Talk:MU puzzle

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Okay. I am but a simple academic who has only been pestered with mathematics for ten years, so it is obviously my fault dat this lemma might as well have been written in Arabic. Now, the puzzle is explained in Math rather than English. Maybe someone who has read the book can elaborate, or translate? (Brrrtje 19:48, 24 December 2006 (UTC))

Explanation: Consider the number of "I"s in a string before / after the application of one of the rules. With rules 1 and 4, the number is not affected. With rule 2, the number is doubled. With rule 3, the number decreases by three.

Note that if the number of "I"s is a multiple of 3 before the application of one of those rules, it will be a multiple of 3 afterwards. Similarly, if the number is not a multiple of 3 before using a rule, it will not be a multiple of 3 afterwards.

That is, _whether or not the string has a multiple of three "I"s is not changed by any sequence of rules_, or _no sequence of rules can change a string with a nonmultiple of 3 "I"s to a string with a multiple of 3 "I"s, or vice versa_. Since "MI" has 1 "I" (not a multiple), and "MU" has 0 "I"s (a multiple), it is impossible to perform the change. Ralphmerridew 02:08, 17 January 2007 (UTC)

[edit] a and b

i \cdot 2^{a} -3b

a is the number production rule 2 is used and b is the number production rule 3 is used, right? --Abdull 11:25, 4 December 2007 (UTC)

[edit] Proposed change

I would like to change the desription of the puzzle in a way that is more readable by common people. I was thinking about something like this:

Let's suppose to have the symbols M, I, and U which can be combined to produce strings of symbols or "words". The MU puzzle asks to start with a the "axiomatic" word MI and transform it into the word MU using in each step only the folowing transformation rules:

  1. At the end of any string ending in I, you can add a U, such as changing MI to MIU.
  2. You can double any string after the M (that is, change Mx, to Mxx), such as changing MIU to MIUIU.
  3. You can replace any III with a U, such as changing MUIIIU to MUUU.
  4. You can remove any UU, such as changing MUUU to MU.
Using these 4 rules is it possible to change MI into MU in a finite number of steps?
We can write the production rules in a more schematic way. Suppose x and y behave as variables (standing for a string of symbols) then the production rules can be written as:
  1. xI → xIU
  2. Mx → Mxx
  3. xIIIy → xUy
  4. xUUy → xy,
can we obtain the word MU, using these rules?

I'm not a native english speaker so I ask you if you for corrections. What do you think?--Pokipsy76 (talk) 12:04, 26 March 2008 (UTC)