The next problem may be way too easy, but will post it anyway.

Riddick, trying to escape from the space police, lands on a deserted planet. How many cops should the space police send to the planet, so that Riddick will be eventually caught?

We assume that the planet is a perfect sphere and the speed of Riddick and all cops is the same. All of the characters have perfect information about the location of the others and make instant decisions in real-time. Also, they are dots.

P.S. The question seems very natural, I hope it is not a repeat.

  • $\begingroup$ Yeah, it is the same, please erase the question or mark it as duplicate - whichever is better. Sorry for the repeat. $\endgroup$ Jul 16 '15 at 22:11
  • $\begingroup$ This question is not a duplicate of the hare-wolves one. In that question, the creatures have a small but nonzero radius (see second comment). In this one, the players are points. This changes the answer: in the other question, two pursuers can catch the evader, in this one, two pursuers cannot catch the evader. $\endgroup$ Jul 17 '15 at 0:08
  • $\begingroup$ That's true, but the first solution there gives the strategy for 2 cops. I posted the problem mostly because of my strategy for 3 cops, but I guess will try to make up some twist and come up with a modified problem. $\endgroup$ Jul 17 '15 at 0:16

Assuming the space police want to send as few units as possible

they should send three (3) units

This is because

This is a standard pursuit game on $S^2$. Riddick can evade any two pursuers indefinitely (for example, by moving in a direction perpendicular to the great circle containing the locations of the pursuers as they approach him), but three pursuers can inevitably trap him in a kind of "collapsing triangle", as well as with other strategies.

Of course, he'll probably just kick their arses to Hades and back, but...

  • 1
    $\begingroup$ 3 is correct. However, I am not totally convinced with the "shrinking triangle" part. Since they are on a sphere, there are two triangles defined by any 3 points - which one do you shrink? $\endgroup$ Jul 16 '15 at 22:19
  • $\begingroup$ The one with Riddick in it, I'd assume $\endgroup$
    – StephenTG
    Jul 17 '15 at 14:03

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