Homework # 1 - Math 2236
The problems on this homework must be done alone. The honor code is in effect.
You may submit the solutions twice, if you wish.
First Name: Last Name:
Questions 1 - 11 deal with the 12 coins puzzle. For the sake of convenience, we'll number the coins 1 through 12.
1. Before you use the scale the first time, how many possibilities are there? For instance, one possiblility is that the counterfeit coin is coin number 1, and that it's heavier than all the other coins. Another possibility is that coin 1 is the counterfeit, and that it's lighter than all the other coins.
a. 6
b. 12
c. 18
d. 24
e. 30
2. If you begin by weighing coin 1 on one side and coin 2 on the other side, and coin 1 is heavier, how many possibilities are left?
a. 1
b. 2
c. 3
d. 4
e. 5
3. If you begin by weighing coin 1 on one side and coin 2 on the other side, and they balance, how many possibilities are left?
a. 5
b. 10
c. 15
d. 20
e. 25
4. At most, how many possibilities can be left after your first weighing, no matter what happens,so that you have a hope of solving the problem?
a. 3
b. 6
c. 9
d. 18
e. 27
5. Based on your answers for questions 2-4, is it possible that a solution to this problem can begin by weighing one coin on one side with one coin on the other side as the first weighing?
a. Yes.
b. No.
6. If you begin by weighing coins 1 and 2 on one side and coins 3 and 4 on the other side, and coin 1 and 2 are heavier, how many possibilities are left?
7. If you begin by weighing coins 1 and 2 on one side and coins 3 and 4 on the other side, and they balance, how many possibilities are left?
a. 8
c. 16
e. 24
8. Based on your answers for questions 6, 7, and 4, is it possible that a solution to this problem can begin by weighing two coins on one side and two coins on the other side as the first weighing?
9. If you begin by weighing coins 1, 2, and 3 on one side and coins 4, 5, and 6 on the other side, and coin 1, 2, and 3 are heavier, how many possibilities are left?
a. 2
b. 4
c. 6
d. 8
e. 12
10. If you begin by weighing coins 1, 2, and 3 on one side and coins 4, 5, and 6 on the other side, and they balance, how many possibilities are left?
d. 10
11. Based on your answers for questions 9, 10, and 4, is it possible that a solution to this problem can begin by weighing three coins on one side and three coins on the other side as the first weighing?