1991 AMC 8 Problem 17
Attempt Problem 17 of the 1991 AMC 8 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 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
An auditorium with rows of seats has seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is
Answer: C
Small hint:
In a row of seats, the most students with no two adjacent is
Big hint:
Row has seats; add over the rows
Solution:
Row has seats, so it holds students. For rows through (seats through ) the maxima are
These sum to
Thus, the correct answer is C .
Problem 17 in other years
- 1985 AMC 8
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