OpenLab #3: The MIU puzzle

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. The MIU game asks one to start with the “axiomatic” word MI¬†and transform it using the following four rules, to obtain some “goal” word. ¬†The rules state:

  1. You must always begin with the word MI, and attempt to reach the goal word.
  2. You may add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
  3. You may double any string after the M¬†(that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
  4. You may replace any III with a U. For example: MUIIIU to MUUU
  5. You may remove any UU. For example: MUUU to MU

WARM UP.  In each example, 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 1: Goal word MIU
Example 2: Goal word MIIU
Example 3: Goal word MIIUIIU
Example 4: Goal word MUUII
Example 5: Goal word MUUIIUIIU

Here is a sample solution to Example 2:
Our goal is to reach the word MIIU.  According to rule 1, we begin with
MI to MII (rule 3)
MII to MIIU (rule 2)

Assignment (due Thursday, 10/17): Your assignment has three parts.

PART 1. ¬†First, create an MIU puzzle — that is, make up a goal word, and post it in the comments. Your¬†goal word should be between 8 and 16 letters long. ¬†Try to make it¬†tricky to reach, requiring at least four steps to reach (but the more the better!). ¬†See if you can find a clever use of the rules!

PART 2. ¬†The second part of your assignment is to solve someone else’s puzzle. ¬† 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, MIU puzzle: ¬†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.

29 thoughts on “OpenLab #3: The MIU puzzle

    1. try to solve abdelmajid’s puzzle MUIIIIUUIIIIU
      MI – MII (RULE 3)
      MII – MIIII (RULE 3)
      MIIII – MUI (RULE 4)
      MUI – MUIU (RULE 2)
      MUIU – MUIUUIU (RULE 3)
      MUIUUIU – MUIIU (RULE 5)
      MUIIU – MUIIUUIIU (RULE 3)
      MUIIUUIIU – MUIIIIU (RULE 5)
      MUIIIIU – MUIIIIUUIIIIU (RULE 3)
      MUIIIIUUIIIIU – MUIIIIIIIIU (RULE 5)
      MUIIIIIIIIU – MUIIIIIIIIUUIIIIIIIIU (RULE 3)
      MUIIIIIIIIUUIIIIIIIIU – MUIIIIIIIIIIIIIIIIU (RULE 5)
      MUIIIIIIIIIIIIIIIIU – MUIIIIUUIIIIUU ( RULE 4)
      MUIIIIUUIIIIUU – MUIIIIUUIIII( RULE 5)
      MUIIIIUUIIII – MUIIIIUUIIIIU ( RULE 2)

      1. Unless I’m crazy, I think you actually got to the solution after only 9 steps — the line reading:
        MUIIIIU ‚Äď MUIIIIUUIIIIU (RULE 3)
        seems to contain the answer, so no need to go farther. Great work, Xiong!

  1. I really enjoyed this puzzle because It really challenged my mind and encouraged me to think more and focus, aplaying rules and thinking of getting a head in the puzzle at the same time is really challeging. I think there is a connection between this puzzle and union and intersection of intervals for instance replacing the string III by U the same as replacing the intervals [1,2] [2,3] [3,4] by one interval [1,4].

    1. Part 2 Solving MUIIIIUUIIIIU
      S1: MUI – rule 2
      S2: IIIU – rule 2
      S3: UI – rule 2
      S4: IIIU – rule 2

      Part 3
      I did enjoy this assignment! It was quite different and abnormal to me since I’ve never played a game like such. I think this game is relevant to what we learn and do in class since it forces one to think of side of the box. Similarly, to the in class do-now questions where the ant and pole question were given to us, making one really wonder what the logic of a question is.

    2. MI
      MII – rule 2
      MIIII -rule 2
      MIIIIIIII – rule 2 (8 I’s)
      MIIIIIIIIIIIIIIII – rule 2 ( 16 I’s)
      MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII -rule 2 (32 I’s)
      MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIu – rule 1 (32 I’s and one u)
      MIUIUIIIUUUUUU -rule 4
      MIUIUIIIUU – rule 5

    3. Solving Rahat word goal: MIUIUIIIUU
      MI – MII (RULE 3)
      MII – MIIII (RULE 3)
      MIIII-MIIIIIIII (RULE 3)
      MIIIIIIII-MIIIIIIIIIIIIIIII (RULE 3)
      MIIIIIIIIIIIIIIII-MIUIUIIIUU (RULE 4)

  2. Goal Word: MUIUIIUIIUIIUIU

    I really love this game, it is very tricky but not so hard. It was nice to play around with the rules and create conjectures as to what could and could not be done. I think this game is similar to proofs, because like proof we must know the rules and follow those rules. In general, I enjoy playing this game.

