MATH 302. Discrete Mathematics
Extra-credit Assignment 3. Due on May 5, 2009
Please show your argument and computation. Calculators and computers are not permitted.
1. How many positive perfect squares less than 106are multiples of 24?
2. Prove that Pn
k=1 kn
k=n2n−1.
3. How many ways are there to travel in xyz space from the origin (0,0,0) to the point
(100,200,300) by taking steps one unit in the positive xdirection, one unit in the
positive ydirection, or one unit in the positive zdirection? (Moving in the negative
x, y or zdirection is prohibited, so that no backtracking is allowed. )
4. Assume that in a group of six people, each pair of individuals consists of two friends or
two enemies. Show that there are either three mutual friends or three mutual enemies
in the group.
5. Let Abe a set with 100 elements. How many relations on Athat are reflexive and
anti-symmetric?
