Problem Solving Through Recreational Mathematics by Bonnie Averbach & Orin Chein

Author:Bonnie Averbach & Orin Chein
Language: eng
Format: epub
ISBN: 9780486131740
Publisher: Dover Publications
Published: 2012-07-17T16:00:00+00:00

PRACTICE PROBLEMS 7.H

In each of the positions in Figure 7.45, it is your move. Do you have a winning move? If so, what is it?

FIGURE 7.45

In each of the positions in Figure 7.46, it is your move. Do you have a winning move? If so, what is it?

FIGURE 7.46

THE GAME OF NIM

While the techniques we have discussed so far in this chapter are often helpful in analyzing games, they do not always en A B L e us to reduce the necessary case analysis to manage A B L e proportions. Many games (such as chess and checkers) are still not analyzed for this reason. Sometimes, though, seemingly unrelated mathematical considerations lead us through the l a B yrinth. One such example is an application of the binary system (see Chapter 5) to the game of Nim, presented in Problem 7.3.

Before we present this application, we try to solve the problem with the techniques we have discussed so far in this chapter.

If you haven’t already solved Problem 7.3 (page 214),

try it again now.

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