, 28482, 35853, 36363, 41314, 43734, 43834, 45654, 47874, 49494, 49794, 49894, 51015, 51315, … Continue reading

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Num3er 32123 (sphenic palindrome)

    32123   is a 5-digit sphenic palindrome A sphenic number is a positive integer that is the product of three distinct prime numbers. Here’s the list of all sphenic palindromes below 4000 : 66,   222,   282, … Continue reading

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Num3er 105700299921216001

    105700299921216001   is a prime number.   105700299921216001   has the representation :   Confirm that this number is the smallest value that is palindromic in over 1000 bases.                   … Continue reading

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Num3er 112

    112   has 10┬ádivisors:   1   2   4   7   8   14   16   28   56   112 Sum of divisors:     248   112   divides   Palindromic in : 112 … Continue reading

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Powers consisting of n distinct digits, averaging n

    Could we have more than 6 distinct digits?                                  

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Triangular numbers, product of three triangular in 2 or more ways

  My older posts : 3-/4-/5-digit triangular numbers, product of three triangular 6-digit triangular numbers, product of three triangular 7-digit triangular numbers, product of three triangular 8-digit triangular numbers, product of three triangular 9-digit triangular numbers, product of three triangular … Continue reading

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