Monday - Day 1

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Pre-test

Introduction

• Go over the schedule
• Go over the rules and sign contract
• About me
• Ice breaker

Decorate Notebooks

• Make sure they are right-side up
• Write a personal bio

Permutations and Combinations

• Go over the problems

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http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Permutations: How many rainbows can you draw with these colors (red, orange, yellow, green, blue)? Each rainbow can only have 3 colors, no repeated colors.

Where n is the number of things to choose from, and you choose r of them (No repetition, order matters)

n!/(n-r)!

Permutations with Repetition: Each passcode is 5 numbers long. How many passcodes are possible?

n^r

Combinations: How many ways can a group of three students be selected from a class of 21 students?

(21!)/(18!)(3!) = 1330

"n choose r"

Where n is the number of things to choose from, and you choose r of them (No repetition, order doesn't matter)

Combinations with Repetition: You get 4 scoops of ice cream, how many different combinations can you make from Chocolate, Vanilla, and Strawberry?

"(n + r - 1) choose r"

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Game Theory

• Story: Prisoner's Dilemma : Activity

• Rock Paper Scissors
• Dominant Strategy

Games

• counterfeit coins: https://www.dropbox.com/s/y4x62yr6aenfs1h/Math%20Puzzles%20and%20Games.ppt
• divide in groups of 4
  • bean game
  • x&o game
  • box game: http://www.math.ucla.edu/~tom/Games/dots&boxes.html
  • hex game

Writing Time

• What are your best strategies for each game?
• Which games are similar? How?
• What is the prisoner's dilemma?
• What did you do today?