Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 641. (April 2015)

A. 641. Determine whether there is a finite, nonempty subset $\displaystyle S$ of the square grid in the plane such that every element of $\displaystyle S$ has at least two neighbours in $\displaystyle S$ and $\displaystyle S$ 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)

Deadline expired on May 11, 2015.

### Statistics:

 1 student sent a solution. 5 points: Fehér Zsombor.

Problems in Mathematics of KöMaL, April 2015