Combinatorics - MATH 0345
Exam 1
October 13, 2006
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Directions: Please complete all but 1 problem. There is a time limit of 2 hours.
1. Show that a magic square of order 3 must have a 5 in the middle position. Deduce
that t
Combinatorics - MATH 0345
Exam 2
April 16, 2009
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Directions: Please complete all but 1 problem. If you complete all six problems, I
will count your best ve.
1. Prove that
n1 +n2 +n3 +n4 =n
n
(1)n1 n2 +n3 n4 = 0,
n1 n2 n3
Combinatorics - MATH 0345
Exam 3
May 18, 2009
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Directions: Please complete all but one problem.
1. Prove that the addition table of Z4 is a Latin square without an orthogonal mate.
2. How many 2 by n Latin rectangles have
Combinatorics - MATH 0345
Exam 3
December 18, 2006
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Directions: Please complete all but 1 problem. If you complete all seven problems, I
will count your best six.
1. Solve the following recurrence relation by examining the
Combinatorics - MATH 0345
Exam 2
November 17, 2006
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Directions: Please complete all but 1 problem. If you complete all six problems, I
will count your best ve.
1. Let n and k be positive integers. Give a combinatorial proo
MATH 345 - Fall 12
Problem Sets
1. Due September 17: Pages 2025 numbers - 2, 4(a), 16, 17, 32, 38
For n = 4, 5 calculate the number of ways of returning n hats to n people so that
each person is wearing the wrong hat. In each case calculate the ratio of t
Combinatorics - MATH 0345
Exam 1
March 12, 2009
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Honor Code Pledge:
Signature:
Directions: Please complete ALL the problems. There is a time limit of 25 r(3, 3)
minutes.
1. Consider an n-by-n board and L-tetrominoes (4 squares joined in the shape of