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410

Part of 1985 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 410 All Soviet Union MO 1985 sum of |a_i - b_i| = n^2

Source:

8/5/2019
Numbers 1,2,3,...,2n1,2,3,...,2n are divided onto two equal groups. Let a1,a2,...,ana_1,a_2,...,a_n be the first group numbers in the increasing order, and b1,b2,...,bnb_1,b_2,...,b_n -- the second group numbers in the decreasing order. Prove that ∣a1−b1∣+∣a2−b2∣+...+∣an−bn∣=n2|a_1 - b_1| + |a_2 - b_2| + ... + |a_n - b_n| = n^2
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