Problem 16 · 2020 Math Kangaroo
Medium
Spatial & Visual Reasoning
Logic & Word Problems
cube-viewsspatial-reasoning
Andrew bought 27 little cubes of the same size, each with three adjacent faces painted red and the other three painted a different color. He wants to use all of these little cubes to build one bigger cube. What is the largest number of completely red faces he can make on this big cube?
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Answer: E — 6
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Hint 1 of 2
Each small cube can show its three red faces all meeting at one corner; think about where each cube sits in the 3×3×3.
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Hint 2 of 2
Corner cubes show 3 faces, edge cubes 2 adjacent faces, face cubes 1 — can every position be served by a red corner?
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Approach: place each cube so red faces point outward
- A small cube's three red faces meet at a vertex, so they cover any single face, any two adjacent faces, or any corner of three.
- Corner positions need 3 mutually adjacent faces (matches a cube's red corner), edges need 2 adjacent, centers need 1 — all achievable.
- So every outer face of the big cube can be made fully red, giving all 6 faces, choice E.
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