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Choose number such that...

Source: INMO 1998 Problem 6

October 7, 2005
number theory unsolvednumber theory

Problem Statement

It is desired to choose nn integers from the collection of 2n2n integers, namely, 0,0,1,1,2,2,…,n−1,n−10,0,1,1,2,2,\ldots,n-1,n-1 such that the average of these nn chosen integers is itself an integer and as minimum as possible. Show that this can be done for each positive integer nn and find this minimum value for each nn.
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