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Upstart Puzzles: Proving Without Teaching/Teaching Without Proving

Proving without Teaching/ Teaching without Proving, illustration

Amazing Sand Counter claims to know the number of grains in the bucket just by looking at it. Do you believe him?

Credit: Andrij Borys Associates / Shutterstock

Peter Winkler's mathematically elegant, often whimsical puzzles have been a joy to read and wrestle with. My columns now embark on a different path. Each will come in two parts: one quite doable, for which I will provide a solution, the other an "upstart," or insolent variant, I do not know how to solve and that will be an open problem for the community. Here we go.

"Zero knowledge" proofs entail interaction between someone (the Prover) asserting a statement and someone else (the Verifier) determining whether it is true. The proofs give zero knowledge to the Verifier, as the Verifier gains no knowledge other than that the statement is true, either absolutely or beyond a reasonable doubt.1 The statement in question is normally of a mathematical nature, but, in this case, it resembles, well, child's play.


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