Nim: Serious Math with a Simple Game Book

Children will practice inductive thinking as they find winning strategies for 22 variations on the game of NIM. All they need is this book and a pile of paperclips, buttons, checkers, or whatever is handy. Students begin by learning the five rules of the Basic Game of NIM:1. There is 1 pile of objects. 2. There are 13 objects. 3. There are 2 players. 4. Players take turns removing either 1 or 2 objects from the pile. 5. Whoever takes the last object loses.As students play, the book’s thoughtful questions lead them to discern the game’s winning strategy. Students then consider variations. They may play with 15, 20, 30, or more objects in the pile. They may allow players to “Take 1, 2, or 3” or “Take 1, 2, 3, or 4” objects from the pile. They may experience the power of generalization when they formulate the winning strategy for all games of the type “Take 1, 2, . . ., max.” They may play games with two or more piles. Advanced students may even change the number of players. Winning strategies involve patterns and sequences. Young students may describe a sequence of winning numbers as “starting at one and counting up by threes.” Older students may use algebra to describe “numbers of the form 3n+1,” or use modular arithmetic to refer to “numbers equivalent to 1 in modulo 3.” Advanced students analyzing a 3-player game may use probability to determine which moves are more likely to win. The book provides attractive game rules to give to students, leading questions for teachers to ask, and complete descriptions of strategies. These games are enjoyed by a wide range of students.Read More