Talk:Prisoners and hats puzzle
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At the suggestion of Ludraman, I looked over this article. Not being an expert in logic or logic puzzles, I can't speak much to that aspect. I will observe that the diagram characters have an amusing resemblance to Pacman (the yellow, probably) and that the hats might be colored in such a way as to indicate indeterminacy. Red and blue polka dots maybe?
- Ah, I was wondering why it looked familiar. Pacman, of course! Arvindn 17:19, 19 Apr 2004 (UTC)
There are other variants of this puzzle. What are some of their names?
The significance of the puzzle in logic history might be mentioned, as well as perhaps an amusing if not necessarily connected aside to the problem of self consciousness. That is, very few animals can be experimentally shown to be aware of themselves in the sense of noticing that something is wrong or changed about themselves as seen in a mirror reflection. At last count, my memory tells me, chimps (both bonobos and common??), dolphins, and homo sapiens have done so. For dogs, cats, parrots, ... and all others tested so far, no way of elicting a demonstration of such awareness has been found. The tempting inference is that no way can be found as all except the small group listed are incapable.
Thus the prisoners here should be limited to those from the listed species??
Minor wording nits, but nothing important.
Perhaps this may be of some help? ww 16:21, 19 Apr 2004 (UTC)
I've seen a variant with 5 hats and no screen, but can't remember the details. Arvindn 17:19, 19 Apr 2004 (UTC)
[edit] Diagram
Is the diagram okay? (BTW its resemblance to pacman is not intentional). When I was writing the article I thought a diagram would help but I'm not much of an artist and scribbled something in Paint that would do for the time being. Would anyone be willing to make a better diagram? LUDRAMAN | T 02:16, 21 Apr 2004 (UTC)
[edit] Is waiting necessary?
I frequently fall into traps in logic puzzles, so I invite all and sundry to explain to me why I'm wrong. That said, is it necessary for B to determine whether or not C is going to act? Wouldn't B (or whichever person saw that the other two were wearing the same color hats, as two of them must be) immediately notice the other hats' colors, and act accordingly?
- Yep, it's necessary. Remember, B can only see A's hat. C is behind him (and the prisoners aren't able to look backwards--this is an important rule), and of course the fourth man is behind the screen. The crux of this game is that even with empirical evidence that doesn't seem strong enough to guarantee an answer, B can infer from C's (assumed completely rational) action what the answer must be. Thus the prisoners can always go free. --140.103.133.75 08:02, 18 July 2005 (UTC)
