Problem 25 · 2009 Math Kangaroo
Stretch
Geometry & Measurement
factorizationarea
Kangoo has 2009 unit cubes that he puts together to make one big cuboid. He also has 2009 square stickers measuring 1 × 1 with which he tries to cover the surface area of the cuboid. He manages to do this and even has some spare stickers. How many are left over?
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Answer: B — 763
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Hint 1 of 2
The cuboid uses all 2009 unit cubes, so its dimensions multiply to 2009 = 7·7·41.
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Hint 2 of 2
Only one shape has surface area small enough to cover with 2009 stickers — find it.
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Approach: pick the factorization whose surface area fits 2009 stickers
- 2009 = 7·7·41, so the cuboid dimensions are a factorization of 2009.
- The compact shape 7×7×41 has surface area 2(49 + 287 + 287) = 1246.
- Every other factorization needs more than 2009 stickers, so 7×7×41 is the one he can finish.
- Leftover stickers = 2009 − 1246 = 763.
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