Geometry / Cube Unfolding

Shortest wall path across a 10×10×10 cube

An ant starts at one corner and must reach the opposite corner while staying on the cube's surfaces. The trick is to unfold the walls so the surface path becomes a straight line.

Visualize the unfolding

Two adjacent faces become a 20×10 rectangle

Face 1 Face 2 Start Opposite corner 20 10
Straight lines are shortest in the unfolded plane, so this diagonal corresponds to the shortest path on the cube's walls.
Interview idea

Reduce 3D geometry to 2D

1
Don't restrict the ant to edges. It may walk diagonally across faces.
2
Cut and unfold two neighboring faces. They form a 20×10 rectangle.
3
Use Pythagoras. The shortest route is the rectangle's diagonal.
Shortest distance
√(20² + 10²)
10√5 ≈ 22.36
Along edges
30
Across walls
22.36