The MU Puzzle is a formal system
puzzle that I first discovered when I read Douglas R. Hofstadter
's book Gödel, Escher, Bach: an Eternal Golden Braid
You start with a string of letters MI
. From this you try to derive the string MU
, but you have to follow a few rules of course. The order of the characters in a string does
matter. Each time you follow a rule to create a new string, you have "added" the new string to your "collection".
If you possess a string whose last letter is I
, you can add on a U
at the end.
Suppose you have Mx
. Then you may add Mxx
to your collection.
A lowercase x here represents a string of any size.
, you may get MIUIU
, you may get MUMUM
, you may get MUIUIMUIUIM
occurs in one of the strings in your collection, you may make a new string with U
in place of III
, you may get UMUMU
, you may get MIU
, you may get nothing.
, you may get MU
occurs inside one of the strings, you can drop it.
, you may get U
, you may get MUIII
The opposites of these rules are not allowed, you can not replace U
, etc. etc.
That's all the rules. Note that you do not have to follow a rule just because you can. If you have UU
in your string you do not have to drop it, likewise if you have III
in your string you do not have to replace it with U
MU puzzle solution