Problem 21 · 2015 Math Kangaroo
Stretch
Spatial & Visual Reasoning
net-foldingfolding
Nina wants to make a cube from the paper net. You can see there are 7 squares instead of 6. Which square(s) can she remove from the net, so that the other 6 squares remain connected and from the newly formed net a cube can be made?
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Answer: D — only 3 or 7
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Hint 1 of 2
A cube net needs the remaining 6 squares to stay connected AND to fold up without two squares landing on the same face.
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Hint 2 of 2
Test each candidate removal: most leave a shape that overlaps when folded; only certain end squares work.
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Approach: test which removals leave a connected, foldable 6-square net
- Removing a square must keep the other six joined and able to fold into a cube with no doubled-up face.
- Taking out an interior square breaks the net or makes two squares fold onto the same face, so those fail.
- Removing square 3 works, and removing square 7 works, while no other single removal does — so the answer is only 3 or 7.
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