Geek Challenge Results: Mind Swapping

Four people correctly answered last month’s Geek Challenge:  Shanti Ahluwalia, Sanjay Sheth, Brian Page, and DMC’s own John Sullivan.

The September DMC Geek Challenge was based on a recent episode of Futurama where a mind-switching machine had several of the characters minds and bodies switched up.  However the machine could switch the same minds back again.  How to get all of the people back to normal?

I presented a question with just the first 3 switches from the episode:

Farnsworth switched with Amy
Farnsworth's mind (in Amy's body) switched with Bender
Amy's mind (in Farnsworth's body) switched with Leela

All of our respondents correctly switched them back optimally in 3 switches:

1. Swap Farnsworth & Leela's minds ... which puts Farnsworth back in his own body and Leela in Bender's body.
2. Swap Bender & Amy's minds ... which puts Amy back in her own body and Bender in Leela's body.
3. Finally, swap Bender & Leela's minds ... which puts Bender back in his own body and Leela in her own body.

Congratulations to all!

Amazingly this math problem and a new theorem that solves it were created for this episode by Furturama writer and PhD mathematician Ken Keeler.  A full write-up of Keeler’s theorem can be found here:  http://theinfosphere.org/The_Prisoner_of_Benda#cite_note-1

But if you don’t have an hour to spend immersing yourself in Group Theory and Futurama trivia, you can watch this 3 minute video version: //www.youtube.com/watch?v=8M4dUj7vZJc&feature=iv&annotation_id=annotation_24473

So now that you are versed on the theorem, try to solve the full problem with 7 transformations.  (No points for this one, since the answer can be found at the above links.)  Have fun!

1. Professor Farnsworth - Amy (each in their own bodies)
2. Farnsworth's mind (in Amy's body) switch with Bender's mind in Bender Body
3. Amy's mind (in Farnsworth body) switch with Leela's mind in Leela's body
4. Bender's mind (in Amy's body) switch with a robotic wash bucket
5. Bender's mind (in the Wash Bucket) switch with Emperor Nikolai
6. Fry's switches with Zoidberg (each in their own bodies)
7. Hermes's (in his own body) switch with Amy's mind in Leela's Body.

So, after 7 switches,

Amy Body:  Wash Bucket Mind
Bender Body: Farnsworth Mind
Leela's Body: Hermes's mind
Farnsworth's body: Leela's mind
Wash Bucket "Body": Emperor Nikolai
Emperor Nikolai's Body: Bender's mind
Fry's Body: Zoidberg's mind
Zoidberg's Body: Fry's mind
Hermes' Body: Amy's mind

And these mind swaps cannot be repeated:
Farnsworth - Amy
Farnsworth – Bender
Amy – Leela
Bender - wash bucket
Bender mind - Emperor Nikolai
Fry – Zoidberg
Hermes - Amy