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length of selfintersecting curve C is an integer

Source: Austrian Polish 1987 APMC

April 30, 2020
circlearcscurveinteger sidelengthsgeometrycombinatorial geometry

Problem Statement

A circle of perimeter 11 has been dissected into four equal arcs B1,B2,B3,B4B_1, B_2, B_3, B_4. A closed smooth non-selfintersecting curve CC has been composed of translates of these arcs (each BjB_j possibly occurring several times). Prove that the length of CC is an integer.
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