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Square Table

Source: 1989 National High School Mathematics League, Exam Two, Problem 3

February 25, 2020

Problem Statement

Given n×nn\times n square table, fill in each square with −1-1 or 11. For nn squares that any two of them are neither in the same line nor in the same column, we call the product of the numbers in the squares basic term. Prove that she sum of all basic terms is always a multiple of 44.
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