Problem 23 · 2014 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-viewscasework
The diagram shows two different views of the same cube, which is made from 27 small cubes that are either white or black. At most how many black cubes are there?
Show answer
Answer: D — 9
Show hints
Hint 1 of 2
The two pictures show the same cube, so every visible black square must be consistent.
Still stuck? Show hint 2 →
Hint 2 of 2
Maximise the hidden black cubes while keeping both views possible.
Show solution
Approach: the two views pin some faces; make every other small cube black
- The two pictures show the outside of the same 3×3×3 cube, so a small cube touching a face that looks white in either view must itself be white there.
- Mark white only the surface cubes the pictures force, and colour every remaining small cube black, including the fully hidden ones.
- Doing this leaves at most 9 black cubes.
Mark:
· log in to save