Problem 22 · 2019 Math Kangaroo
Stretch
Spatial & Visual Reasoning
spatial-reasoningcomposition
Marta sticks several triangles on top of each other and makes a star that way. What is the minimum number of triangles she has used?
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Answer: B — 3
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Hint 1 of 2
The star has a five-sided centre with five points; one triangle can cover the centre plus a couple of points.
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Hint 2 of 2
Try the fewest big triangles that, overlapped, leave no point uncovered.
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Approach: cover the star with overlapping triangles
- A single triangle can cover the central pentagon together with two of the points.
- Two more triangles, rotated, cover the remaining points.
- Three overlapping triangles are enough, and fewer cannot cover all five points.
- So the minimum is 3 (B).
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