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2022 Polish Junior Math Olympiad Second Round P3

Source: 2022 Polish Junior Math Olympiad Second Round

May 21, 2023

combinatorics

Problem Statement

Let

n

be a positive integer. Each of the numbers

1,2,3,\ldots,100

is painted with one of

n

colors in such a way that two distinct numbers with a sum divisible by

4

are painted with different colors. Determine the smallest value of

n

for which such a situation is possible.