MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 1
Hints & Model Solutions
Compulsory questions
1 (a) In a maths exam, there are two sections A and B. There are 5 problems
in Section A and 8 problems in Section B; student
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 6
Hints & Model Solutions
Compulsory questions
1 We have 10 points in a square of side 3cm. Show that two of the points
are within 2cm of each other.
Divide the square into
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 5
Hints & Model Solutions
Compulsory questions
1 Let an be dened recursively by an =
a0 = 1.
n
ani (1)i1
i=1
i!
for n
1, and
(a) Find the generating function for an .
n=0
T
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 4
Hints & Model solutions
Compulsory questions
1 On a table there are 129 coins, 128 of which are fair, one of which is twoheaded (i.e. it always gives heads when it is tos
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 2
Hints & Model Solutions
Sheet 1
6 Suppose we have a cube made of n n n smaller cubes (n
2). We
call a line through the cube a set of n of the smaller cubes such that the
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 3
Hints & Model Solutions
Compulsory questions
1 (a) What is the probability that a randomly dealt 5-card poker hand is a
straight? [But not a straight-ush.]
There are 552
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 7
Due: Wednesday 19th March: 1:30 PM
Compulsory questions
1 Which of the following graphs have Euler circuits?
(a) . e
.
ee
e
e
ee
.
.
.
.
All vertices have even degree,
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 8
Due: Wednesday 26th March: 1:30 PM
Compulsory questions
1 Find minimal spanning trees for the following graphs:
(a)
15
.
12
.A 7 .
AA
AA
AA
AA 11
AA
2 AA
A
.
9
.
8
Using
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Midterm Examination
Calculators not permitted. Answers may be left in reasonably simplied
forms e.g. binomial coecients, factorials, etc. Justify all your answers.
Section A Wednesday 5th
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Midterm Examination
Calculators not permitted. Answers may be left in reasonably simplied
forms e.g. binomial coecients, factorials, etc. Justify all your answers.
Section A Wednesday 5th
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Final Examination
Saturday 19th April, 14:0017:00
Calculators not permitted. Justify all your answers.
Compulsory questions
1 (a) Write down the adjacency matrix for the graph:
. PP
PPP
P
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Homework Sheet 9
Hints & Model Solutions
Compulsory questions
1 (a) Show that if we 3-colour the complete graph on 17 vertices, we get a
monochromatic triangle.
Pick a vertex. It has 16 n
MATH 2113/CSCI 2113, Discrete Structures II
Winter 2008
Toby Kenney
Final Examination
Hints & Model Solutions
Justify all your answers.
Compulsory questions
1 (a) Write down the adjacency matrix for the graph:
. PP
PPP
PPP
PPP
PPP
PPP
PPP
P.
.
i.
~
nnn ii