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Powerful Couple (Posted on 2011-03-16) Difficulty: 3 of 5
(A) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten expansion of 2P is equal to P-1.

(B) For a base ten positive integer P drawn at random between 10 and 99 inclusively, determine the probability that the first two digits (reading left to right) in the base ten expansion of 6P is equal to P-1.

No Solution Yet Submitted by K Sengupta    
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re(2): exploration turned up something strange | Comment 4 of 6 |
(In reply to re: exploration turned up something strange by Charlie)

So much for a trusty calculator. 

It turns out I encountered a flaw in the way it finds the intersection of two functions.  The first-two-digits function has discontinuities similar to a greatest integer function.   P-1 passes through most of these gaps.  Whatever variation of Newtons method it uses, sometimes things just go wrong in these cases.  Instead of reporting no solution it reported a solution that isnt even very close.

Yesterday, I though I was going to get solutions like 2^13.55075 = 12000.026738460294.  I will leave it at this.  This could make a nice extension of the problem.
  Posted by Jer on 2011-03-17 13:58:24

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