Nim’s first game:

Begin with one pile of noodles on the table. On your turn, you take one noodle. (Last person to take one wins.)

1. If the pile has 3 noodles, do you want to go first or second? After you've made that decision, what strategy do you use?

2. What if there are 4 noodles? 5? 10? 50? 57? 248? 3. How do you decide whether to go first or second, and what

to do after that?

Nim’s second game:

This time, you can take one, two, three, or four. Answer the questions above for this game.

Nim’s third game:

Start with one pile of 8 noodles and one pile of 7. Take turns dividing one pile in two.

Nim’s Die Game:

A goal number is chosen (usually 31). The first player places the die down with some number pointing up to start the game. The number on the top is the first sum.

After the first move, players take turns making moves. A move consists of tilting the die 90 degrees in any direction. The number that ends on the top is added to the sum to get a new sum. Play continues as long as the new sum is not more than the goal. The last player to make a move wins.

Try to make tables of winning moves for any of Nim’s games.