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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)

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Solution The solution is in the problem. | Comment 1 of 10

Why 26 integers?

Assume there were 25 integers; then those from 26-50 could be chosen, none of which divides another. As to the 26th number, any integer chosen from 1-25, must have its multiple by two in those from 26-50.

Edited on November 25, 2016, 9:35 pm
  Posted by broll on 2016-11-25 13:26:35

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