100 unit squares of an infinite squared plane form a 10×10 square. Unit segments forming these squares are coloured in several colours. It is known that the border of every square with sides on grid lines contains segments of at most two colours. (Such square is not necessarily contained in the original 10×10 square.) What maximum number of colours may appear in this colouring?
Author: S. Berlov analytic geometrycombinatorics unsolvedcombinatorics