Problem 13 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
spatial-reasoning
Some edges of a cube are coloured red so that each face of the cube has at least one red edge. What is the minimum number of red edges that the cube must have?
Show answer
Answer: B — 3
Show hints
Hint 1 of 2
A cube has 6 faces and 12 edges; each edge borders 2 faces, so one red edge can cover 2 faces.
Still stuck? Show hint 2 →
Hint 2 of 2
Try to cover all 6 faces with as few edges as possible — can 3 well-chosen edges touch every face?
Show solution
Approach: cover all six faces using each edge's two adjacent faces
- Each edge lies on exactly two faces, so k red edges can touch at most 2k faces.
- To cover all 6 faces you need at least 3 edges.
- Three suitably placed edges (one near each of three corners) do touch all six faces.
- So the minimum is 3 (B).
Mark:
· log in to save