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union of finitely many disjoint subintervals of [0,1], total length <= 1/2

Source: 1995 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p2

January 27, 2020
intervalcombinatoricsunion

Problem Statement

Let SS be a union of finitely many disjoint subintervals of [0,1][0,1] such that no two points in SS have distance 1/101/10. Show that the total length of the intervals comprising SS is at most 1/21/2.
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