2016 AMC 10A Problems/Problem 13
Contents
Problem
Five friends sat in a movie theater in a row containing 
seats, numbered 
to from left to right. (The directions "left" and "right" are from the point of view of the people as they sit in the seats.) During the movie Ada went to the lobby to get some popcorn. When she returned, she found that Bea had moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada been sitting before she got up?
Solution 1
Bash: we see that the following configuration works.
Bea - Ada - Ceci - Dee - Edie
After moving, it becomes
Ada - Ceci - Bea - Edie - Dee.
Thus, Ada was in seat 
.
Solution 2
The seats are numbered 1 through 5, so let each letter (
) correspond to a number.
Let a move to the left be subtraction and a move to the right be addition.
We know that 
. After everyone moves around, however, our equation looks like 
because 
and 
switched seats, 
moved two to the right, and 
moved 1 to the left.
For this equation to be true, 
has to be -1, meaning 
moves 1 left from her original seat. Since is now sitting in a corner seat, the only possible option for the original placement of is in seat number 
.
See Also
| 2016 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2016 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 9 |
Followed by Problem 11 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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