Problem 1 · 2003 AMC 8
Easy
Geometry & Measurement
spatial-reasoning
Jamie counted the number of edges of a cube, Jimmy counted the corners, and Judy counted the faces. They then added the three numbers. What was the resulting sum?
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Answer: E — 26.
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Hint 1 of 2
Picture a die or a box in your hand and count the three kinds of parts separately: pointy corners, line edges, flat faces.
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Hint 2 of 2
A cube's part-counts are worth memorizing: 8 corners, 12 edges, 6 faces.
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Approach: count the three kinds of cube parts and add
- Count each kind separately so nothing gets mixed up. Corners (the points): 8. Edges (the lines): 12. Faces (the flat sides): 6.
- 8 + 12 + 6 = 26.
- Worth keeping: for any cube or box these never change — 8 corners, 12 edges, 6 faces. (They even fit Euler's rule: corners − edges + faces = 8 − 12 + 6 = 2 for any solid like this.)
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