Homework for Week 2

This homework deals with the game we played in class this week. Specifically, you and your friend are adding 1 and 2 cent stamps to a package, and whoever reaches 7 cents first looses.

1. There is a way to always win at this game, no matter what your friend does, but only if you go second. Figure out what this winning strategy is.
2. If the rate is increased to 15 cents, there is still a way to always win, but do you need to go first or second to guerentee a win?
3. If you now can use 1, 2, and 3 cent stamps to add up to 15 cents, what strategy can you use to always win?