Ant in a Cube
An ant is at one corner of a cube with side length 1. The exit is a tiny hole on the corner diagonally opposite the ant. What is the length of the shortest path the ant can take to the exit? The ant must stay on the surface — it can't fly through the interior.
Solution
Answer: 5
The ant needs to travel along the surface from corner A to corner G. The trick is to unfold the cube into a flat net — then the shortest path becomes a straight line.
On the unfolded surface, we can form a right triangle:
- The horizontal distance is 2 (the width of two faces)
- The vertical distance is 1 (the height of one face)
Using Pythagoras’ theorem: 22+12=5.
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