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KöMaL 2009 B4172

    Let nn be a positive integer and let k1,k2,k3,…,knk_1, k_2, k_3,\ldots,k_n denote an arbitrary order of the integers 1 to nn. What is the largest possible value of the expression (1-k1k_1)2^2+(2-k2k_2)2^2+(3-k3k_3)2^2+...+(nn-knk_n)2^2 of nn terms?

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