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

2 Answers on this Question

1. Imagine a 3-D box, now each wall is a square with 4 edges.
   We mark all edges of one square return to same vertex and
   then move to next square , then mark its 4 sides.
   Now we cannot move further.
   So, its 4+1+4=9

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2. Maximum number of edges = 9. Start from one corner. Select any face including that corner. Complete a square (4 edges) around the face to reach at the starting corner point . Now, move to the opposite face through the edge joining them and passing through the starting point(1 edge). Now, complete the square of edges around this face(4 edges). Total = 4+1+4 = 9 edges

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