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100 squares of an infinite squared plane form a 10x10 square

Source: Tuymaada 2008, Junior League, First Day, Problem 3.

July 20, 2008
analytic geometrycombinatorics unsolvedcombinatorics

Problem Statement

100 unit squares of an infinite squared plane form a 10×10 10\times 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 10\times 10 square.) What maximum number of colours may appear in this colouring? Author: S. Berlov
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