A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Textbook Question

Chapter 1.1, Problem 4MC

Consider a game where you have two distict piles of objects.

Two players alternates moves, each player taking any number $( not 0 )$ of objects desired from a single pile.

The player who takes the last objects (so nothing is left in either pile) is the winner.

If there are $a$ objects in one pile and $b$ objects in the second, we write $( a , b )$ .

Given the game $( 1 , 1 )$ , the first player loses because if she takes $1$ from a pile, the second player takes $1$ from the other pile. Answer the following:

a. Show that the first player can win the game $( 1 , 2 )$ as well as $( 1 , 100 ) .$

b. Who will win the game $( 1 , a )$ if $a > 1$ ? Why?

c. Which player will win the games $( 2 , 2 )$ , $( 3 , 3 )$ , $( 4 , 4 )$ ?

Why?

d. Which games can the first player always win? Why?

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Chapter 1.1, Problem 3MC

Chapter 1.1, Problem 5MC

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Chapter 1 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 1.1 - Mathematical Connections 1-2 a. If a fixed number...Ch. 1.1 - Mathematical Connections 1-2 A student says she...Ch. 1.1 - Mathematical Connections 1-2 Abby and Dan are...Ch. 1.1 - Consider a game where you have two distict piles...Ch. 1.1 - Mathematical Connections 1-2 A mathematician named...Ch. 1.1 - Mathematical Connections 1-2 The figure below...Ch. 1.1 - Mathematical Connections 1-1 The distance around...Ch. 1.1 - Work in pairs on the following versions of a game...Ch. 1.1 - John asks why the last step of Polyas four-step...Ch. 1.1 - Mathematical Connections 1-2 Connecting...

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Solution Summary: The author explains that there are two distinct piles of objects. The first player wins the game (1,2) and the second player takes the last object from the pile.

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Chapter 1 Solutions