CPMA 515: Advanced Discrete Math
Homework Assignment #3
Due: 2/13/2009
- Exercise #3 from page 353. Also, do the same problem for 6 pairs
of brown gloves and 6 pairs of black gloves where the person must select
a pair of gloves. Note that gloves have a left and a right whereas
socks do not.
- Exercise #36 on page 354.
- Prove that there are two trees somewhere on earth which have
exactly the same number of leaves on them (and they are not both bare
of leaves). You may make (reasonable) assumptions about trees, but
state what assumptions you have made in your answer.
- Exercise 42 on page 362
- How may strings of 10 bits are there whose longest consecutive
run of 1 bits is length 5 exactly? Can you generalize your answer
to the case where the bit string is of length M and the longest substring
of consecutive 1 bits is exactly N, subjct to the the condition that N
> M/2?
Last modified: Feb. 6th, 2009
Dr. Donald L. Simon,
simon@mathcs.duq.edu