Envy-free matching

Ok kiddo, imagine you have three best friends - Adam, Ben, and Carl. You also have three delicious cupcakes - chocolate, vanilla, and strawberry. Now, you want to share these cupcakes with your friends but you want them to be happy about the cupcake they get.

Now, let's say Adam loves chocolate cupcakes, Ben loves vanilla cupcakes, and Carl loves strawberry cupcakes. You would want to give each friend the cupcake they like without making any of the other friends jealous or upset that they didn't get the cupcake they wanted.

This is kind of like envy-free matching. It's a way to make sure everyone gets what they want without feeling bad about it.

In more complex situations, envy-free matching can be used in things like job assignments or college admissions. It's a way to make sure that everyone gets assigned to something they really want and that no one is unhappy with the outcome.

So, basically, envy-free matching is all about making everyone happy and nobody feeling left out or jealous. It's a way to be fair to everyone involved.