21 Dec 2008

Puzzle by IBM: PONDER!

Puzzle taken from IBM.

Source: IBM Research | Ponder This | November 2008 challenges


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.
shalini_goel14

shalini_goel14

Branch Unspecified
23 Dec 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 😔.
30 Dec 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”.

Source: IBM Research | Ponder This | November 2008 solutions

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