1987 AMC 12 Problem 27
Attempt Problem 27 of the 1987 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 1987 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
A cube of cheese is cut along the planes and How many pieces are there? (No cheese is moved until all three cuts are made.)
Answer: B
Small hint:
Within one piece, the relative order of cannot change
Big hint:
Count the strict orderings of three distinct coordinates
Solution:
The three planes are precisely the boundaries where two coordinates are equal. Away from them, each piece is determined by a strict ordering of such as Every one of the orderings occurs inside the cube, so there are pieces.
Thus the correct answer is B.
Problem 27 in other years
- 1950 AMC 12
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