# Difference between revisions of "1971 IMO Problems/Problem 6"

(Created page with "Let A = (aij), where i, j = 1, 2, ... , n, be a square matrix with all aij non-negative integers. For each i, j such that aij = 0, the sum of the elements in the ith row and t...") |
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− | Let A = ( | + | ==Problem== |

+ | Let <math>A = (a_{ij})(i, j = 1, 2, \cdots, n)</math> be a square matrix whose elements are non-negative integers. Suppose that whenever an element <math>a_{ij} = 0</math>, the sum of the elements in the <math>i</math>th row and the <math>j</math>th column is <math>\geq n</math>. Prove that the sum of all the elements of the matrix is <math>\geq n^2 / 2</math>. |

## Revision as of 14:10, 29 January 2021

## Problem

Let be a square matrix whose elements are non-negative integers. Suppose that whenever an element , the sum of the elements in the th row and the th column is . Prove that the sum of all the elements of the matrix is .