Domino tiling

Okay kiddo, so have you ever played with dominoes before? You know, those little rectangular tiles that you can line up and knock down? Well, sometimes people use dominoes to make really cool patterns on the floor or a table. That's called domino tiling!

Now, imagine you have a big square or rectangle and you want to cover it completely with dominoes. But there's a catch – each domino has to cover exactly two squares, and they can only be placed horizontally or vertically, not diagonally.

If the big square or rectangle is an even number of squares on each side, then it's pretty easy to cover it with dominoes. You just keep placing them side by side until you've covered the whole thing. But if it's an odd number of squares on each side, things get a bit trickier.

You see, no matter how you try to cover an odd-sized square or rectangle with dominoes, there will always be one square left over that can't be covered. It's like having one extra piece of pizza but not enough slices to share it evenly with your friends.

So, mathematicians have been studying this problem for a long time, and they figured out something pretty cool. They discovered that if you remove any one square from the big odd-sized square or rectangle, then you can cover the rest of it completely with dominoes!

It's kind of like solving a puzzle. By removing one square, you create a pattern with the remaining squares that can be covered by dominoes. And the best part is, it works for any odd-sized square or rectangle.

So, that's the basic idea of domino tiling. It's a fun and challenging problem that mathematicians love to play with. Who knew a simple game like dominoes could lead to such interesting discoveries?