Timeline for Can the Policeman catch the Thief?
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2016 at 20:21 | comment | added | Milo Brandt | @Ankoganit I think that would be an interesting question. I've been thinking a lot about it, and have yet to come to an answer. (Nor any interesting approaches - I could definitely write a computer program to decide efficiently whether the policeman moving exactly twice as fast as the thief could make the catch, but that wouldn't be a terribly satisfying way to go about it) | |
| Jun 25, 2016 at 3:58 | comment | added | Ankoganit | @ministic2001 If the police follows the exact strategy as in this answer, it may be impossible. For example,when the police starts from the center, the thief from the NW corner, and sweeps the perimeter counter clockwise. I don't yet know about the general case; maybe the lowest necessary speed for the police would be a nice follow-up? | |
| Jun 24, 2016 at 19:12 | comment | added | Trenin | @Falco Agreed. That is why I thought the problem was unclear. It was trivial the way I was looking at it and I needed to review this answer before I discovered I was making a different assumption. | |
| Jun 24, 2016 at 15:36 | history | edited | Milo Brandt | CC BY-SA 3.0 |
added 306 characters in body
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| Jun 24, 2016 at 14:46 | comment | added | ministic2001 | Why did the OP state that the policeman run a little over 2 times faster than the thief? Does that mean that if the policeman just nice runs 2 times faster than the thief, is impossible to shoot the thief? | |
| Jun 24, 2016 at 14:10 | comment | added | Chris | I agree with f'' that I'd have understood the plan better if it was described as running the perimeter and going in and out of the centre every time you pass one of the mid points. Otherwise excellent answer. :) | |
| Jun 24, 2016 at 13:57 | comment | added | Milo Brandt | @Lordofdark The thief's best strategy against the strategy I propose is to start such that, after the officer has run the two edges to the top left, the thief is just going around the bottom left corner. Then, the thief just runs counterclockwise until being caught. (It's pretty close to what the graph shows) | |
| Jun 24, 2016 at 13:54 | comment | added | Milo Brandt | @MatthiasBäßler If the officer looks ahead of himself on the first 3 edges of each loop, and behind himself for the next edge, then stops at the center for a small amount of time to look around (but not so long that his average speed decreases below half the thief's), this strategy still works. He could also always look forwards, taking a moment to look around at the center and after the first edge. | |
| Jun 24, 2016 at 13:51 | comment | added | Falco | @Trenin, if the policeman knows where the thief is, this becomes trivial, because he is faster he can simply follow the exact same path the thief is running and will easily catch him very fast. Maximum distance of the two is 4 units (if the whole thing is 2x2) so if the thief runs 4 units, the policeman will run 8 in the same time and catch him. | |
| Jun 24, 2016 at 12:23 | comment | added | Trenin | @Falco I assumed that they both know exactly where eachother are, but this answer assumes that they do not. | |
| Jun 24, 2016 at 11:21 | comment | added | Matthias Bäßler | This answer assumes that the policeman looks in all directions: while running and at every crossroad. Otherwise a thief (knowing the pattern) could avoid the policeman forever (e.g. staying behind the officer). | |
| S Jun 24, 2016 at 9:55 | history | suggested | psmears | CC BY-SA 3.0 |
Fix a few typos; add an image description
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| Jun 24, 2016 at 9:48 | review | Suggested edits | |||
| S Jun 24, 2016 at 9:55 | |||||
| Jun 24, 2016 at 9:43 | comment | added | Falco | @f'' Is it implied that the thief always knows the position of the policemen, but the policemen doesn't know where the thief is? Because if the thief doesn't know where the policemen is, I don't think he can have a perfect strategy, even if he is 1000 times faster than the policeman, because as soon as he sees him it is over, and before that he can just run around randomly.... | |
| Jun 24, 2016 at 9:38 | comment | added | BmyGuest | @Lordofdark the best Thief's strategy... Hmm, sounds like an extension to the puzzle. "How long can the Thief hold out in best case...?" | |
| Jun 24, 2016 at 8:55 | comment | added | Fabich | An animation of the best thief strategy would be awesome ! | |
| Jun 24, 2016 at 5:46 | vote | accept | Ankoganit | ||
| Jun 24, 2016 at 5:45 | comment | added | f'' | @MiloBrandt This strategy can also be described as going around the perimeter and making some visits to the center. That could make it easier to show why the policeman will catch up to the thief. | |
| Jun 24, 2016 at 5:42 | history | edited | Milo Brandt | CC BY-SA 3.0 |
Fixed pronouns, made parameter of graph more sensible.
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| Jun 24, 2016 at 5:42 | comment | added | f'' | @wrangler If they run at the same speed, the thief can evade forever by choosing one square and staying on the opposite side of it from the policeman. | |
| Jun 24, 2016 at 5:40 | comment | added | wrangler | Is this possible if both run at same speed? so i can apply strategy in counter strike. | |
| Jun 24, 2016 at 5:35 | history | answered | Milo Brandt | CC BY-SA 3.0 |