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Geometric Generalization (Posted on 2013-02-28) Difficulty: 3 of 5
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    
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Solution 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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