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