IMO 1989 LL THA97

Origin: THA

Problem

Let n be a positive integer, X = {1, 2, . . ., n}, and k a positive integer such that n/2 \leqk \leqn. Determine, with proof, the number of all functions f : X \toX that satisfy the following conditions: (i) f 2 = f; (ii) the number of elements in the image of f is k; (iii) for each y in the image of f, the number of all points x in X such that f(x)=y is at most 2.