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Closed interval

Source: Canadian Mathematical Olympiad - 1997 - Problem 2.

May 7, 2011
combinatorics unsolvedcombinatorics

Problem Statement

The closed interval A=[0,50]A = [0, 50] is the union of a finite number of closed intervals, each of length 11. Prove that some of the intervals can be removed so that those remaining are mutually disjoint and have total length greater than 2525. Note: For reals a≤ba\le b, the closed interval [a,b]:={x∈R:a≤x≤b}[a, b] := \{x\in \mathbb{R}:a\le x\le b\} has length b−ab-a; disjoint intervals have empty intersection.
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