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Length of polygonal chain in square

Source: Czech and Slovak Olympiad 1973, National Round, Problem 6

July 16, 2024
geometrycombinatorial geometry

Problem Statement

Consider a square of side of length 50. A polygonal chain LL is given in the square such that for every point PP of the square there is a point QQ of the chain with the property PQ≤1.PQ\le 1. Show that the length of LL is greater than 1248.
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