Problem:
An anditorium 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 Choices:
A.
B.
C.
D.
E.
Solution:
The first row has seats, so students can sit in row . The second row has seats, so students can sit in row . The third row has seats, so students can sit in row . ... The last row has seats, so students can sit in row . The sum is . Regrouping yields
Draw a diagram:
Thus, the sum is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions