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segment S of length 50 is covered by several segments of length 1

Source: 2015 Argentina OMA Finals L3 p4

January 16, 2023
combinatoricscombinatorial geometry

Problem Statement

An segment SS of length 5050 is covered by several segments of length 11 , all of them contained in SS. If any of these unit segments were removed, SS would no longer be completely covered. Find the maximum number of unit segments with this property.
Clarification: Assume that the segments include their endpoints.
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