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
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
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
DUE WEDNESDAY, JANUARY 29
(1) Which of the following are true and which are false?
(a) 10! = 10
(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
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
DUE WEDNESDAY, MARCH 5
(1) Find the number of integers between 1 and 10,000 inclusive that are not divisible
(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
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
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
(2) How many ways are there to select pieces of f