Problem 4 · 2024 Math Kangaroo
Easy
Spatial & Visual Reasoning
spatial-reasoning
Julio cuts off all four corners of a regular tetrahedron (see picture). How many corners does the object have now?
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Answer: D — 12
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Hint 1 of 2
A tetrahedron starts with 4 corners (vertices).
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Hint 2 of 2
Slicing off one corner replaces that single vertex with a small triangular face that has its own corners.
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Approach: count new vertices created by truncating each corner
- A regular tetrahedron has 4 vertices.
- Cutting off one corner removes that vertex but creates a small triangular face with 3 new corners.
- Doing this at all 4 corners gives 4 × 3 = 12 corners.
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