Monthly Archives: October 2013

OpenLab #4: The MIU puzzle, continued

UPDATE: See the “Assignment Version 2” added below.

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

Conjecture. ¬†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 Thursday 11/14.  Submit your answer between Tuesday, 11/12 and Thursday, 11/14). Is the conjecture above true?  If so, prove this fact.  If not, provide an example of a goal word that cannot be obtained, and prove that it is impossible for your word to be obtained.

IMPORTANT: Because of the nature of this assignment, DO NOT SUBMIT YOUR ANSWER BEFORE  TUESDAY 11/12. However, I strongly recommend getting started on this problem well before that date!


If you wish, you can respond to the assignment below INSTEAD of completing the assignment above.  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 Рno proof necessary.
  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)?

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



Improve your grade on Exam #2.

You can earn additional points towards your Exam #2 grade by completing the following assignment.

Due Thursday, 11/7.  Choose TWO problems from Exam #2 (Hint: choose the two problems that you did worst on).  Re-do these problems.  Hand in all the following, STAPLED TOGETHER, on Thursday 11/7:

  1. For each of the two problems:
    1. Clearly state how many points you received on each problem.
    2. Give an explanation consisting of at least one complete sentence explaining your error, and how you fixed it.
    3. Give a complete, correct solution to the problem.
  2. Hand in your exam paper along with your corrections.

You will be able to earn up to half the points you missed on the two selected problems, to be added back into your Exam #2 score.

Example.  Suppose you received 68 on the exam.  You choose problem #3 (scored 8 points out of 20), and problem #5 (scored 4 points out of 20).  You complete the assignment perfectly.  Since you missed a total of 28 points on these two problems (12 on problem 3, and 16 on problem 5), you will have 14 points added to your exam score.

Homework Week 10

Homework Week 10
Written work¬†–¬†Chapter 8 p143: 3, 8, 18, 19, ¬† ¬†Chapter 9 p150: 3, 4, 5 (Due Tuesday 11/5)
WeBWorK Рnone
OpenLab РOpenLab #4, The MIU puzzle continued, is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14.  (The assignment will be posted after class on Tuesday 10/29.)

Office hours today

I will be available between 2pm Р3pm today in my office N707.  My usual office hours (11:15-1:15) are canceled.


Prof. Reitz

IMPORTANT – Bring Written Work Chp 4-5 to class on Thursday

Hi everyone,

If you picked up your (graded) written work from Chapters 4 and 5 today, please bring it with you on Thursday to class — I need to record your score in my gradesheet, or you will not get credit for the assignment. ¬†Oops!


Prof. Reitz

Exam 2 Review UPDATE

Hi everyone,

Two things about the review sheet:

1. ¬†There is a typo in problem #5c — it should read |X|=3, instead of |A|=3.

2. As I told a number of you in my office today, I will NOT put a problem like #12 (There is no largest prime number) on the exam.

Best of luck with your studying,

Mr. Reitz

Homework Week 9

Homework Week 9
Written work РChapter 7: One odd-numbered problem and one even-numbered problem of your choice from Chapter 7, p127.
WeBWorK Рnone
OpenLab Р(reminder: OpenLab #3, assigned last week,  is due Tuesday 10/29).

Office hours Tuesday 1-2 by request

Hi everyone,

If you have questions for me BEFORE the exam on Thursday, I can be available tomorrow (Tuesday) between 1 and 2 pm, BUT only if you notify me ahead of time (by email, or by leaving a comment here, or by telling me in class tomorrow).

Best of luck with your studying,
Prof. Reitz

Exam Review 2 UPDATE – review of division and remainders

Hi everyone,

First, the answer key for the Exam 2 review is now complete (it follows the questions in the Review document).  Second, you will notice that there are a few places (especially in problems 8 and 12) that I use basic facts about remainders when one number is divided by another.  These are facts that you understand intuitively from working with dividing numbers, but it might help to have them stated explicitly.  This is the basic fact about dividing and remainders:

Fact (The Division Algorithm).  Given two integers a and b with b>0, there exist unique integers q and r for which a=qb+r and 0\leq r <b.

What does this mean?  It expresses the fact that when we divide one integer a by another integer b, and it will go in some number of times q with a remainder of r.  The remainder r must be less than the number b that we are dividing by.  If the remainder is zero, then b divides a (because r=0 means a=qb), and if the remainder is not zero, then b does not divide a.

If you have any questions, feel free to leave a comment here.  Best of luck with your studying!

-Prof. Reitz

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 that you may:

  1. Add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
  2. Double any string after the M¬†(that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
  3. Replace any III with a U. For example: MUIIIU to MUUU
  4. 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:
MI to MII (rule 1)
MII to MIIU (rule 2)

Assignment (due Tuesday, 10/29): 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. ¬†Try to create a goal word that balances the following two requirements:

  1. The goal word should not be too long – definitely not more than 10 letters (but the shorter the better).
  2. The goal word should be 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.