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 Geometric Generalization (Posted on 2013-02-28)
Three positive integers are chosen at random without replacement from 1,2,....,64. What is the probability that the numbers chosen are in geometric sequence?

Order of choice doesn't matter. For example, 4-1-2 would qualify as numbers in geometric sequence.

Bonus Question:
Generalise this result (in terms of n) covering the situation where three positive integers are chosen at random without replacement from 1,2,.....,n2.

 No Solution Yet Submitted by K Sengupta No Rating

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 answer spoiler | Comment 1 of 6
p=54/41664=0.001296   ....edited

i have counted 54  possible triplets from  (1 2 4 ) to  (49 56 64 )

REMARK:

COMPARING MY MANUALLY PRODUCED LIST WItH
THAT OF CHARLIE'S - I fouund that I missed four triplets
, so the  correct answer is
58/41664 =   approx.  0.001392

Edited on February 28, 2013, 3:36 pm
 Posted by Ady TZIDON on 2013-02-28 10:51:53

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