Problem 12 · 2010 Math Kangaroo
Medium
Spatial & Visual Reasoning
cube-views
A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green and the bottom face is red. How many of the small cubes have 3 green faces?
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Answer: A — 4
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Hint 1 of 2
A small cube shows 3 green faces only if it is a corner of the big cube with all three faces on green sides.
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Hint 2 of 2
The bottom face is red, so bottom corners can't have 3 green faces — only the top corners can.
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Approach: check which corner cubes touch three green faces
- Only corner cubes can show three faces.
- The four bottom corners each touch the red bottom, so they have at most 2 green faces.
- The four top corners each touch the green top and two green sides — 3 green faces.
- So 4 small cubes have three green faces.
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