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If you ask me it's difficult

Source: Iran TST 2002

May 28, 2004
geometryrectanglelinear algebramatrixvectorabstract algebrafunction

Problem Statement

Suppose from (m+2)×(n+2)(m+2)\times(n+2) rectangle we cut 44, 1×11\times1 corners. Now on first and last row first and last columns we write 2(m+n)2(m+n) real numbers. Prove we can fill the interior m×nm\times n rectangle with real numbers that every number is average of it's 44 neighbors.
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