What are proofs by contradiction?

A proof by contradiction is like solving a puzzle by showing that something can’t be true because it would make the whole puzzle impossible.

Imagine you have a box of crayons, and you think one of them is missing. You don’t know which one, but you decide to prove it by contradiction. You assume the opposite: that no crayon is missing. Then you go through your drawings, or maybe even count all the crayons used, and find out that this assumption leads to something impossible: like using a color you didn't have! That means your original guess was right, a crayon is definitely missing.

1. You start by assuming the opposite of what you want to prove.
2. Then you follow the logic, just like when you try every possible way to solve a puzzle.
3. If you end up with something that doesn’t make sense, or an obvious mistake, then your original assumption must be wrong.

It’s like playing "Guess Who?" and saying, “If it's not this person, then it has to be someone else, but that can't be true because there are no more people left!”