1990 AJHSME Problems/Problem 19
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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
If there are 
seats occupied, then it is possible to get an occupation of the seats where no person sits next to someone else. However, the only way is through alternating seats.
Thus, if another person joins, two people must sit next to each other, so 
.
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 | ||
