[Pickett]

First off, sorry if this has been posted. I haven't seen it on here, and searching for this one was difficult (since "MI" and "MU" are both under 3 letters, and the search doesn't like that...). So again, I apologize if this is a duplicate.

Can you use only the following 4 rules to convert MI to MU?

1) xI --> xIU

2) Mx --> Mxx

3) xIIIy --> xUy

4) xUUy --> xy

Please note: "x" and "y" are placeholders for any string of characters. For example, MUUI would match rule 1 (x=MUU), rule 2 (x=UUI), or rule 4 (x=M, y=I)

Also note: the unidirectional nature of the rules...meaning you CANNOT go from MUU to MIIIU using rule 3...you can only go from MIIIU to MUU.

Also: Before anyone asks, you can use the rules as many or as few times as you like, but you can ONLY use those 4 rules.

I like to use the convention of XXX --#--> YYY where "XXX" is the start string, "#" is the rule number used, "YYY" is the resulting string. So here's a quick example showing a valid conversion:

Convert MUI to MIU

MUI --1--> MUIU --2--> MUIUUIU --4--> MUIIU --1--> MUIIUUIIU --4--> MUIIIIU --3--> MUUIU --4--> MIU

Anyways, this is a classic puzzle. Hope this makes sense! Good luck!

[Guest]

"MI"

(2) M --> M[iI]

(2) M[iI] --> M[iIII]

(1) [MIII]I --> [MIII]IU

(3) [MI]III --> [MI]U

(2) M[iUU] --> M[iUUIUU]

(4) [MIIUUI]UU[] --> [MIIUUI][]

(4) [MII]UU --> [MII]

(3) [M]III[] --> [M]U[]

"MU"

[Pickett]

"MI"

(2) M --> M[iI]

(2) M[iI] --> M[iIII]

(1) [MIII]I --> [MIII]IU

(3) [MI]III --> [MI]U

(2) M[iUU] --> M[iUUIUU]

(4) [MIIUUI]UU[] --> [MIIUUI][]

(4) [MII]UU --> [MII]

(3) [M]III[] --> [M]U[]

"MU"

This is not a correct answer. Very good try.

"MI"

(2) M --> M[iI]

(2) M[iI] --> M[iIII]

(1) [MIII]I --> [MIII]IU

(3) [MI]III --> [MI]U

(2) M[iUU] --> M[iUUIUU]

(4) [MIIUUI]UU[] --> [MIIUUI][] - You added an extra "I" after the "M" between these two steps.

(4) [MII]UU --> [MII]

(3) [M]III[] --> [M]U[]

"MU"

[Guest]

No. It is impossible to transform MI to MU using only the 4 given rules.

Of rules 1 and 3, the number of I's does not change.

Of rule 2, the number of I's is multiplied by 2.

Of rule 3, the number of I's is decreased by 3.

Both 2 and 3 are prime factors, thus it is impossible for

the transformation.

Edited July 16, 2010 by Dej Mar