Question

If you take a marker and start from any corner of a cube, what is the maximum number of edges you can trace if you never trace the same edge twice, never remove the marker from the cube and never trace anywhere on the cube except for corners and edges?

Hint:

In problems like these, think about the cube’s structure and try to visualize or sketch the movement along its edges.

Answer 1

Step 1: Understanding the problem.
A cube has 8 vertices, 12 edges, and 6 faces. Starting from any corner (vertex), you can trace 3 edges leading to 3 other corners. Each edge can only be traced once, and you must move along the edges without lifting the marker.
Step 2: Analyzing the maximum number of edges.
The maximum number of edges you can trace, without repeating any edge, is 9. This can be achieved by tracing most of the cube’s edges. The restriction of not lifting the marker and not revisiting edges limits you to 9 edges.
Step 3: Conclusion.
The maximum number of edges you can trace is 9.