The Checkerboard

Nov 07, 2023

Time for the new puzzler for today. 

Here we go.

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. 

Good luck.
 

 

Answer: 

And the answer to this puzzler is going to annoy some of you. Sorry about that. 

This was a trick question! My brother loved that. This one, is not possible. 

The question was, 64 squares on a checkerboard. Take away two. Then you have 62. Then you have dominos. And it takes one domino to cover 2 squares. You can cover the original 64 squares with 32 dominoes. But now you have 62. 

Explain in three sentences or less, how you would arrange the dominoes now to cover the 62 squares. You can use as many as you need, but they can't overlap each other. And each domino must cover one red square and one black square.

And the answer is, you can't. It is not possible. It was a tricky question! 

Because you removed one red and one black square, you are now unable to line up the dominoes to each cover one red and one black square.

Trick question. Sorry about that! 


Get the Car Talk Newsletter