Red or blue
Three intelligent women, Alice, Barb and Carol, sit down to try out a test in logical reasoning. They are so arranged that each can see the color of a label which is either red or blue, attached to the hats worn by the other two but none of them can see the color of the label attached to her own hat. They are told that at least one of the labels is red. If any one of them can logically deduce the color of the label on her hat, she is to declare it. Carol decides to play this game with her eyes closed, knowing that the other two women have their eyes open. After a little time Carol, who has not seen the label on any of the hats declares her label colour. What is Carol's label colour (and why)?
Labels: logic
posted by Chris at
8:30 PM
6 Comments:
They all have red hats
A sees B+C
if B+C are both blue then A knows A=Red
this does not occur so at least one of B+C is Red
B sees A+C
if A+C are both blue then B knows B=Red
this does not occur so at least one of A+C is Red
Now A+B both know this. But if C is Blue then they would each know that their hat must be red since the other must see at least one Red hat. This does not occur, thus Cs hat must be Red.
C deduces that their hat must be Red.
Cam
I should have noted that:
While Cs hat must be red ,
A+B have may have blue or red hats. i.e. both blue, one blue one red, or both red
Only C's hat color is determined.
Cam
I should have noted that:
While Cs hat must be red ,
A+B have may have blue or red hats. i.e. both blue, one blue one red, or both red
Only C's hat color is determined.
Cam
I don't have the solution, but I disagree with Cam...
If both A and B have red hats they would each see the other's red and keep quiet, thus C could be either blue or red....so no conclusion could be made in this scenario.
regards, Curtis
Curtis,
A,B,C=B,B,B invalid, at least one must be R
A,B,C =B,B,R =A +B can not immediately figure out what hat they have
A,B,C= B,R,B=B knows his hat is red
A,B,C= B,R,R= A +B can not immediately figure out what hat they have
A,B,C= R,B,B= A knows his hat is red
A,B,C= R,B,R= A +B can not immediately figure out what hat they have
A,B,C=R,R,B= A +B can not immediately figure out what hat they have
A,B,C= R,R,R = A +B can not immediately figure out what hat they have
All the scenarios where C has a blue hat....
We have 3 scenarios:
A,B,C= B,R,B=B knows his hat is red
A,B,C= R,B,B= A knows his hat is red
A,B,C=R,R,B= A +B can not immediately figure out what hat they have
If A or B has not immediately yelled out the color of their hat. And they see Cs blue hat, they can deduce that they must be in the only remaining scenario where B has a blue hat. A,B,C=R,R,B.
Thus, after a short pause they can both yell out Red.
This didn't happen thus C must not have a blue hat. C must have a Red hat.
We are in one of the remaining scenarios:
A,B,C =B,B,R =A +B can not immediately figure out what hat they have
A,B,C= B,R,R= A +B can not immediately figure out what hat they have
A,B,C= R,B,R= A +B can not immediately figure out what hat they have
A,B,C= R,R,R = A +B can not immediately figure out what hat they have
Cam
Nice to see you struggling Cam ;) But, of course, you got it.
_ CBA
1 BBB not allowed
2 BBR A would immediately say R
3 BRB B would immediately say R
4 BRR After a while, A and B would both say R.
5 RBB
6 RBR
7 RRB
8 RRR
4 A realises that she can't be wearing B because B didn't
immediately say R. The same goes for B.
So if C is wearing B, A or B (or both) could deduce their own hat
colour.
As neither A nor B could state their own hat colour, C must be wearing R. In fact, in cases 5-8, A and B are stuck. Each would be
seeing R or B on each other and would each realise it's the
same for each other.
C realises all of that, so knows she must be wearing R.
Post a Comment
Links to this post:
Create a Link
<< Home