Puzzle by IBM: PONDER!

Puzzle taken from IBM.

Source: #-Link-Snipped-#


ponder[sup]this[/sup] = ponder...

​ I.e., the result of raising the 6-digits number "ponder" to the power of the 4-digit number "this" starts with the six most significant digits of "ponder", then what is the value (translated back to letters) of the first four digits of the following expression?

|.dr-.psi+.norton| |.ret-.en+.pier| ​ ----------------- + ---------------- ​ .poor*.heron . distorted*.terrier ​ Note the decimal points: .dr = 0.dr = (10*d+r)/100; and the absolute value signs (|).

Note that "ponder" and "this" should be six and four digits numbers respectively; i.e. "p" and "t" should not be zero.

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  • shalini_goel14
    shalini_goel14

    @shalini-goel14-ASmC2J • Dec 23, 2008

    This one is too difficult for me. I do not have enough time to try so many permutations and combinations . I give up for it 😔.

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  • Kaustubh Katdare
    Kaustubh Katdare

    @thebigk • Dec 30, 2008

    Here we go -

    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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