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190 couples (Posted on 2018-05-03)

The set S consists of 20 distinct positive integers, each below 70.

Create a set S' of 190 pairwise absolute values of differences between two distinct members of S.

Prove that in S' there must exist at least one value that appears more than 3 times.

Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Solution: (Hide)

see Steve Herman's proof by contradiction.

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

Subject	Author	Date
A much stronger proof (spoiler)	Steve Herman	2018-05-06 18:19:44
There must be at least 4 such numbers (spoiler)	Steve Herman	2018-05-03 20:58:03

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