ELI5: Explain Like I'm 5

Branch and cut

Okay kiddo, do you know what a jigsaw puzzle is? It's a picture made up of tiny little pieces that you have to fit together. Branch and cut is a way to solve really hard jigsaw puzzles but instead of pieces, we use numbers and math.

First, we start with a really big jumbled mess of numbers and try to find the answer to a math problem. But we can't just try to solve the whole thing at once, it's too hard! So we start by picking one number and guessing what it should be. Then we see if that guess helps us find the answer we're looking for.

If it doesn't, we try a different guess for that same number. And we keep trying different guesses for that same number until we either find the right answer or run out of guesses. This is what we call branch.

But if we guess for all of the numbers and still can't find the answer we're looking for, we start cutting things out. We look at the guesses we made and see if there are any that contradict each other. If there are, we know that those guesses can't be right, so we cut them out and start over from where we left off. We keep doing this until we finally find the right answer. This is what we call cut.

So in summary, branch and cut is a way of solving really hard math problems by breaking them down into smaller parts, guessing and checking what the answers could be, and eliminating possibilities that don't work until we finally find the right answer.