Problem 21 · 2016 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellation
Clara is forming one big triangle made up of identical little triangles. She has already put some triangles together (see diagram). What is the minimum number of little triangles she still has to add?
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Answer: B — 9
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Hint 1 of 3
A big triangle with little triangles has a square-number count: side 2 holds 4, side 3 holds 9, side 4 holds 16.
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Hint 2 of 3
Find the smallest such big triangle that still fits around the pieces already placed.
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Hint 3 of 3
Then subtract the pieces already there from that total.
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Approach: complete to the smallest big triangle that fits
- The widest row already placed forces the big triangle to be 4 little triangles along each side, and a side-4 triangle holds \(4 \times 4 = 16\) little triangles.
- Counting what is already placed and taking it away from 16, Clara must add 9 more little triangles, choice (B).
Mark:
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