Math576 Combinatorial Game Theory
Homework 4 Solution
1. Two players play a subtraction game S (2, 5, 6) of three heaps of sizes 7, 8, 9.
Who wins this game? What is the best move for the rst player?
Solution: The subtraction game S (2, 5, 6) has the nim
Math576 Combinatorial Game Theory
Homework 2 solutions
1. Let C (2, n) be the game value of the rectangle 2 n in the Cut Cake game.
Prove C (2, n) = n 1 for all n 2.
2
Proof: We use induction on n.
Initial cases, n = 1, 2. We have
C (2, 1) = cfw_| 2C (1,
Math576 Combinatorial Game Theory
Solution of Homework 1
1. Draw two red-blue Hackenbush games with the same game value 1 1 .
4
Solution:
2. State the simplicity rule. Use it to nd the following game values:
(a) cfw_
1
1
|3
2
2
1
(b) cfw_2, 1 |
4
(c) cf
Name:
Score:
Math 576 Combinatorial Game Theory
Exam 1
March 19, 2013
1. (15 points) Indicate whether the following statements are true or false by circling T
or F . Here true means always true and false means sometimes false. Explanations are
not require