Math 3103 Combinatorics
NAME:
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Third Quiz (take-home)
Due 10 Feb 2014
You need not simplify answers provided they are expressed using only numbers, combined by
the following operations: addition, subtraction, multiplication, division
Math 3103 Combinatorics
NAME:
(Please print clearly)
First Quiz, version A (solutions)
22 Jan 2014
1. A box labeled A contains 5 high-priced items, and a box labeled B contains 9 lowpriced items (all dierent).
(a) Suppose a contest winner is instructed to
Math 3103 Combinatorics
NAME:
(Please print clearly)
Tenth Quiz (solutions)
Due 14 Apr 2014
1. For each of the group codes below answer the questions: (i) What is the minimum distance
between code words? (ii) What is the largest number of errors that can
Math 3103 Combinatorics
NAME:
(Please print clearly)
First Quiz, version B (solutions)
22 Jan 2014
1. A box labeled A contains 6 high-priced items, and a box labeled B contains 8 lowpriced items (all dierent).
(a) Suppose a contest winner is instructed to
Math 3103 Combinatorics
NAME:
(Please print clearly)
Fifth Quiz ver. A (solutions)
24 Feb 2014
1. For each of the following rst order recurrence relations, nd the solution that satises
the given initial condition.
(a) an = 3an1 , n 1 ,
a0 = 2 .
Ans: an =
Math 3103 Combinatorics
NAME:
(Please print clearly)
Eleventh Quiz (solutions)
Due 23 April 2014
1. Write out the group G of rigid motions of the gure depicted below. It is a regular
hexagon with three of the vertices connected in an equilateral triangle.
Math 3103 Combinatorics
NAME:
(Please print clearly)
Seventh Quiz, vers. A (with solutions)
10 Mar 2014
1. The following recurrence relation has a particular solution of the form a(p) = A(3)n . Find
n
the value of A.
an 4an1 2an2 = 4(3)n
Ans: Putting an =
Math 3103 Combinatorics
NAME:
(Please print clearly)
Second Exam, version B (solutions)
19 March 2012
1. Solve the following rst order recurrence relations.
(a) an = 3an1 , n 1 ,
a0 = 4 .
Ans: an = 4(3)n
(b) an = an1 + 5 , n 1 ,
a0 = 8 .
Ans: an = 8 + 5n
Math 3103 Combinatorics
NAME:
(Please print clearly)
Final Exam, ver. B (solutions)
5 May 2014
Note: Some problems ask for the the answer in elementary form. For these you must
write your answer using only numbers, addition, subtraction, multiplication, d
Math 3103 Combinatorics
NAME:
(Please print clearly)
Final Exam, ver. A (solutions)
5 May 2014
Note: Some problems ask for the the answer in elementary form. For these you must
write your answer using only numbers, addition, subtraction, multiplication, d
Math 3103 Combinatorics
NAME:
(Please print clearly)
Ninth Quiz, vers. B (solutions)
4 Apr 2014
Write all answers on this sheet. (If you dont have room, you are writing too much, but
attach any extra sheets to this one.)
1. Consider the group S4 of all pe
Math 3103 Combinatorics
NAME:
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Third Exam (version A)
25 Apr 2014
1. Let G be the group of rigid motions of a regular hexagon (see gure below). Let
be the element of G that rotates the gure two places (120 degrees), and let H be the
Math 3103 Combinatorics
NAME:
(Please print clearly)
Seventh Quiz, vers. B (with solutions)
10 Mar 2014
1. The following recurrence relation has a particular solution of the form a(p) = A(3)n . Find
n
the value of A.
an 4an1 4an2 = 4(3)n
Ans: Putting an =
Math 3103 Combinatorics
NAME:
(Please print clearly)
Practice Quiz
14 Feb 2013
1. Consider the following equation. The variables x1 , x2 , and x3 are integers that must
satisfy the given conditions.
x1 + x2 + x3 = n
8 x1 17
12 x2
0 x3 9
(a) Write out the
Math 3103 Combinatorics
NAME:
(Please print clearly)
Fourth Quiz (solutions)
Due Feb 14 2014
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 removal wil
Math 3103 Combinatorics
NAME:
(Please print clearly)
Second Quiz (solutions)
Due 29 Jan 2014
You need not simplify your answers, but each must be expressed with numbers combined
using only addition, subtraction, multiplication, division and factorials.
1.
Math 3103 Combinatorics
NAME:
(Please print clearly)
Ninth Quiz, vers. A (solutions)
4 Apr 2014
Write all answers on this sheet. (If you dont have room, you are writing too much, but
attach any extra sheets to this one.)
1. Consider the group S4 of all pe
Math 3103 Combinatorics
NAME:
(Please print clearly)
Eighth Quiz (solutions)
Due 17 Mar 2014
Instructions: You do not need to show work unless explicitly asked to. Write your answers
and your work on this sheet. (If you dont have room, you are writing too
Math 3103 Combinatorics
NAME:
(Please print clearly)
Second Exam, version A (solutions)
19 March 2012
1. Solve the following rst order recurrence relations.
(a) an = 5an1 , n 1 ,
a0 = 6 .
Ans: an = 6(5)n
(b) an = an1 + 3 , n 1 ,
a0 = 7 .
Ans: an = 7 + 3n
Math 3103 Combinatorics
NAME:
(Please print clearly)
Sixth Quiz (solutions)
Due 5 Mar 2014
Instructions: Please write your nal answers on this sheet and as much of your work as will t.
Additional work may be written on additional sheets stapled to this on
Math 3103 Combinatorics
NAME:
(Please print clearly)
First Exam, ver. A (solutions)
17 Feb 2014
Note: Some problems ask for the the answer in elementary form. For these you must
write your answer using only numbers, addition, subtraction, multiplication,
Math 3103 Combinatorics
NAME:
(Please print clearly)
Fifth Quiz ver. B (solutions)
24 Feb 2014
1. For each of the following rst order recurrence relations, nd the solution that satises
the given initial condition.
(a) an = 5an1 , n 1 ,
a0 = 2 .
Ans: an =
Math 3103 Combinatorics (Luecking)
NAME:
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Fifth Quiz (solutions)
Due 19 Feb 2016
1. In the following equation, n is an integer and the variables x1 , x2 and x3 are integers that
must satisfy the given conditions. Write down the gener