Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
First Quiz (solutions)
25 Jan 2016
You do not have to simplify these numerical answers, but you must present your answer
using only numbers and the operations of addition, subtraction, multip

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Fourth Quiz (solutions)
16 Sep 2016
1. Find the rook polynomial of the following chessboard. Write it as a sum of terms
consisting of numbers times powers of x. Hint: pick a square whose remo

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Second Quiz (solutions)
7 Sep 2016
You do not have to simplify these numerical answers, but you must present your
final answer using only numbers and the operations of addition, subtraction,

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Fifth Quiz (solutions)
Due 23 Sep 2016
1. In the following equation, n is a nonnegative integer; the variables x1 , x2 , x3 , x4 and x5
are integers that must satisfy the given conditions. Wr

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Sixth Quiz (solutions)
5 Oct 2016
1. For each of the following first-order recurrence relations, find the solution that satisfies
the given initial condition.
(a) an = an1 + 3 , n 1 ,
a0 = 4

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Third Quiz (solutions)
Due 12 Sep 2016
You do not have to simplify these numerical answers, but you must present your answer
using only numbers and the operations of addition, subtraction, mu

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Practice Quiz (solutions)
1. Answer the following questions for the ring Z15
(a) Which elements of this ring are units?
(b) Which elements are proper zero divisors?
(c) Which element is the n

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Sixth Quiz B (solutions)
2 Mar 2016
1. For each of the following first-order recurrence relations, find the solution that satisfies
the given initial condition.
(a) an = an1 + 4 , n 1 ,
a0 =

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Ninth Quiz (solutions)
Due 18 Mar 2016
Find the generating function F (x) for the sequence an that satisfies the following
recurrence relation with the given initial conditions:
an 3an1 + 2an

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Eighth Quiz A (solutions)
16 Mar 2016
Instructions: You must simplify all answers completely. For example, in the ring Z10 , for
6 + 6 you would write 2.
All uses of + and refer to the operat

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Seventh Quiz (solutions)
Due 9 Mar 2016
1. For each of the following second order recurrence relations, find the solution that satisfies
the given initial conditions. If complex roots occur,

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Fourth Quiz A (solutions)
12 Feb 2016
1. Find the rook polynomial of the following chessboard. Write it as a sum of terms
consisting of numbers times powers of x. Hint: pick a square whose re

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
First Exam A (solutions)
22 Feb 2016
Note: If a problem states that the answer must be in elementary form, that means you
must write your answer using only numbers, addition, subtraction, mul

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Third Quiz (solutions)
Due 8 Feb 2016
You do not have to simplify these numerical answers, but you must present your answer
using only numbers and the operations of addition, subtraction, mul

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
Second Quiz A (solutions)
1 Feb 2016
You need not simplify numerical answers, but you must present your answer using only
numbers and the operations of addition, subtraction, multiplication,

Math 3103 Combinatorics (Luecking)
NAME:
(Please print clearly)
First Quiz (solutions)
29 Aug 2016
You do not have to simplify these numerical answers, but you must present your final answer using only numbers and the operations of addition, subtraction,