IBM Research | Ponder This | November 2008 solutions
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November 2008

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Instead of computing the thousands of digits of ponderthis, we can use the following inequality to quickly verify that the first six digits are, indeed, “ponder” (frac stands for the fractional part):

frac(Log10(ponder)) ≤ frac(this*Log10 (ponder)) < frac(Log10 (ponder+1))

Out of the all permutations, only three match the condition:
ponder=504271 this=6983
ponder=813760 this=2459
ponder=835402 this=7619

Here comes the interesting part – although the expression gives three different results, in all three cases, the first four digits, translated back to letters, are “oded”.

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