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)

Do you know variant of 10-hat puzzle with 3,4,5 etc. colors? kknop 14:11, 29 May 2007

Contents

[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)

[edit] Clarification

I was trying to solve this puzzle, and want to clarify something. It says "The prisoners can see the hats in front of them but not on themselves or behind." Now, based on the diagram, and the description, this means B can only see A's hat, A can see none (since he's in front), and I assume that C can only see B's hat, correct? This is not clarified, i.e. can C see B AND A's hat?

If C can only see B's hat, and B only A's, perhaps the wording should be: "The prisoners can see the hat of the prisoner directly in front of them, but not themselves or behind." Before I make the change, I want to be sure I'm interpreting the description correctly. GregTheVirus 23:25, 26 July 2007 (UTC)

[edit] A different hat puzzle

There are 3 prisoners, seated so that A can't see B or C, B can see A, C can see A & B. The villian shows the prisoners 2 white hats & 3 black hats, then blindfolds them and puts a hat on each head. He says "When I remove the blindfolds I will give you 30 minutes. If one of you, in 30 minutes can tell me the color of his own hat & prove it, you all go free, otherwise all die. If any more than one speaks you all die." When the blindfolds are removed, there is a 29 minute pause, then prisoner A says something, and they are all released. What does he say? -- Answer: "If C saw two white hats in front of him he would have known he had on a black hat. He said nothing, therefore either C & B both have on black hats, or one has a black hat and the other a white one. If B had seen a white hat, and heard nothing from C, he would have known that his own hat was black. Since he said nothing, I must have on a black hat."

I don't know how to include this puzzle in the article, since it is of a somewhat different type. Should I broaden the article, or start a new one? Will someone else help me? Too Old (talk) 04:55, 10 June 2008 (UTC)