Problem 14 · 2020 Math Kangaroo
Hard
Spatial & Visual Reasoning
cube-views
Maria has exactly 9 white cubes, 9 light-grey cubes and 9 dark-grey cubes, all the same size. She glues them all together to form one larger cube. Which of the cubes below is the one she made?
Show answer
Answer: A
Show hints
Hint 1 of 2
A 3x3x3 cube has 27 small cubes; here each colour is used exactly 9 times.
Still stuck? Show hint 2 →
Hint 2 of 2
Count the visible faces of each colour in each option - the right cube must allow exactly 9 of each colour overall.
Show solution
Approach: match the visible colour counts to 9-9-9
- The big cube is 3x3x3 = 27 small cubes, painted 9 white, 9 light grey, 9 dark grey.
- For each option, see whether the visible and forced hidden cubes can split into three nines.
- Only cube A is consistent with using each colour exactly nine times.
Mark:
· log in to save