Problem 7 · 2017 Math Kangaroo
Medium
Spatial & Visual Reasoning
spatial-reasoningtiling-tessellation
A \(4 \times 1 \times 1\) cuboid is made up of 2 white and 2 grey cubes as shown. Which of the following cuboids can be built entirely out of such \(4 \times 1 \times 1\) cuboids?
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Answer: A
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Hint 1 of 2
Each building block is a 4x1x1 bar with a fixed white-white-grey-grey colour pattern.
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Hint 2 of 2
A target box can be built only if its grey and white cubes split into such fixed bars; check the colour layout, not just the shape.
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Approach: check which target colouring can be partitioned into the fixed WWGG bars
- Every available bar is 4 cubes long with colours white, white, grey, grey in that order.
- Try to cover each candidate box with these bars so that every bar's colour pattern matches.
- Only box A has a colour layout that can be cut entirely into such WWGG bars.
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