IMO Shortlist 1989 problem 23


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2. travnja 2012.
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A permutation \{x_1, \ldots, x_{2n}\} of the set \{1,2, \ldots, 2n\} where n is a positive integer, is said to have property T if |x_i - x_{i + 1}| = n for at least one i in \{1,2, \ldots, 2n - 1\}. Show that, for each n, there are more permutations with property T than without.
Izvor: Međunarodna matematička olimpijada, shortlist 1989