Difference between revisions of "1987 AHSME Problems/Problem 27"
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Latest revision as of 17:45, 7 December 2020
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
