*NOTE: I made a correction on 10/23 to the “Solution to EXAMPLE 1” below – I had listed the rules used in the incorrect order. It should be OK now. Thanks to Farjana for the catch!*

We are going to play a game with strings of symbols. This game was invented by a man named Douglas Hofstadter and found in his book *Gödel, Escher, Bach*. Here are the rules:

Suppose there are the symbols ‘M’, ‘I’, and ‘U’, which can be combined to produce strings of symbols called “words”, like MUI or MIUUU. In the MIU game, we always start with the “axiomatic” word MI, and transform it using the following four rules, to obtain some “goal” word. The rules state that you may:

- Add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
- Double any string after the M (that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
- Replace any III with a U. For example: MUIIIU to MUUU
- Remove any UU. For example: MUUU to MU

EXAMPLE 1

Goal Word: MIIU

Solution:

**Start with MI (axiomatic word)
MI to MII (rule 2)
MII to MIIU (rule 1)**

EXAMPLE 2

Goal Word: MIIIIIIU

### Assignment, Due TUESDAY 10/28 (end of day)

**Warm up** *(This Warm Up is** just for practice – you must complete it but you do NOT need to submit your answers – see below for the three-part Assignment to be submitted). *In each example below, **start with the axiomatic word MI **and show, step-by-step, how to obtain the goal word (in each step, state which of the rules you used). *These are just for practice (you do NOT need to submit your answers).*

EXAMPLE 3: Goal word MIIUIIU

EXAMPLE 4: Goal word MUII

EXAMPLE 5: Goal word MUUII

EXAMPLE 6: Goal word MUUIIUIIU

**Assignment.** Your assignment has 3 parts:

PART 1. Challenge your friends: Create two different MIU puzzles — that is, make up two different goal words, and post them in the comments. Try to create goal words are tough to figure out!

PART 2. The second part of your assignment is to solve someone else’s puzzle. Choose one puzzle by another student, and type your solution step-by-step, indicating which rule you used at each step. Leave your comment as a response to their puzzle. Only one solution per puzzle!

PART 3. The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt. Be sure to respond to each part:

*Writing Prompt**: **Did you enjoy this assignment? Why or why not? Describe a connection between this assignment and our work in the class. (If you don’t believe there is a connection, try to *imagine* why we are doing this). Leave your response in the comments.*

1) my challenge : MIUUIIUIIUI

Hi Julia,

Great challenge – I look forward to seeing if anyone can solve it!

-Prof. Reitz

(but just so we’re clear, you were not required to complete this puzzle – as I think you know).

1) my challenge : MIUUIIUIIUI

My… isn’t this random?

Give me a few…

its not random!! Solve this and you will win a prize….

Define: “prize”

you get a free meal

define this “meal” you speak of…

Part 1 : Challenge

1st – Goal word : MIIIIIUIUIUII

2nd – Goal word : MIIUIUUIIUI

Part 1 : Challenge words

word 1: MIIIIUIIIUUU

Word 2: MIUIUIUIU

Word 3: MIIIUIIIUUU

Part 3: I really enjoyed this assignment even though it is very challenging and need a

lot of thinking but it is very interesting. I think there is a connection between this puzzle and the class because both of them need thinking about figuring out ways to prove things. In class we need to do many steps in order to prove the solutions and in this puzzle, it also needs steps in order to get to the solution and prove it.

Part 2: solving challenged goal word

Goal word: MIUIUIUIU

Solution:

MI (axiomatic word)

MII (rule 2)

MIIII (rule 2)

MIIIIIIII (rule 2)

MIIIIIIIIIIIIIIII (rule 2)

MIUIIIIIIIIIIII (rule 3)

MIUIUIIIIIIII (rule 3)

MIUIUIUIIII (rule 3)

MIUIUIUIU (rule 3)

Part 1:challenges

1- MUIUIUIUII

2-MUIIUUIIIIIUIUUIIIU

Goal Word: MUIIUUIIIIIUIUUIIIU

MI (axiomatic word)

MII (Rule 2)

MIIII (Rule 2)

MIIIIIIII (Rule 2)

MIIIIIIIIIIIIIIII (Rule 2)

MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII (Rule 2)

MUIIUUIIIIIUIUUIIIU (Rule 3)

Part 1:

Challenges:

-M (no really, I’m not kidding)

-MUUIUIIUIIU

-MUU

Part 3:

This game is somewhat enjoyable and fulfilling if you manage to successfully get the goal word. It’s a good analogy to the proofs we have to write in class because we have to explain why we choose to do as we do. Now if the goal is unsolvable, I might either condemn myself to solve it, find out why, or just give up entirely in anger.

-MUUIUIIUIIU

oops…

-MUUIUUIIUIIU

missed that U

Part 2 : Solving challenge goal work

Solution:

Goal word : -MUIUIUIUII ( Leonardo)

MI (axiomatic word)

MIU (Rule 1)

MIUIU(Rule 2)

MIUIUIUIU ( Rule 2)

MIUIUIUIUII ( I can not figure out where you get the two II at the end)

Part 2 : Solving challenge goal work

Goal word: MUUIUIIUIIU

MI(axiomatic word)

MII (rule 1)

MII (rule 1)

MIIII (rule 1)

MIIIIIIII (rule 1)

MIIIIIIIIIIIIIIII (rule 1)

MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII (rule 1)

MUIIIIIIIIIIIIIIIIIIIIIIIIIIIII (rule 3)

MUUIIIIIIIIIIIIIIIIIIIIIIIIII (rule 3)

MUUIUIIIIIIIIIIIIIIIIIIIIII (rule 3)

MUUIUIIUIIIIIIIIIIIIIIIII (rule 3)

MUUIUIIUIIUIIIIIIIIIIII (rule 3)

MUUIUIIUIIUUUIIIIII (rule 3)

MUUIUIIUIIUUUUIII (rule 3)

MUUIUIIUIIUUUUU (rule 3)

MUUIUIIUIIUUU (rule 4)

MUUIUIIUIIU (rule 4)

Part 3: I enjoyed the game it was challenging but fun. I reason I enjoyed the game was because it forced me to think and find a solution proving that the “Goal Word” is correct. I think this game has a connection with class because we are trying to prove the word just like in class we are trying to prove a proposition,so it help me find ways to come up with an answer.

I accidentally repeat MII… sorry about that

Part 3:

Yes i have enjoyed this assignment. This puzzle game was interesting to solve even though it was sometimes difficult to get a solution for a goal, but it also makes you try again and again until you get frustrated. I think this puzzle game has a connection to our class work of solving proofs. The similarity is that this puzzle has an answer/goal word given and in our class work a proposition to proof, so for the puzzle game we had to use the rules provided and find steps to prove the goal word, on the other hand in our class work we used theorem/definitions in steps to show the proof.