A Prisoner Coordination Puzzle and Some Generalizations

Document Type

Presentation Abstract

Presentation Date

11-7-2016

Abstract

One hundred prisoners are playing a game for their freedom. They start by developing a collective strategy. Then the warden places a hat and a hat number (range 1 to 100, repetition allowed) on each prisoner’s head such that they can see everyone’s number except their own. They must then, simultaneously, shout a number. If everyone shouts the same number and that one number appears on at least one hat, the prisoners win. Otherwise, they lose.

We discuss the elegant solution to this puzzle and how it relates to Sperner’s lemma from combinatorial topology and a hardness-of-approximation result regarding hypergraph labelings. We then discuss generalizations including when the shouted number must appear more than once, and what happens when the underlying graph dictating hat visibility is changed.

Additional Details

Monday, November 7, 2016 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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