Sidon

Sidon is a special game that you can play with numbers. Let's imagine that we have a big box of numbers, and we want to pick some of them without picking any that are the same. That means, if we pick the number 5, we can't pick it again later on. We call this a Sidon set.

Now, imagine that we have a bunch of boxes like this, each one with different numbers inside. We want to see how big of a Sidon set we can make from each box. The goal is to have the biggest Sidon set possible, because that's more fun to play with.

But here's the tricky part: we don't want to pick any two numbers that are the same when we add them together. For example, if we pick the number 2 and the number 3, we can't pick the number 5, because that's what you get when you add 2 and 3 together.

So, in short, Sidon is a game where you try to pick as many numbers as you can without picking any that are the same, and without picking any two that add up to a number you've already picked. It can be a lot of fun, but it also takes some careful thinking to do it right!