35th Polish Mathematical Olympiad Problems 1984

35th Polish Mathematical Olympiad Problems 1984A1.  X is a set with n > 2 elements. Is there a function f : X → X such that the composition f n-1 is constant, but f n-2 is not constant? A2.  Given n we define ai,j as follows. For i, j = 1, 2, ... , n, ai,j = 1 for j = i, and 0 for j ≠ i. For i = 1, 2, ... , n, j = n+1, ... , 2n, ai,j = -1/n. Show that for

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