Logic puzzles...
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 see any hats. When A is asked if he knows the color of the hat he is wearing, he says no. When B is asked if he knows the color of the hat he is wearing he says no. When C is asked if he knows the color of the hat he is wearing he says yes and he is correct. What color hat and how can this be? There is no play on words and there are no tricks. If I used had instead of has it is purely accidental.
Maybe I got off on the right foot, but it seemed very straightforward:
A can't tell what color his hat is.
If B and C's hats were both white, A would know his is black, since there are only 2 white hats.
Thus B and C's hats are either black/black, white/black or black/white.
B can't tell what color his hat is.
If C's hat was white, B would know his is black, since B's and C's can't both be white.
Thus C's is black.
Thus C knows his own hat is black.
Afterwards I made the truth table just for kicks, but it wasn't really necessary.
The NS13 door code puzzle was a bit harder. You need to get a 3 digit code to a door lock from 4 guards, who happen to be playing bridge. One always lies, one always tells the truth, one alternates between the two, and one craves human flesh:
The guard playing South says, "I suppose you want the combination to the other door, then? I'm getting really tired of people asking about that."
"He's lying," says North.
"No," says East, "you're the one lying."
"Graaaaagh," says West.
"Well," says South, "the first digit is 6."
"No it isn't," says East. "It's 1."
North shakes his head. "They're both lying -- it's 3."
"The second digit now -- that's 9," says South.
"Graaaaagh," says West.
"It's 0, in fact," says North.
East grumbles, "It's definitely more than that."
"Sorry, I meant to say 8," replies North. "And the last digit is 4."
"Don't listen to him," says South. "It's 7."
"No, it is 4, I'm sure of it," says East.
"Graaaaagh," says West.
At least it should be easy to figure out which one craves human flesh... ;) Happy puzzling!
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 see any hats. When A is asked if he knows the color of the hat he is wearing, he says no. When B is asked if he knows the color of the hat he is wearing he says no. When C is asked if he knows the color of the hat he is wearing he says yes and he is correct. What color hat and how can this be? There is no play on words and there are no tricks. If I used had instead of has it is purely accidental.
Maybe I got off on the right foot, but it seemed very straightforward:
A can't tell what color his hat is.
If B and C's hats were both white, A would know his is black, since there are only 2 white hats.
Thus B and C's hats are either black/black, white/black or black/white.
B can't tell what color his hat is.
If C's hat was white, B would know his is black, since B's and C's can't both be white.
Thus C's is black.
Thus C knows his own hat is black.
Afterwards I made the truth table just for kicks, but it wasn't really necessary.
The NS13 door code puzzle was a bit harder. You need to get a 3 digit code to a door lock from 4 guards, who happen to be playing bridge. One always lies, one always tells the truth, one alternates between the two, and one craves human flesh:
The guard playing South says, "I suppose you want the combination to the other door, then? I'm getting really tired of people asking about that."
"He's lying," says North.
"No," says East, "you're the one lying."
"Graaaaagh," says West.
"Well," says South, "the first digit is 6."
"No it isn't," says East. "It's 1."
North shakes his head. "They're both lying -- it's 3."
"The second digit now -- that's 9," says South.
"Graaaaagh," says West.
"It's 0, in fact," says North.
East grumbles, "It's definitely more than that."
"Sorry, I meant to say 8," replies North. "And the last digit is 4."
"Don't listen to him," says South. "It's 7."
"No, it is 4, I'm sure of it," says East.
"Graaaaagh," says West.
At least it should be easy to figure out which one craves human flesh... ;) Happy puzzling!