Sum of the corners?

Logic Level 2

You have an $m\times n$ grid of squares with $m>7$ and $n>7$ .

Each square is filled with an integer such that the sum of any two squares sharing an edge is odd.

What is the sum of the corner squares?

It could be odd or even. It can't be done. Odd Even

1 solution

Geoff Pilling
Jul 11, 2017

The rules imply that if the squares were colored like a checkerboard, we can say that all the black squares contain odd numbers and all the white squares contain even numbers, or vice versa.

And the four corners will always contain an even number of white squares and an even number of black squares.

Therefore, since an even number of odd numbers and an even number of even numbers will always add up to an even number, the sum of the corner squares will always be $\boxed{\text{even}}$ .

Sum of the corners?

1 solution

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