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National Spain Olympiad 2004, Problem 1

Source: National Spain Olympiad 2004

May 30, 2017

math olympiadMatricesmatrixArithmetic Progressionalgebra unsolved

Problem Statement

We have a set of

{221}

real numbers whose sum is

{110721}

. It is deemed that the numbers form a rectangular table such that every row as well as the first and last columns are arithmetic progressions of more than one element. Prove that the sum of the elements in the four corners is equal to

{2004}

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