Problem 21 · 2009 Math Kangaroo
Hard
Spatial & Visual Reasoning
path-tracing
A beetle walks along the edges of a cube. Starting from point P it first moves in the direction shown. At the end of each edge it changes the direction in which it turns, turning first right, then left, then right, etc. Along how many edges will it walk before it returns to point P?
Show answer
Answer: C — 6
Show hints
Hint 1 of 2
Follow the beetle edge by edge, alternating a right turn then a left turn at each vertex.
Still stuck? Show hint 2 →
Hint 2 of 2
Track when it first lands back on P - the path closes into a loop.
Show solution
Approach: trace the alternating-turn path
- Starting at P along the given edge, the beetle turns right, then left, then right, ... at successive vertices.
- Following this rule the path closes into a loop returning to P.
- It walks 6 edges before getting back to P.
Mark:
· log in to save