Logic puzzles...

Sep 10, 2007 09:53

shadeofnight posted a logic puzzle:

There are 3 black hats and 2 white hats in a box. Three men (we will call them A, B, & C) each reach into the box and place one of the hats on his own head. They cannot see what color hat they have chosen. The men are situated in a way that A can see the hats on B & C's heads, B can only see the hat on C's head and C cannot ( Read more... )

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free_of_whip September 10 2007, 18:09:38 UTC
Hmm... I'm not a gamer, but I came up with:

East alternates between telling the truth and lying.
North always lies.
West craves human flesh.
South always tells the truth.
The combination is 697.

How did I figure that out? Well, North says different things on the same subject at different times, so he cannot be the one who always tells the truth. He must always lie, or sometimes tell the truth and sometimes lie.

East says that the second digit is more than 0, which would be true if it were either 8 or 9. Thus, East cannot always be lying, because this would mean that South and North were also lying about the second digit, and one of them always tells the truth. So East is either the one who always tells the truth, or the one who sometimes tells the truth and sometimes lies.

East cannot be the one who always tells the truth, because if he did, North would have to be lying in the first exchange, but telling the truth about the third digit. So North would have to be the one who sometimes lies and sometimes tells the truth. This would mean that South always lies. However, East and South agree in the first exchange, so if East always tells the truth, then South has told the truth at least once, so South cannot be the one who always lies. Thus, East must sometimes tell the truth and sometimes lie. This means that North must always be lying. And since there is only one left, South must always be telling the truth.

And (checking my logic), if South always tells the truth, then East would be telling the truth in the first exchange about how North was lying, would be lying about the first digit, would be telling the truth about the second digit, and would be lying about the third digit. This would mean that East would be the one that sometimes told the truth and sometimes lied. Then, North would always have to be lying, because there is not more than one who sometimes tells the truth.

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re: I'm not a gamer... nminusone September 10 2007, 18:52:44 UTC
Perhaps not, but I think "lawyer" is slightly above "gamer" on the "logical, precise and detail-oriented" scale, so you're more than qualified here. ;)

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