Difference between revisions of "2020 AMC 8 Problems/Problem 9"
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Revision as of 14:52, 18 November 2020
Akash's birthday cake is in the form of a inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into
smaller cubes, each measuring
inch, as shown below. How many of the small pieces will have icing on exactly two sides?
Solution 1
Notice that all the faces with the exception of the bottom faces have the two center edge pieces with 2 faces with icing on them. This is . Additionally, on the bottom face, the corners have 2 faces with icing, as the bottom face does not have icing. This is
cubes. The total is
~Windigo
Solution 2
This is just careful casework. Consider the following diagram: [img]https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi82Lzk1NjIyMDEyYzEwMmU2MGRhM2U3OGMzYzA0MDNmOGFmZjdkMDk3LnBuZw==&rn=YW1jIDggbm8gOS5wbmc=[\img]
The face on the opposite side of the front face (hidden) is an exact copy of the front face. So the answer is .
-franzliszt
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
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