2009 AMC 8 Problem 18
Attempt Problem 18 of the 2009 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 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
The diagram represents a -foot-by--foot floor that is tiled with -square-foot shaded tiles and unshaded tiles. Notice that the corners have unshaded tiles. If a -foot-by--foot floor is to be tiled in the same manner, how many unshaded tiles will be needed?
Answer: C
Small hint:
Look for the pattern in the unshaded tiles of the floor.
Big hint:
For an odd side length the unshaded tile count follows
Solution:
In the example, there are rows that contain unshaded tiles, for unshaded tiles.
For a floor with the same pattern, there will be such rows with unshaded tiles each.
Thus the number of unshaded tiles is
Thus, C is the correct answer.
Problem 18 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
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- 1991 AMC 8
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