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Problem 1509

National Olympiad, first round

Combinatorics Difficulty 6.0 Find the answer KöMaL problem A · Hungary · 2015

Determine whether there is a finite, nonempty subset $S$ of the square grid in the plane such that every element of $S$ has at least two neighbours in $S$ and $S$ does not contain four points that are the vertices of a square (with sides not necessary parallel to the coordinate axes)?
Proposed by: Mátyás Sustik, San Francisco
(5 pont)

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