Monthly Archives: October 2012

Happy Halloween! Time for Vampire Num3ers (including a puzzle)

Definition: http://mathworld.wolfram.com/VampireNumber.html A number   v = x * y   with an even number of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order)   x   … Continue reading

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Num3er 36

The factors of   36   are:     1   2   3   4   6   9   12   18   36 The prime factors are:     2 * 2 * 3 * 3     36 … Continue reading

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Num3er 159

The factors of   159   are:        1   3   53   159 The prime factors are:     3 * 53   Using each of 9 digits 1-9 once: 159   *   48   =   7632 … Continue reading

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Num3er 100001

Goal:   To find positive integers   a, b, c, d, e   so that 1^2   +   a^2   +   b^2   =   c^2   +   d^2   +   e^2,   and 1   … Continue reading

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In how many ways x + y + z = 1000

In how many ways can you make sums of three distinct positive integers total (a)   24 (b)   25 (c)   1000 For example, 1 + 2 + 21 = 24,    1 + 2 + 997 = 1000, … Continue reading

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Patterns: Num3ers of the form 1001, 110011, …

My focus:   To examine numbers of the form,   1001, 110011, 11100111, 1111001111, … and to replace the middle two digits (00) with the prime numbers 11 and 13 For example: (1)   1001   =   7 * … Continue reading

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Num3er 10001

Goal:   To find positive integers   a, b, c, d, e   so that 1^2   +   a^2   +   b^2   =   c^2   +   d^2   +   e^2,   (sum of three … Continue reading

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Num3er 1001

Goal:   To find positive integers   a, b, c, d, e   so that 1^2   +   a^2   +   b^2   =   1001   =   c^2   +   d^2   +   e^2, … Continue reading

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Pairs (a,b); a^2 + a*b + b^2 = c^2

If   (a, b)   are two positive integers, we know that,   a^2 + 2 ab + b^2   is a perfect square. [ a^2 + 2 ab + b^2   =   (a + b)^2 ] Goal: To … Continue reading

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Palindromic prime 313

313   is a palindromic prime (Palprime). Palindromic primes: prime numbers whose decimal expansion is a palindrome: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, … Continue reading

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