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We consider a prism which has the upper and inferior basis the pentagons:

A_{1}A_{2}A_{3}A_{4}A_{5}

and

B_{1}B_{2}B_{3}B_{4}B_{5}

. Each of the sides of the two pentagons and the segments

A_{i}B_{j}

with

i,j=1,\ldots,5

is colored in red or blue. In every triangle which has all sides colored there exists one red side and one blue side. Prove that all the 10 sides of the two basis are colored in the same color.

4

Problems(1)