Problem 7 · 2013 Math Kangaroo
Medium
Spatial & Visual Reasoning
net-foldingcube-views
A cube is coloured on the outside as if it were made up of four white and four black small cubes, with no two cubes of the same colour next to each other (see picture). Which of the following figures could be a net of the coloured cube?
Show answer
Answer: E
Show hints
Hint 1 of 2
Track which faces end up opposite each other when the net folds into the cube.
Still stuck? Show hint 2 →
Hint 2 of 2
Each face is split into a checkerboard; only one net folds so that no two same-coloured small cubes touch.
Show solution
Approach: fold each net mentally and check the colouring rule
- The cube is coloured so that small cubes of the same colour never sit next to each other.
- Folding each candidate net, only one keeps that colouring consistent along every shared edge.
- That net is option E.
Mark:
· log in to save