The MU Puzzle Strings:- Definition: The MIU System utilizes three letters: M, I,

Question

The MU Puzzle

Strings:- Definition: The MIU System utilizes three letters: M, I, and U. The strings of the system are strings of letters consisting entirely of these three letters. Example:- The following are strings of the MIU System:

MIU

UIMUUI

MMMMMMM

Rules:-

There are four rules that say how we may transform a string into a new string: 1. If a string ends in the letter I, you may create a new string by appending a U.

2. If a string has the form Mx, where x is an arbitrary string, you can create a new string by appending x, i.e. you may create the string Mxx.

3. If III occurs in a string, you may make a new string by replace III with U.

4. If UU occurs in a string, you may create a new string by deleting UU.

Example:-

You can create MIU from MI (rule 1).

You can create MII from MI (rule 2).

You can create MIIII from MII (rule 2).

You can create MUI from MIIII (rule 3).

You can create MUIU from MUI (rule 1).

You can create MUIUUIU from MUIU (rule 2).

You can create MUIIU from MUIUUIU (rule 4)

Theorems and Axioms:-

In the previous example, all the strings began with M. This is getting a bit ahead of ourselves, since we

Explanation / Answer

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