A prover claims to have 3-colored a map so neighbors never match, but refuses to show it. Instead: cups over every region, you pick one border, the two cups lift — different colors, every time you check. After enough rounds you're as certain as you like, and yet you could have faked every transcript yourself. That's a zero-knowledge proof, the idea running inside modern cryptography.
The prover has colored a map so that no two neighbouring regions share a color, and refuses to show it. So it puts a cup over every region and lets you audit one border at a time: you point, two cups lift, you see two colors. Different colors means that border is honest. Then the cups go back down — and the prover repaints, permuting the three colors before you may point again.
One peek proves one border. The repaint burns the evidence: what you saw was a costume, and the next round issues new costumes. So the peeks never accumulate into knowledge — but they do accumulate into certainty, because a liar has to survive every audit you feel like running.
Where does the certainty come from? A map with a bad border cannot hide it: any repainting of a monochrome border leaves it monochrome. The liar's only hope is that you never point there.
And if the suspense is unbearable, the cabinet will just tell you the answer — the one thing your certainty never needed.