Day 02: Heart of Mathematics

First of all, what do you think of the book? (First Impressions)
Your mission (should you have chosen to accept it):

read Section 1.1, and start #1, 3, 4, 5, 7, 8.
You were allowed a gander at hints (1.2), but were not to peek at solutions (1.3).
Today is not about "solutions", but rather about process: how have you attempted to solve (and possibly succeeded at solving) these problems?
Before we talk about individual games, however, let's vote: the fun and games were:

Genie Fountain Trou Dodge Deal Dot

Favorite

Least Favorite

Solved
What made these puzzles hard? easy? fun?
What strategies did you employ to attempt to solve them?
Did you find the hints helpful (if you used any)? If so, which ones?
Which "lessons for life" 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.

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