Suppose the side length of the swimming pool is 2. At first, the cat may be in a corner or edge.
1. If the cat is on one side. Suppose the cat is next to BC, as shown in the picture.
A - B
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As long as the mouse swims vertically to the edge of AD, the total swimming distance is 1. No matter which route the cat pursues, the total distance is greater than 3. Rats can run away.
2. If the cat is in a corner. Let's assume that the cat is at corner B. As shown in the figure.
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The mouse swam straight to point d first. Suppose the cat follows the BCD route.
When the mouse swam halfway, it swam vertically to the AD side instead. As shown in the figure.
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So the total distance of the mouse L=(√? x 1/2+ 1/2 .
The total distance of cats is M=4+ 1/2. M & gt3L. Rats can run away.