perplexus.info :: Numbers : True for nine and up

True for nine and up (Posted on 2017-03-24)

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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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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