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 word MI¬†and transform it using the following rules, to obtain some goal word (which is given to you). ¬†The rules state:

  1. You must always begin with the word MI.
  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

Example: Goal word MUI
Step 1: MI  (we always start with this word)
Step 2: MI to MII (rule 3)
Step 3: MII to MIIII (rule 3)
Step 4: MIIII to MUI (rule 4)

Assignment (due Thursday, 9/15): 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.