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190 couples (Posted on 2018-05-03) Difficulty: 3 of 5
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
SolutionA much stronger proof (spoiler)Steve Herman2018-05-06 18:19:44
Some ThoughtsThere must be at least 4 such numbers (spoiler)Steve Herman2018-05-03 20:58:03
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