Day 03: Heart of Mathematics

Announcements:
- Books are on their way! The off-campus book store should have 8 copies by Tuesday at the latest.
- Assignment (for next time): Read section 1.4 and attempt #2, 5, 7, 8, 9, 14 for discussion. This assignment will be handed in: write up solutions for each (or at least progress, if you can't solve them!). What did you try? What worked? Etc. Be verbose!
Since folks don't have their books yet, it's not possible for everyone to have perused the book and made their section selections. I'll postpone that for another week (due Friday), and take control of next week's material myself.
I would like, however, to collect any "section requests" that have been done, so that I can begin deciding how we're going to proceed.
Our mission today: consider solutions of the puzzles.
Okay, be honest: how many of you have peeked at the solutions?
Before we talk about individual games, however, let's vote: the fun and games were:

Genie Damsel Fountain Trou Dodge Weave Deal Dot

Favorite 6 5 8 0 2 0 1 5

Least Favorite 0 0 0 3 8 5 9 1

Solved 10 5 7 2 3 0 4 6
What questions remain?
Any "lessons for life" which were helpful?:
1. Just do it.
2. Make mistakes and fail, but never give up.
3. Keep an open mind.
4. Explore the consequences of new ideas.
5. Seek the essential.
6. Understand the issue.
7. Understand simple things deeply.
8. Break a difficult problem into easier ones.
9. Examine issues from several points of view.
10. Look for patterns and similarities.
Solutions and strategies:
- "Let's make a deal" problem: empirical probabilities?
  
  stick switch
  
  totals 42 98
  
  fraction 0.3 0.7
  
  fraction expected 1/3=.33333 2/3=.66667
- Dodge can always be won by player two, using a process of reversing the diagonal element chosen by player one. It's a fixed game.
  - Consider modifications to the original game? (Some modification of an existing problem might make a good project....)
    - Constrain choices (e.g. must use 3x and 3o)
    - Whoever starts loses...
  - Consider extreme cases? (What's special about 6?)
- Trou - demonstration using model
- Genie
- Fountain
- the "Dot" problem
- Damsel and Weave?

Website maintained by Andy Long. Comments appreciated.

	Genie	Damsel	Fountain	Trou	Dodge	Weave	Deal	Dot
Favorite	6	5	8	0	2	0	1	5
Least Favorite	0	0	0	3	8	5	9	1
Solved	10	5	7	2	3	0	4	6

	stick	switch
totals	42	98
fraction	0.3	0.7
fraction expected	1/3=.33333	2/3=.66667