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2

Part of 1997 Canada National Olympiad

Problems(1)

Closed interval

Source: Canadian Mathematical Olympiad - 1997 - Problem 2.

5/7/2011
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.
combinatorics unsolvedcombinatorics