Problem 6 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
cube-viewscomplementary-counting
Laura glues together 18 cubes. Then she stretches two rubber bands around them — see picture. How many cubes are not touched by any of the rubber bands?
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Answer: D — 10
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Hint 1 of 3
Find the cubes each rubber band touches first, then the leftover cubes are the answer.
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Hint 2 of 3
The 18 cubes make a box that is 3 cubes wide, 3 cubes deep and 2 cubes tall.
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Hint 3 of 3
Count the cubes a band runs across, then count how many cubes nothing touches at all.
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Approach: find the touched cubes, then count the ones left over
- The 18 cubes are stacked into a box 3 wide, 3 deep and 2 tall.
- Follow each rubber band and mark every cube it presses against — the two bands touch 8 cubes in all.
- The cubes nothing touches are the 18 minus those 8, which is 10. The answer is D.
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