Problem 1 · 2014 Math Kangaroo
Easy
Spatial & Visual Reasoning
cube-viewscareful-counting
If one removes some 1×1×1 cubes from a 5×5×5 cube, you obtain the solid shown. It consists of several equally high pillars built on a common base. How many little cubes have been removed?
Show answer
Answer: C — 64
Show hints
Hint 1 of 2
Build it in two parts: a solid base layer, then the equal pillars standing on it.
Still stuck? Show hint 2 →
Hint 2 of 2
Count how many of the 125 unit cubes are LEFT, then subtract from 125.
Show solution
Approach: count what remains, then subtract
- The full cube has 5×5×5 = 125 unit cubes.
- One complete bottom layer stays in place: that is 5×5 = 25 cubes.
- On top sit 9 equal pillars (a 3×3 arrangement), each rising the remaining 4 levels: 9×4 = 36 cubes.
- So 25 + 36 = 61 cubes remain, and 125 − 61 = 64 were removed.
Mark:
· log in to save