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Arrangement of ones and zeroes

Source: Moscow Olympiad 2018, Grade 10, P4

July 13, 2018

combinatorics

Problem Statement

We call the arrangement of

n

ones and

m

zeros around the circle as good, if we can swap neighboring zero and one in such a way that we get an arrangement, that differs from the original by rotation. For what natural

m

and

n

does a good arrangement exist?

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