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.
(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 20161128 08:05:55 