HOMEWORK 1
DUE WEDNESDAY, JANUARY 22
(1) A combination lock has a combination that consists of three integers, not necessarily distinct, from 0 to 39. Find the number of possible lock combinations.
(2) Find the number of seven-letter words that use letter
HOMEWORK 4
DUE WEDNESDAY, FEBRUARY 12
(1) Prove that for each positive integer n, then number (2n)! is divisible by (n!)2 .
(Hint: show that the ratio of these two numbers must be an integer.)
(2) A tennis club has 2n members. We want to pair up the membe
HOMEWORK 3
DUE WEDNESDAY, FEBRUARY 5
(1) There are currently 55 Fort Lewis students taking Calculus III. Each student has
a 9 digit student ID that starts with 900. Show that there must be two students
in Calc III whose student ID numbers have the same su
HOMEWORK 2
DUE WEDNESDAY, JANUARY 29
(1) Which of the following are true and which are false?
(a) 10! = 10
9!
(b) 4! + 4! = 8!
(c) 2! 1! = 1!
(d) n! = n(n 1)! for n > 1
(e) n! = (n2 n)(n 2)! for n > 2
(2) Determine the largest power of 10 that is a factor
HOMEWORK 5
DUE: WEDNESDAY, FEBRUARY 26
(1) (a) Find the coecient of x3 y 2 z 4 w in the expansion of
(x + y + z + w + v )10
(b) Find the coecient of x3 y 3 zw2 in the expansion of
(x y + 2z 2w)9
(2) Consider a three-dimensional grid whose dimensions are 1
HOMEWORK 6
DUE WEDNESDAY, MARCH 5
(1) Find the number of integers between 1 and 10,000 inclusive that are not divisible
by
(a) 4, 5 or 6
(b) 4, 6, 7, or 10.
(2) Find the number of integers between 1 and 10,000 that are neither perfect squares
nor perfect
PROJECT 3: COMBINATIONS AND LOCKS
The Simplex company makes a combination lock that is used in many public buildings.
These 5-button devices are purely mechanical (no electronics). You can set the combination
using the following rules:
A combination is a
PROJECT 2: SET
The game Set is based on an unusual deck of cards in which each card has four
dierent properties: Color, Number, Shape and Texture. Each property can have one
of the three distinct values. Each of the 81 possible combinations of these prope
PROJECT 1: CHINESE DICE
In an ancient Chinese game, players roll six 6-sided dice in a single throw. Players
place bets, categorizing the results according to the number of dice that show the
same value, rather than the value itself. For example the throw
HOMEWORK 7
DUE MONDAY, MARCH 17
(1) How many ways are there to pick 2 books, not both on the same subject, from
5 algebra books, 7 geometry books, and 4 calculus books, where the books are
distinguishable?
(2) How many ways are there to select pieces of f