The Checkerboard
Imagine you have a checkerboard. A big square checkerboard. Standard type.
So, it is 8 squares by 8 squares and they alternate in color from black to red and black to red, and so on. And 8 times 8 is 64, so there are 64 squares total.
So now, imagine that you have a bunch of dominoes. Say, 32 dominoes. Each Domino was big enough to cover two squares on the checkerboard. One black square and one red square.
So it's easy to figure out that with the checkerboard having 64 squares, half that number, or 32, would be enough to cover every single square on the checkerboard.
So now, I'm gonna add a little wrinkle to this. Make it not so easy. Let's say you took a saw and you removed the right-hand corner square of the checkerboard. You just cut it off. And you did the same with the one in the left-hand corner. You just cut it right out.
So now, you have a checkerboard with 62 squares, because you just cut out two of them. The two are diagonally across from either other on the board. One black square and one red square.
Here is the puzzler.
Explain in three sentences or less, how you would arrange the dominoes now to cover all the squares, knowing that each domino must cover one red square and one black square. You can use as many as you need, but they can't overlap each other.
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