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A mouse is at the center of a square. There are 4 cats each on the mid-points of different sides of the square. Mouse is looking to escape to any corner of the square. Mouse and cats have the same maximum running speed. Can the cats always catch the mouse? Or can the mouse always escape with some strategy?

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(Please consider all animals as point objects)

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2 Answers 2

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Trivial solution:

The mouse can never escape.

Because:

The mouse has to reach a corner to escape.
There are four cats and four corners. The cats are closer to the corners than the mouse, so they can just go straight to the nearest clockwise corner and sit there.
All the corners are covered by a cat, so the mouse can never escape.

But can the cats catch the mouse?

From the corners, the cats can all just head toward the mouse, always staying directly between the mouse and their corner. (This is possible because the mouse is further from the corner than the cat, so the cat needs to cover less distance to maintain a blocking position.)

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For the sake of this answer, I'm going to assume that the square's width and height are 10 units. This means that the Mouse is 7.071 units away from any corner, but each cat is only 5 units away.

As said by @fljx,

there are four cats and four corners. This means that each cat can go to a corner, as long as K is low enough.

If I calculated correctly,

K must be greater than 1.4142.

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  • $\begingroup$ Yes, thanks for your response! You are right, mouse must have speed > 1.41... times that of the cat to go to the corner. $\endgroup$
    – thisIs4d
    Apr 4, 2023 at 10:18

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