    1. MI -> MII Rule 3 (2 I’s)
      MII -> MIIII Rule 3 (4 I’s)
      MIIII -> MIIIIIIII Rule 3 (8 I’s)
      MIIIIIIII -> MIIIIIIIIIIIIIIII Rule 3 (16 I’s)
      MIIIIIIIIIIIIIIII -> MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Rule 3 (32 I’s)
      MIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII -> MUIUIIUIIUIIUIUUU Rule 4 (8 U’s 8 I’s)
      MUIUIIUIIUIIUIUUU -> MUIUIIUIIUII Rule 5 (6 U’s 8 I’s)

      Good game. GG

  3. part 1) my goal word is MUIIUUIIU

    part 3) I enjoyed this assignment because it required me to understand that I can use the rules in different ways to get something I wanted. This assignment is like what we do in class because we needed to understand that there is no one way to answer a question. Also much like what we do in class we are required to use all of the information provided to us with all of the information we already have.

    1. Im solving rayn puzzzle:
      His Goal Word: UIIUUIIU
      My solution to it :
      MI TO MII RULE 3
      MII TO MIII RULE 3
      MIIII TO MIIIIU RULE 2
      MIIIIU TO MIIIIUIIIIU RULE 3
      MIIIIUIIIIU TO MUIUUIU RULE 4
      MUIUUIU TO MUIUUIUUIUUIU RULE3
      MUIUUIUUIUUIU TO MUIIUUIIU. RULE 5

  4. Part 1 Puzzle : MIUIIUIIU

    Part 3: This reminds me of my Java class back in high school where String generation was one of the assignments. Sometimes the rules would intertwine in such a mess that we called it “spaghetti” code. I think this game helps to break down a problem into a variety of steps starting with what we know and then what we can do with what we know. I feel like that’s really the basis of any math problem proof and algorithm.

    1. Hi, chen, I tried to solve your puzzle. I tired many times…Could you give me a hint: how may steps did you actually use?

  5. 1ÔľČ My goal word is: MUIUIUIUIU

    3) I enjoyed this assignment because it is tricky. At first, I thought it was a complicated assignment as there are so many words to read. However, it is getting interesting when I really get myself in this string question. This makes me think of the “loops” in my CST class that requires us to go back to the prior steps. In this class, we also need this kind of thinking. When we could not get a solution at the end, we had to go back to check what else we can do to get the problem solved.

  6. Part 1: MUUIUIUUIUI
    Part 3: I really enjoyed this assignment. I have loved puzzles ever since I was little and with this assignment I got to create one as well as solve the ones others have created. It allows our minds to really think any try and find a pattern. This assignment is related to what we do in class because we try and solve things in class and derive the solutions by really thinking about the big picture.

  7. Part 1: MUUIIIIIU

    Part 3: I have always enjoyed puzzles since I was like 3 years old. This assignment was amazing because it challenged me and it requires you to think hard to make a puzzle as hard as possible. I believe this has a connection with logics, a topic we will cover soon. I’m not sure why it’s just a gut feeling.

    1. MI- step 1
      MII- R3, double
      MIIII- R3, double
      MIIIIIIII- R3, double
      MUUII- R4, replace III with U x2
      MUUIIUUII- R3, double
      MUUIIII- R5, remove UU
      MUUIIIIUUIIII- R3, double
      MUUIIIIIIII- R5, remove UU
      MUUIIIIIU- R4, replace III with U

  8. Part I
    MUIIUIUUIUIIUUU

    Part III
    Initially I found this puzzle challenging. However, once I became accustomed to the rules it is meticulous but relatively simple. I believe this is to have us become more comfortable with using a series of simple steps to do complex operations. This will come in handy the further we delve in to logic along with many other areas of mathematics.

  9. Part 1 : MIIUIIUIIUIIU

    I do not like to complain but it was not that bad. I am not smart enough to make a tricky puzzle. Comparing this with class work has similar of critical of thinking creative way to find a pattern that can be proven.

  10. I’m sorry for late comment on open lab#3, when i got home planed to post I crashed for 12 hours.
    Part 1: MIUIUUIIIIIIUUIIIIIIUIIIU

    Part 2: To Joe post: MUUIIIIIU -> MUUIIUU-> MUUII-> MI?

    Part 3: I enjoy this assignment, because all option change for “III” and removable for “UU” it can be confusing for everyone. I admit while making my puzzle I can confused myself couple times, because all combination tricks I can move into it. It relate to topic we doing today on 9/17/2015, when trying see between true or false and statements can be either one. The statement are so outrages you see it trick with words same this puzzle.

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