olymmath

KöMaL 2024 A869

    Let AA and BB be given real numbers. Let the sum of real numbers 0≤x1≤x2≤⋯≤xn0\le x_1\le x_2\le\dots\le x_n be AA, and let the sum of real numbers 0≤y1≤y2≤⋯≤yn0\le y_1\le y_2\le\dots\le y_n be BB. Find the largest possible value of ∑i=1n(xi−yi)2{\sum_{i=1}^n (x_i-y_i)^2}.

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