Tag Archives: MIU puzzle

OpenLab #4: The MIU puzzle, continued

This assignment is a continuation of OpenLab #3, on the MIU puzzle.  Your assignment this time is a little different.  Consider the following statement about the MIU puzzle:

Statement.¬† Any goal word (any word with first letter M, followed by a combination of U’s and I’s) can be obtained from the starting word MI using the rules of the MIU puzzle.

Assignment (Due Friday¬†9/25 – Because of the nature of this project, please do not post your answer before¬†Wednesday 9/23). Do you think the statement¬†above is true or false? ¬†I would like you to think about it and see if you can convince yourself of the answer. ¬†Try out different things! ¬†If one idea doesn’t go anywhere, see if you can come up with a different approach. ¬†¬†This is an assignment about metacognition as well as puzzle-solving – pay attention to your thoughts and ideas, even (especially) the ones that don’t work out!

In the assignment below, you will be writing about your experience working on the MIU puzzle above.  Be sure to respond to EACH PART Рdetailed answers to part 2 and 3 below will gain the MOST credit.

  1. Write down what you think the answer is (is the statement TRUE or FALSE?).
  2. Describe in as much detail as you can the process of working on the assignment.  What did you think in the beginning? What are the different things you tried in order to solve the problem?  Describe each one, in the order that you tried them.
  3. Give a detailed list of the resources you used, and how you used each one (these could include anything – your brain, pen & paper, a computer (what applications did you use), the internet, other people, and so on).
  4. What activity or resource do you feel was most effective for you in working on the assignment (what helped you the most in understanding the assignment and figuring out an answer)?
  5. If you believe the statement is TRUE, post an example of a goal word that you encountered in your work that you think was most difficult to solve.  If you believe the statement is FALSE, post an example of a goal word that you believe is impossible to obtain by starting with the axiomatic word MI and following the rules.

Extra Credit. ¬†Respond to one of your classmates’ submissions.

 

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.