10

Part of 2002 Iran Team Selection Test

Problems(1)

If you ask me it's difficult

Source: Iran TST 2002

(m+2)\times(n+2)

rectangle we cut

4

1\times1

corners. Now on first and last row first and last columns we write

2(m+n)

real numbers. Prove we can fill the interior

m\times n

rectangle with real numbers that every number is average of it's

4

geometryrectanglelinear algebramatrixvectorabstract algebrafunction