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2014 balls arranged around a circle.

Source: Turkey Junior MO 2014 Problem 3

November 16, 2014
pigeonhole principlecombinatoricsTurkey

Problem Statement

There are 20142014 balls with 106106 different colors, 1919 of each color. Determine the least possible value of nn so that no matter how these balls are arranged around a circle, one can choose nn consecutive balls so that amongst them, there are 5353 balls with different colors.
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