Problem 17 · 2017 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-views
A big cube is made up of 9 identical building blocks. Each building block looks like the one shown. Which big cube is possible?
Show answer
Answer: A
Show hints
Hint 1 of 2
Nine identical blocks of three cubes each build the 3×3×3 cube; check which surface colouring a real assembly allows.
Still stuck? Show hint 2 →
Hint 2 of 2
Track the grey/white cubes — only one pictured cube can be made from nine copies of the given block.
Show solution
Approach: test which cube can be assembled from the given block
- Each block is three cubes in a row (grey-grey-white), and nine of them fill the 27 small cubes of the big cube.
- On a workable cube every block must sit as a straight 1×3 run, and the grey/white pattern on the faces has to be reachable from such a packing.
- Checking the visible faces, four of the pictured cubes force a colouring that no straight-block packing can produce.
- Only one colouring can actually be built, namely (A).
Mark:
· log in to save