Solutions to Mini-Quiz Mar. 17
Problem 1 (8 points).
Starting with some number of 4-cent and 7-cent stamps on the table, there are two ways to change
the stamps:
(i) Add one 4-cent stamp, or
(ii) remove two 4-cent AND two 7-cent stamps (when this is possi
Final Examination
Your name:
This exam is closed book except for a three page, 2-sided crib sheet. Total time is 3 hours.
Write your solutions in the space provided with your name on every page. If you need more
space, write on the back of the sheet c
Mini-Quiz May 5
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on th
Solutions to Mini-Quiz Feb. 17
Problem 1 (5 points).
Prove that log4 9 is irrational. Your proof should be clear and well-organized, and should explicitly
indicate where particular properties of primes are assumed.
Solution. Proof. Suppose to the contrary
Mini-Quiz Apr. 21
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on
Solutions to Mini-Quiz May 5
Problem 1 (6 points).
You would like to give a bouquet for Mothers Day. You nd an online service that will make
bouquets of lilies, roses and tulips, subject to the following constraints:
there must be at most 3 lilies,
ther
Mini-Quiz Apr. 7
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on t
Mini-Quiz Mar. 17
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on
Solutions to Mini-Quiz Apr. 21
Problem 1 (13 points).
The queen and king of hearts decide to host a poker game and invite their six fellow royals the
queen and king of clubs, diamonds, and spades. The queen of hearts has a round table with eight
chairs P1
Mini-Quiz Mar. 3
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on t
Solutions to Mini-Quiz Mar. 3
Problem 1 (6 points).
Each year, Santas reindeer hold Reindeer Games, from which Rudolph is pointedly excluded.
The Games consist of a sequence of matches between pairs of reindeer. Draws are not possible.
On Christmas Eve, S
Mini-Quiz Feb. 17
Your name:
This quiz is closed book. Total time is 25 minutes.
Write your solutions in the space provided. If you need more space, write on the back of the
sheet containing the problem. Please keep your entire answer to a problem on