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Graduate Seminar

Christopher Cox
Carnegie Mellon University
Title: 1 hat, 2 hat, red hat, blue hat

Abstract: At a prison in Pennsylvania, a new cruel and sadistic warden gets hired. After being there for awhile and watching way too many of the Saw movies, the new warden gets bored and decides to play a game a game with the prisoners. He gathers the prisoners around and says that he will place hats of various colors on each of their heads, and then, without being able to look at their own hat, the prisoners will be asked to guess its color based on (possibly restricted) knowledge of the other prisoners' hats. The warden promises to set free any prisoner who guesses correctly, but he will kill anyone who guesses incorrectly. After discussing the particular rules of the game, the warden decides to leave the prisoners alone to say their goodbyes.

Luckily, the prisoners are all mathematicians and decide to use this time to devise a strategy to beat the warden at his own game! They quickly realize that there is no way to ensure that any given one of them can be sure to guess correctly, so they decide to all act selflessly (after all, they've bonded during their time in prison) and try to maximize the number of prisoners that will be set free. Knowing that the warden is also a mathematician (because why not?) and probably has the room bugged, they realize that they must devise a strategy that will perform well no matter what the warden does. Knowing how cruel and intelligent the warden is, after knowing the prisoners' strategy, he will likely place the hats so that as many prisoners as possible will die.

Given the particular rules to the game, how many people can the prisoners be sure to save?

Date: Tuesday, February 28, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: