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6

Part of 2003 Polish MO Finals

Problems(1)

There exists a permutation - Poland Third Round 2003

Source:

11/1/2010
Let nn be an even positive integer. Show that there exists a permutation (x1,x2,…,xn)(x_1, x_2, \ldots, x_n) of the set {1,2,…,n}\{1, 2, \ldots, n\}, such that for each i∈{1,2,…,n},xi+1i \in \{1, 2, \ldots, n\}, x_{i+1} is one of the numbers 2xi,2xi−1,2xi−n,2xi−n−12x_i, 2x_{i}-1, 2x_i - n, 2x_i - n - 1, where xn+1=x1.x_{n+1} = x_1.
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