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Must differ by 3 (Posted on 2015-10-23) Difficulty: 2 of 5
Let S consist of 16 elements of the set (1,2,3, ... , 106) so that no two elements of S differ by 6; 9; 12; 15; 18; or 21.

Prove that at least two of the elements of S must differ by 3.

No Solution Yet Submitted by Ady TZIDON    
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re: analytic solution Comment 3 of 3 |
(In reply to analytic solution by Paul)

Very nicely done, Paul.  In fact, you have proved a stronger statement, namely that this is true if 16 elements were picked from (1,2,3,...,120).  I wonder why the puzzle author used a smaller set. 
  Posted by Steve Herman on 2015-10-27 11:26:45

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