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total length of sum of segments < 0.5 - VI Soros Olympiad 1999-00 Round 1 9.4

Source:

May 21, 2024
combinatoricscombinatorial geometry

Problem Statement

A single segment contains several non-intersecting red segments, the total length of which is greater than 0.50.5. Are there necessarily two red dots at the distance: a) 1/991/99 b) 1/1001/100 ?