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Three sets having the same color

Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P3

September 15, 2012

graph theorycombinatorics proposedcombinatorics

Problem Statement

Prove that if

n

is large enough, then for each coloring of the subsets of the set

\{1,2,...,n\}

with

1391

colors, two non-empty disjoint subsets

A

and

B

exist such that

A

B

and

A\cup B

are of the same color.