MAD 4302
Quiz I and Key
Sept 11, 2013
Prof. S. Hudson
1) [30 points] Suppose a game of Nim starts with three piles, with sizes 2, 4 and 8. What
is Player Ones best move ?
2) [35 points] How many ways can a 2x8 board be tiled with dominoes ?
3) [35 points]

MAD 4302
Quiz 5
Nov 19, 2013
Prof. S. Hudson
1) [30pts] Solve this: hn = hn1 + 3hn2 + 5hn3 + 2hn4 with h0 = 1 , h1 = 0 , h2 = 1
and h3 = 2. Hint: the characteristic equation has two distinct roots, both in cfw_1, 1, 2, 3.
The larger of the two roots has m

MAD 4302
Quiz 4 and Key
Oct 24, 2013
Prof. S. Hudson
1) Show by example that the union of two equivalence relations does not have to be an
equivalence relation.
2) Answer True or False to each; you do not have to explain. Let S = cfw_1, 2, 3, 4, 5.
P (S )

MAD 4302
Quiz 2 and Key
Sept 26, 2013
Prof. S. Hudson
1) How many ways can 2 blue rooks, 2 white rooks and 2 red rooks be placed on an 8x8
chessboard so that no two attack each other ?
2) Answer True or False to each; you do not have to explain.
K5 K3 , K

MAD 4302
Final Exam
Dec 12, 2013
Prof. S. Hudson
You have approx 2 hours. Unlabeled problems are 10 points each.
1) Express the multinomial coecient
10
4321
as a product of binomial coecients.
2) How many ways can you place 5 non-attacking rooks on an 8x8

MAD 4302
Quiz 3 and Key
Oct 10, 2013
Prof. S. Hudson
1) Show that among 20 people at a party, there are two who have the same number of
acquaintances (since knowing yourself does not count, your number of acquaintances could
vary from 0 to 19).
2) How man