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Statistics 155 Homework Assignment 1
1. (A subtraction game)
Consider a subtraction game in which a player can remove from 0 to 4 chips, but removing 0 chips is only allowed if the previous player removed at least 1 chip. We can model this game as the following chip-and-cup game:
There is a pile of n ≥ 0 chips and a cup that can hold either 0 or 1 chip. A legal move is to either remove from 1 to 4 chips from the pile, placing one of them in the cup if it is empty, or to remove a chip from the cup.
(a) Show that the game is progressively bounded.
(b) Find the sets N and P.
(c) Describe the winning strategy.
(a) Show that the game is progressively bounded.
(b) Find the sets N and P.
(c) Describe the winning strategy.
3. Partisan games
Karlin and Peres, Exercise 1.2.3, p22: Prove Theorem 1.2.2.