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ASU 441 All Soviet Union MO 1987 tennis x_1^2+...+x_{10}^2=y_1^2+...+y_{10}^2

Source:

August 7, 2019

Sum of SquaresalgebracombinatoricsTournament

Problem Statement

Ten sportsmen have taken part in a table-tennis tournament (each pair has met once only, no draws). Let

xi

be the number of

i

-th player victories,

yi

-- losses. Prove that

x_1^2 + ... + x_{10}^2 = y_1^2 + ... + y_{10}^2