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True for nine and up (Posted on 2017-03-24) Difficulty: 3 of 5
If a set N9 = {1, 2, 3, 4, 5, 6, 7, 8, 9} of 9 numbers is split into two subsets, then at least one of them contains three terms in arithmetic progression.
The statement is not true for a set N8 of 8 integers.

Seems obvious?

Prove it.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re: By hand Comment 3 of 3 |
(In reply to By hand by Jer)

Good reasoning.

..there are four possibilities where this subset has no APs.  In each case the other subset has an AP in its 4 numbers instead...

Absolutely correct, however the last digit in the 4th line should be 7, not 9.

  Posted by Ady TZIDON on 2017-03-25 05:55:41
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