1990 AJHSME Problems/Problem 19
Problem
There are 
seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
Solution
Let 
be a person seated and 
is an empty seat
The pattern of seating that results in the fewest occupied seats is 
.
We can group the seats in 3s like this: 
There are a total of 
groups
See Also
| 1990 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
