1987 AHSME Problems/Problem 27
Problem
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.)
Solution
The cut separates the cube into points with and points with , and analogous results apply for the other cuts. Thus, which piece a particular point is in depends only on the relative sizes of its coordinates , , and - for example, all points with the ordering are in the same piece. Thus, as there are possible orderings, there are pieces, which is answer .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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