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This is a continuation to the puzzle I created in part 1 found here.

A cat and mouse are in a square side length 2.

The same rules and starting conditions apply as in part 1:

  • The mouse has to move a distance equal to the corner to centre of the square.
  • The cat has to move a distance equal to half the length of the square.
  • Both cat and mouse must move the full required distance in a straight line. I.e. if they hit the wall before reaching the required distance that move is not allowed.
  • They both start in the same corner.
  • The mouse moves first.
  • The cat wins if it ever crosses the mouse at any point. (Does not have to move the full distance if it reaches the mouse first)

If the cat and mouse move optimally,

What is the shortest distance the cat will ever get to the mouse?

Optimally referring to the mouse trying not to get caught and stay as far away from the cat as possible, and the cat to get as close to the mouse as possible.

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    $\begingroup$ Part 3 could perhaps ask : what (using same notion of optimally) is the longest distance the mouse will ever stay away from the cat? :-X fwiw: I have guesses and ideas but no proofs yet al all. $\endgroup$ Commented Feb 24 at 22:03
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    $\begingroup$ I’ve got some ideas for part 3 but I’ll keep this in mind. Let’s see if we get there first :) $\endgroup$ Commented Feb 25 at 8:41
  • $\begingroup$ I am afraid this one is more Math than Puzzle...are you sure this can be solved by a puzzle way? $\endgroup$ Commented Feb 27 at 6:31

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