Problem 8 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
cube-viewscareful-counting
Hansi sticks 12 cubes together to make this figure. He always puts one drop of glue between two cubes. How many drops of glue does he need?
Show answer
Answer: D — 11
Show hints
Hint 1 of 3
A drop of glue goes wherever two cubes touch each other.
Still stuck? Show hint 2 →
Hint 2 of 3
Think of the cubes joined up like beads on a string with no loops.
Still stuck? Show hint 3 →
Hint 3 of 3
For cubes joined in one piece with no loop, the number of joins is always one less than the number of cubes.
Show solution
Approach: joins = number of cubes minus one (chain idea)
- Every drop of glue sits at one join where two cubes touch.
- The cubes are stuck together in one connected piece, like beads on a string with no loops.
- To link 12 cubes into one piece you need one less than 12, which is 12 − 1 = 11 drops, so the answer is D.
Mark:
· log in to save