Talk:Homicidal chauffeur problem

maths rating field

I know that the field of this article is not just "discrete mathematics", although I would classify game theory as part of discrete for our purposes. The article is also related to analysis.

However, we need to fill in something for the field, and at the moment we have to pick just one. I have plans to change the maths rating template to permit more than one field, eventually. But for now we have to pick from the fields that are available. If you'd prefer analysis, that's fine with me. I am just trying to fill in the incomplete ratings so we have a place to start for future improvements. — Carl (CBM · talk) 03:08, 10 February 2010 (UTC)[reply]

What's really needed is a "game theory" category: most of game theory is discrete, so I can see why it got tagged this way. However, the main subject of this article is explicitly a continuous game, so it's a really bad fit here. "Analysis" would be a possible second choice, but that doesn't really fit either. -- The Anome (talk) 11:21, 10 February 2010 (UTC)[reply]

This article does seem to be hard to classify. My understanding is that the talk page "fields" are meant to be very broad, unlike the actual categories on the article, which are specific.

I am working (slowly by hand) to fill in fields on the articles where the talk page tag doesn't have one. After that, I think the math project should discuss how we'd like the separation to work. As I go, I'm noticing fields that are problematic (game theory, algebraic geometry), so that we can discuss them. But for the short term, the only fields that seem related to this article are discrete (for game theory), analysis, and "applied mathematics" (if game theory counts). Of those three, none is very good. We could go with "general" but I think that's a cop-out. — Carl (CBM · talk) 11:47, 10 February 2010 (UTC)[reply]

Scenario

What happens when the runner and driver both choose their best strategy at evading/catching the other? Who wins? ~A H 1^(TCU) 15:37, 18 March 2011 (UTC)[reply]

For the original (continuous) problem, it would depend on how much faster the car is, and what are the constraints on its maneuverability. For Martin Gardner's discrete version with no left turns or U-turns, C-speed = 2 and P-speed = 1, the pedestrian can successfully evade; and in fact for a pedestrian with speed k, the minimum car speed for a chauffer win is min(2k+1, k+3) = {1, 3, 5, 6, 7, 8, ...}, I believe. As it stands, this is OR, but surely I'm not the first person to grind it out, I hope? Is there a published solution? Joule36e5 (talk) 19:12, 25 May 2022 (UTC)[reply]

It is well known that if the chauffer has perfect reflexes and constant awareness of the position of the target, and can turn instantly to any state within it's turning radius, and can turn both directions, that it can win if it flees far enough away to circle back around and draw a bead on the target. How far away it must flee depends on speed difference and turning radius of the car. In real life, the chauffeur can't turn instantly, so the pedestrian has a better chance to survive.

2600:6C40:700:1378:F0EA:7080:21C6:3B00 (talk) 17:29, 18 July 2022 (UTC)[reply]

"assumed to never tire?"

You're splitting an infinitive. For shame.

You're citing an obsolete 19th century prescriptivist rule of grammar. I'd say "for shame" myself, but that's not a complete sentence, is it? Personally, I try to carefully adhere to correct rules of grammar. Mnudelman (talk) 03:35, 19 August 2015 (UTC)[reply]