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Maximum distance of points on solids in R^n

Source: KoMaL A. 869

February 15, 2024
algebraInequality

Problem Statement

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\ldots \le x_n be AA, and let the sum of real numbers 0≤y1≤y2≤…≤yn0\le y_1\le y_2\le \ldots\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.
Proposed by Péter Csikvári, Budapest
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