Elie's Expositions

A bereaved father blogging for catharsis... and for distraction. Accordingly, you'll see a diverse set of topics and posts here, from the affecting to the analytical to the absurd. Something for everyone, but all, at the core, meeting a personal need.

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Wednesday, August 31, 2005

Logic Puzzle #3: Hat Tricks

Thanks (or should I say a hat tip?) to Soccer Dad for this link to a marvelous logic puzzle. Before you try to solve this one (a correct solution does appear in the comments, as confirmed by the poster), here's a much less complex one along the same lines, which my Dad taught me many moons ago. If you can figure an answer to this one, you're ready to at least try the hard one in that link (no I didn't get that one, but after three days of trying I finally at least understand why the solution works!):

Three men, A, B, and C, are stood in a line and hat is placed on each one's head, out of a set of three black hats and two red ones. None of the men can see his own hat's color, but A can see both B and C, B can see C, and C can't see either of the others. Each man is then asked if he can determine what color hat he is wearing.

After a moment's silence, C says: I am wearing a black hat. How was he able to figure this out?

Answer tomorrow in comments section.


At 9/1/05, 12:22 PM, Blogger Soccer Dad said...

There are 7 possibilities:

1) B B B
2) B B R
3) B R B
4) R B B
5) B R R
6) R B R
7) R R B

5) can be eliminated immediately; else A would know the solution right off.
6) can be eliminated because if B sees a red hat on C, but A can't figure it out, then B must be wearing black.
The one remaining question is how to eliminate 2) from consideration.

At 9/1/05, 1:45 PM, Blogger Elie said...

David got most of it. Option 2 can be eliminated for the same reason as #6. In other words, C knows that he has a black hat, because if C had a red hat, B would be able to deduce that he had a black hat, because if he also had a red hat A would have spoken immediately.

Therefore, since B didn't speak either, it must mean that B has no way of deducing what hat he has because C has a black hat.

What's neat about this is only the guy with the least information can figure it out.


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