perplexus.info :: Probability : Cherry picking

Cherry picking (Posted on 2006-06-17)

Out of a quite large set of random integer numbers, I selected only those that were multiples of M or N, and rejected the rest. In the resulting (obviously smaller) subset, 50% of the numbers were multiples of N. Curiously, M wasn't 50% of N.

What is the minimum possible pair of values for M and N? The next such pair? Are there infinite possible such pairs?

PS. If you don't know the reason for the "Cherry picking" title, check this reference or this other one.

PPS. And if "a quite large set" of numbers doesn't satisfy you, imagine an infinite set, with every possible integer.

Submitted by Federico Kereki

Rating: 4.7500 (4 votes)

Solution: (Hide)

M=2 and N=3.
The next possibility would be M=2 and N=4, but that wouldn´t fit: M is 50% of N. The following that does fit is M=3 and N=4, and, in general, N=M+1.
To see where I got the idea from, check this article by James Randi.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2008-02-06 05:36:29
Answer	e.g.	2006-06-17 22:09:05
More values and a proof	Steve Herman	2006-06-17 14:46:40
Solution	Tristan	2006-06-17 10:51:16

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