So, recently i found a book called "Gödel, Escher, Bach: An Eternal Golden Braid" written by Douglas Hofstadter. Inside it, i read a very interesting puzzle that i decided to share with you.


The puzzle itsself is simple:

There is a system called the MIU-system. It utilises only 3 letters of the alphabet: M, I, and U.
This means that the only strings of this system are strings composed of these 3 letters.
For example:
String #1: MU
String #2: UIMI
String #3: UIIMUMIIUMUIM
et cetera, to strings of any length and letter combination.


Even though these are legitimate strings, the only string of letters you have available is MI. Using a set of rules shown below, you must alter this string, in order to create the final string : MU
When i use the letter x, it symbolises any possible string of letters. For example, MxI can be M followed by any number and combination of M, I, U.

The rules are the following:
~Rule #1:
If you possess a string whose last letter is I, you can add a U at the end of the string.
For example, the string MUII can become MUIIU.
Generally: MxI --> MxIU


~Rule #2:
Suppose you have Mx. You can duplicate the x.
For example, MIU can become MIUIU.
Generally: Mx --> Mxx


~Rule #3:
If III occurs in one of the strings, you can replace it with U.
For example, MIUIIIU can become MIUUU.
Generally: MxIIIx --> MxUx


~Rule #4:
If UU occurs in one of the strings, you can delete it.
For example, MIUUIU can become MIIU.
Generally: MxUUx --> Mxx


These are the 4 rules. Following them, make the MU string from the MI string.
I suggest you give it about half an hour or more of thought before checking the solution.


Solution:


All in all, it was a fun and interesting problem.
I will post more puzzles and problems, if i find any more worthy, whether they are in the book or from other sources.


See you next time!