Fall 2014 MTCA Workshop #2

Post date: Oct 24, 2014 3:14:22 AM

The Futurama Theorem

Presented by

Zachary Miner

The University of Texas at Austin

Thursday, October 23, 2014

NOA 1.124

The Professor and Amy invent a machine that can switch minds between two bodies. They then use this machine on themselves to switch their minds. However, when they go to switch back, they discover a key flaw in the machine's design: once one pair of bodies has switched minds, the same pair cannot reenter the machine to switch back.

In this session we explored the following questions:

1. If they bring in one person who is willing to participate, can Amy and the Professor get their own minds back? If not, can it be done with two or more?

2. When there are n people, there are n! possible permutations of minds and bodies. Are all such permutations attainable by using this flawed machine?

3. After several trips to the machine, n people have their minds and bodies scrambled. Is it always possible to unscramble them? If so, how many people are required? What is the minimum number of people required if you don't know how the scrambling occurred, and so must assume that no pair of the people in question can go through the machine? Supposing you know the moves that brought the n people to the scrambled state they are in, are there configurations in which no additional people are required to return mind to the right body?

For more information, watch the "Prisoner of Benda" Episode of Futurama, or see the attached file written by Cheryl Grood for the Philadelphia Math Teachers' Circle.