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The MU Puzzle
A logic puzzle that introduces you to formal systems
From the book: Godel, Escher, Bach: An Eternal Golden Braid
To do this puzzle you will need a pencil and a piece of paper.
The goal of this puzzle is to produce the string "MU" but there are rules as to how you can do it.

Where do you start?

  • There are only three letters in this system: M, I, and U
  • You start out with the string: MI and you have to get to MU

The Rules:

  • Rule 1: If you have a string whole last letter is I, you can add on a U at the end. For example: if you hav the string MI you can change it to MIU
  • Rule 2: If you have string Mx you can change it to Mxx. For example: if you have the string MIU you can change it to MIUIU; if you have MUM you can change it to MUMUM. Yu see? x is any series of letters after an M. Doesn't matter how long.
  • Rule 3: If  III occurs in your string you can change your string by taking out the III and replacing it with U. For example: UMIIIMU can change to UMUMU or MIIII can change to MUI or MIU

That's the whole puzzle. Now start with MI and using the rules try to get to MU.



Think you have it figured out? Want to learn more? This is an amazing puzzle and you can get very deep into the solving of it. If you want to know the solution and how best to get it you are going to have to get the book!

Interested in this book? Godel, Escher, Bach: An Eternal Golden Braid

The author, Douglas R. Hofstadter has some other really amazing books.