Problem 4 · 2015 Math Kangaroo
Easy
Spatial & Visual Reasoning
net-folding
The diagram shows the net of a cube whose faces are numbered. Sascha adds the numbers that are on opposite faces of the cube. Which three results does he get?
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Answer: A — 4, 6, 11
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Hint 1 of 2
Fold the net into a cube in your head and see which faces end up opposite each other.
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Hint 2 of 2
On a band of four faces in a row, opposite faces skip one; then pair the two faces sticking out.
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Approach: identify the three pairs of opposite faces
- Faces 1, 2, 3, 4 form a band around the cube, so 1 is opposite 3 and 2 is opposite 4.
- The remaining faces 5 and 6 are top and bottom, so 5 is opposite 6.
- The three opposite-face sums are 1+3 = 4, 2+4 = 6, and 5+6 = 11.
- So Sascha gets 4, 6, 11 (A).
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