Cut Corners – Solution

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Let’s take a closer look at that grid.

plain-grid

Maybe you’ve played with this for a while without coming up with a valid domino tiling. It’s definitely not as easy as it looks!

To see why, let’s color this grid like a checkerboard:

checkered-grid

(Give this problem another try before reading more. I’ll wait.)

Okay. The key to finishing here is to notice that every time we place a domino on this checkerboard, we cover up one white square and one green square. No more, no less. But the two missing squares are both green. So we’re trying to cover up 32 white squares and 30 green squares with dominoes that each cover one white square and one green square. This is impossible, so there are 0 ways to tile this grid.

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