SOLUTIONS - Springer
(Canadian Mathematical Olympiad, 2002) 9.AssumethatA, B, andasatisfyA∪B =[0,1], A∩B =∅, B =A+a. Wecanassume that a is positive; otherwise, we can exchange A and B. Then (1 −a,1]⊂B; hence (1 −2a,1 −a]⊂A. An inductive argument shows that for any positive integer n, the interval (1−(2n+1)a,1−2na]is in B, while the interval (1 ...
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