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Consecutive 3 Numbers on a Circle

Source: OME 2014 1

July 16, 2014
inductionsymmetrygraph theorycombinatorics unsolvedcombinatorics

Problem Statement

Is it possible to place the numbers 0,1,2,…,90,1,2,\dots,9 on a circle so that the sum of any three consecutive numbers is a) 13, b) 14, c) 15?
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