Math-MIND 2026 · Department of Mathematics, University of Bologna

Three small problems

One correct answer each. Submit before the solutions go up — the best 3 scores get a lunch with the speaker, just after the speech.

1 Logic

Which product is the match?

Three listings compete for the same query. Exactly one is the perfect match, and exactly one of the three labels is true.

A: “The match is not B.” · B: “The match is not A.” · C: “The match is A.”

2 Information

How many prisoners can they guarantee to free?

100 prisoners stand in a line, each wearing a black or white hat, seeing only the hats in front. From the back, each says one word — “black” or “white” — guessing their own hat: right → freed, wrong → eliminated. Everyone hears every guess, nobody is told whether it was right.

They may agree on a strategy beforehand. In the worst case, how many can they guarantee to free?

3 Optimal stopping

Optimal k/n and success probability as n → ∞?

n products arrive one at a time in random order. You only see relative quality, and each accept/reject is final. Strategy: skip the first k, then take the first product better than everything seen so far. You win only if you take the best of all n.

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Answers received

Thank you. Solutions on the screen in a few minutes — and if you want to talk about the real versions of these problems, find Franco after the session.

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