2003 AMC 8 Problem 13
Attempt Problem 13 of the 2003 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 2003 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
Answer: B
Small hint:
A cube has four painted faces exactly when it touches two other cubes.
Big hint:
Separate the top cubes, bottom corner cubes, and remaining cubes.
Solution:
A cube has exactly four painted faces exactly when it is attached to exactly two other cubes.
The top cubes touch only one other cube, so they have painted faces. The bottom corner cubes touch three other cubes, so they have painted faces.
The remaining cubes each touch exactly two other cubes, so they have exactly four painted faces.
Thus, B is the correct answer.
Problem 13 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
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- 1998 AMC 8
- 1999 AMC 8
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