1973 AMC 12 Problem 2
Attempt Problem 2 of the 1973 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 1973 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
2.
One thousand unit cubes are fastened together to form a large cube with edge length units; this is painted and then separated into the original cubes. The number of these unit cubes which have at least one face painted is
Answer: C
Small hint:
Count the cubes with no painted face instead
Big hint:
Removing the outer layer leaves an cube
Solution:
The unpainted cubes are precisely the interior cube. Therefore the number having at least one painted face is
Therefore, the correct answer is C.
Problem 2 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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