1991 AMC 12 Problem 15
Attempt Problem 15 of the 1991 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1991 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
A circular table has exactly chairs around it. There are people seated at this table in such a way that the next person to be seated must sit next to someone. The smallest possible value of is
Answer: B
Small Hint:
No empty chair can have both neighboring chairs empty
Big Hint:
Between consecutive occupied chairs there can be at most two empty chairs
Solution:
The condition says that every empty chair has an occupied neighbor, so no three consecutive chairs may all be empty. Therefore each occupied chair can account for at most itself and the two empty chairs following it, giving and Repeating the pattern occupied-empty-empty around the table attains
Thus the correct answer is B.
Problem 15 in Other Years
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