Strong Induction

Ordinary induction assumes only the single previous case. But some claims don't break down that way — to prove the statement for n, you might need to lean on cases far below n, not just n − 1. Strong induction gives you that power: assume the claim holds for EVERY value from the base up to k, then prove it for k + 1. Same dominoes, but now each one can rest on all the dominoes behind it.