One essential thing here is that you have a problem that is hard to solve, but easy to check once you have the answer.
Many people incorrectly assuming checking a solution is as hard as solving it in the first place, but it can be millions of times easier.
Imagine you want to factorize 244201131403. You would spend a lot of time doing it, especially if you had to do it by hand. It’s basically impossible by hand.
But if I were to tell you that the solution is 314159×777317, a third grader could check that those are factors in the initial number.
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