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26 out of 50 (Posted on 2016-11-25) Difficulty: 3 of 5
Prove the following statement:

In any set of 26 integers chosen from the set of (1,2,3, ...50) there must be at least a pair of numbers such that one of them divides the other.

Generalize.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Inelegant proof? | Comment 6 of 10 |
(In reply to Inelegant proof? by Steve Herman)

I'm a bit confused by the wording "so 25 numbers are necessarily unused".


I can see the point of the proof, though, but I would have worded it:

"... so 10 numbers are not in this representation. Therefore, when you choose 26 numbers, 16 must come from the shown set. Since there are only 15 subsets, at least two must come from the same subset, and therefore one must divide the other."

  Posted by Charlie on 2016-11-28 08:05:55
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