Problem 11 · 2022 Math Kangaroo
Stretch
Geometry & Measurement
areaspatial-reasoning
Katrin forms a path around each square. For that she uses stones that are 2 long and 1 wide (see picture). How many such stones does she need for a path around the square with side length 5?
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Answer: C — 12
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Hint 1 of 2
Count the stones in the small ring (side 1) and the next ring (side 3) shown in the picture.
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Hint 2 of 2
See how many stones get added each time the side gets bigger, then keep that pattern going up to side 5.
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Approach: continue the picture's stone-count pattern
- In the picture, the side-1 ring uses 4 stones and the side-3 ring uses 8 stones.
- So growing the side by 2 adds 4 more stones each time (4, then 8, then 12).
- The side-5 ring needs 12 stones, so the answer is 12.
For older kids
A 1-stone-thick ring around a square of side \(n\) uses \(2n+2\) of the 2-by-1 stones; for \(n=5\) that is \(2\times5+2=12\).
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