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MU (Posted on 2002-06-20) Difficulty: 4 of 5
(from Gödel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter)

Start with a single sequence of letters: MI

The goal is to apply a series of manipulations to this sequence to produce MU.

The allowable manipulations are:

1. If the sequence ends in I, you can append U

2. If the sequence begins with M, you can duplicate the string after M, e.g. MIII can be replaced by MIIIIII or MIMU can be replaced by MIMUIMU

3. If the sequence contains III, you can replace the III with U, e.g. UIIIM can be replaced by UUM.

4.If the sequence contains UU, you can delete the UU, e.g. UUM can be replaced by M or MIUUI can be replaced by MII.

These rules are all one-way; you can't take a U and replace it with III.

Is it possible to reach MU from MI? If so, what series of steps would you take to get there? If not, why not?

See The Solution Submitted by friedlinguini    
Rating: 3.3333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
answer Comment 6 of 6 |
No, it is not possible to move to MU from MI.
  Posted by K Sengupta on 2007-04-01 15:24:03
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