MathDB

The vertices of a convex

1991

-gon are enumerated with integers from

1

1991

. Each side and diagonal of the

1991

-gon is colored either red or blue. Prove that, for an arbitrary renumeration of vertices, one can find integers

k

and

l

such that the segment connecting the vertices numbered

k

and

l

before the renumeration has the same color as the segment connecting the vertices numbered

k

and

l

after the renumeration.

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