Problem 6 · 2020 Math Kangaroo
Easy
Spatial & Visual Reasoning
Geometry & Measurement
sequence-of-figurestiling-tessellationcareful-counting
The figure of side 1 is formed by six equal triangles, made with 12 matchsticks. How many matchsticks are needed to complete the figure of side 2, shown partially started?
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Answer: D — 36
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Hint 1 of 2
Side 1 (a hexagon of six triangles) uses 12 sticks; side 2 is the next size up of the same pattern.
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Hint 2 of 2
Count the matchsticks in the full side-2 figure — the stick count grows faster than the side.
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Approach: scale the matchstick count to the next size
- Side 1 is six small triangles forming a hexagon and needs 12 sticks.
- Side 2 is the same hexagonal pattern built one size larger, and a full count of its segments comes to 36 sticks.
- So 36 matchsticks are needed to complete the side-2 figure — choice D.
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