The Spider's Web
The above diagram depicts a spider web, where the black lines are fibers of the web, and the intersections of the fibers are called junctions.
The spider caught a bug at the center of the web, which is marked by a blue dot, and plays the following game with the bug:
- Step 1: At a junction, the bug picks a fiber (which passes through the point) to walk along.
- Step 2: The spider chooses the direction along the fiber for the bug to walk along.
- Step 3: The bug walks in that direction till he reaches the next junction.
- Step 4: If the bug touches the boundary of the web (which is marked in ), the bug is allowed to escape. Otherwise, we return to step 1 and the bug picks another fiber.
Can the bug ever manage to escape?