Chapter 4
Quantitative Thinking
Counting is important. Many problems in mathematics, computer science, and other technical fields involve counting the elements of some set of objects. But counting isn’t always easy. In this chapter we will investigate tools for counting certain types of sets, and we will learn how to think about problems from a quantitative point of view.
Figure 4.1 A typical position in chess presents the players with several different possible moves. In order to look two or three moves ahead, players must consider hundreds of combinations, and the number of distinct 40-move games seems almost limitless. Enumerating these possibilities, ...
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