Proof by Contradiction Meets Counting

You can literally prove the impossible just by pretending it’s true. It’s called Proof

by Contradiction and it is the ultimate logic flex. You assume the opposite of what you want

to prove, find a glitch in the logic, and boom, the original statement

has to be true. But it gets wilder when you apply this to counting. We aren't talking

basic addition, we are talking Permutations and Combinations. It’s how you calculate every possible password

or why the Pigeonhole Principle guarantees that if you have ten socks and nine drawers,

one drawer must have double. Math isn't just homework, it's the source

code for reality.