A Beetle and Four Spiders
A beetle is located in the center of a square carpet. The edges of the carpet are colored in red, green, blue, and yellow. Four spiders of the same colors are on the carpet’s corners. Each spider can only move on the edge with its matching color. Can the beetle escape the carpet and flee without encountering the spiders if it is 1.5 times slower than them?
No, the spiders will always be able to contain the beetle within the carpet. We draw two perpendicular lines passing through the beetle which are parallel to the diagonals of the square. The spiders’ strategy is to follow the four points where these lines intersect with the boundary of the square. When a spider’s corresponding intersection point moves to an edge of a different color, the spider waits in the corner. In order to accomplish this strategy, the speeds of the spiders need to be at least √2~1.4 times higher than the speed of the beetle.
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