Day 03: Heart of Mathematics

	Genie	Damsel	Fountain	Trou	Dodge	Weave	Deal	Dot
Favorite	2		7		1			2
Least Favorite			1	5	1		3	2
Lamest Setup
Feeblest Puns
Solved	8		12	1	7		5	5

Any dramatic changes following our discussion from last time?

• Easy: some of them have starred in movies, or have popped up in life before.

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.

• We drew a conclusion from the data last time:

  Students tend to like problems they can solve and dislike problems they can't solve.

  Correlation coefficients measure this, and in your case, the correlation between liking problems and solving them is .86 (strongly positive), whereas the correlation between disliking problems and solving them is -.82 (strongly negative).

• We've seen that "Trou" can be solved by playing with a mathematical model.
• 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?)

• How can one take an experimental approach to solving the "Let's make a deal" problem?
• What element of psychology figures into the "Dot" problem? (It's the reason that I join 2 of you in disliking this problem!)
• Genie?
• Damsel?
• Fountain?
• Weave?