Fall 2006 Math 510 HW3 Solutions
Section 3.6
10. A committee of 5 is to be chosen from a club that boast a membership of 10 men and 12
women. How many ways can the committee be formed if it has to have at least 2 women? How
many ways if, in addition, one
Spring 2007 Math 510 HW6 Solutions
Section 6.7
21. Prove that Dn is an even number if and only if n is an odd number.
Proof. Note that Dn = nDn1 + (1)n . We will use induction on n. When n = 1, then D1 = 0
is even and when h = 2, D2 = 1 is odd. Assume tha
Spring 2007 Math 510 HW5 Solutions
Section 6.7
2. Find the number of integers between 1 and 10,000 inclusive which are not divisible by 4, 6, 7,
or 10.
Solution. Let S = cfw_1, 2, . . . , 10000. Set
A1 = the set of numbers in S that are divisible by 4;
A2
Spring Math 510 Exam II
12:30pm1:20pm, Wednesday, April 11, 2007
Total Score:
/100
Name:
Please read the problems carefully and do all you are asked to do. You need to show your work to indicate
how you do each problem. Your proofs and explanation should
Spring 07 Math 510 HW Solution I
Section 2.4
1. Concerning Application 4, show that there is a succession of days during which the chess
master will have played exactly k games, for each k = 1, 2, , 21. (The case k = 21 is treated in
Application 4.) Is it
Math 510 Exam I
Time: 12:30pm1:20pm, Monday, Feb. 26, 2007
Name:
Please read the problems carefully and do all you are asked to do. You need to show your work to indicate
how you do each problem. Your proofs and explanations should be literally clear.
1.
Spring 2007 Math 510 HW7 Solutions
Section 7.8
12. Solve the recurrence relation hn = 4hn2 (n 2) with initial values h0 = 0 and h1 = 1.
Solution. Rewrite the relation into hn + 0hn1 4hn2 = 0. The characteristic equation is
x2 4 = 0 with characteristic roo
Spring 2007 Math 510 HW8 Solutions
Section 9.5
2. Consider the chessboard B with forbidden positions shown. Construct the domino-bipartite
graph G associated with B . Find a matching of 10 edges in G and the associated perfect cover of
the board by domino
Spring 2007 Math 510 HW4 Solutions
Section 5.8
3. Consider the sum of the binomial coecients along the diagonals of Pascals triangle running
upward from the left. The rst few are: 1, 1, 1 + 1 = 2, 1 + 2 = 3, 1 + 3 + 1 = 5, 1 + 4 + 3 = 8.
Computer several
Spring 2007 Math 510 HW11 Solutions
Section 11.8
18. Let be a trail joining vertices x and y in a general graph. Prove that the edges of can be
partitioned so that one part of the partition determines and chain joining x and y and the other
parts determin
Spring 2007 Math 510 HW11 Solutions
Section 12.3
4. Give an example of a digraph that does not have a closed Eulerian directed trail but whose
underlying graph has a closed Eulerian trail.
Solution. Take the graph G as the complete graph with three vertic
Spring 2007 Math 510 HW10 Solutions
Section 11.8
2. Determine each of the 11 non-isomorphic graphs of order 4 and give a planner description.
Solution.
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