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Student Activity: Bud Brown

Student Activity: Bud Brown

by Daluss Siewert
Black Hills State University

On Friday afternoon, Dr. Ezra (Bud) Brown of Virginia Tech presented a student activity titled ’What is the color of my hat?â? Hat puzzles are very popular these days and are generating significant interest among both students and mathematicians. Nearly 100 students attended the ’hats-onâ? activity. Dr. Brown began by handing out hats, which included Virginia Tech’s school colors of maroon and orange, to help facilitate discussions of possible solutions to the problems he would present.

The first problem discussed involves just two people and two hat colors. A hat is placed on each person’s head and each must guess as to the color of their hat which they cannot see. For the hats distributed, the bottom of the bills were the same color as the hat itself so this presented an obvious problem ’ solved by requiring the hats be worn backwards. In this game it is not required that all colors be represented ’ colors may or may not be repeated. Incorrect guesses are not punished and a win consists of at least one correct guess. The students got together in groups to discuss strategies and to determine if there was a strategy that guarantees a win. After a quick clarification that the game is a team sport and the strategy needed to involve the team, a solution was found and shared with the others. Dr. Brown then discussed a variant with n players and n possible colors. For readers interested in the strategies, these will surely be discussed in the article ’A Dozen Hat Problemsâ? by Jim Tanton and Ezra Brown to appear in Math Horizons in February 2009.

Dr. Brown continued the activity by presenting several other problems and soliciting strategies. For one particular variant where the players stand in a line ’ so they can see the hat color in front of them ’ and guesses are given from back to front, volunteers had fun acting out a strategy on stage. The activity concluded with the ’circle problemâ? variant being discussed. In this game, players are in a circle, incorrect guesses are penalized, but passes are allowed. Dr. Brown discussed how the strategy for the circle problem involves more sophisticated methods and uses coding theory. He ended the session with an assignment and a suggestion. The assignment: What if there were 11 players and 3 colors in the ’circle problemâ?? The suggestion: Try these hat puzzles at your Math Club. All in attendance enjoyed the activities and, as Dr. Brown observed, it appeared that all the hats found a good home.

Ezra Brown is an Alumni Distinguished Professor at Virginia Tech. He received his Bachelor’s degree from Rice University and his Master’s and Ph.D. degrees from Louisiana State University. He has been a faculty member at Virginia Tech for 39 years.