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Posted 09 June 2007 - 09:15 PM
Edit: oh i understand, he put their headbands on in the room with no light, then took them outside >< sorry!
Posted 10 June 2007 - 05:06 PM
If 3rd is confused and 2nd is seeing a red on 1st - then 2nd has to be wearing white and 2nd would not have stayed silent or confused.
if 3rd is confused and 2nd is seeing a white on 1st, then 2nd could be wearing white or red. Therefore 2nd would be confused and silent, so 1st would know that he is wearing white.
Posted 21 June 2007 - 12:47 AM
The one thing that people don't understand is that, the 2nd guy is quiet because
the the 1st guy is white AND that the 3rd guy is quiet! If the 3rd guy spoke up, then the first two would have to be red,
but since the 3rd guy is quiet, the 2nd guy knows that the combinations possible are:
But since #2 is quiet, the 1st must be white, because if the first was red,
2 would have to be white, but if #1 is white then 2 is either Red or White and he doesn't
want to take that 50/50 chance. The first notices this and speaks up. He has to be white!
Posted 22 June 2007 - 01:16 PM
Posted 27 June 2007 - 07:04 PM
The seven possibilities are as follows:
P 1 2 3
1 R R W
2 R W R
3 R W W
4 W R R
5 W R W
6 W W R
7 W W W
In case 1, the third prisoner would (or at least should) immediately know that his headband is White because the two red headbands are on the other prisoners. In cases 2 and three, the second prisoner should know that his headband is white because he can see that the first prisoner's headband is red and would expect the third prisoner to respond immediately if he saw two red headbands. The color of the third prisoner's headband would be irrelevant. In cases 4 through 7, the first prisoner could eliminate that the first three possibilities by the lack of response from the other prisoners, leaving only possibilities where his own headband is white. In all cases, you have to assume that all the prisoners are fairly intelligent and have confidence in the intelligence of their fellow prisoners.
A couple people above seem to be confused about how the prisoners would know how many of each headband were available. I think it is reasonable to accept that the chief was testing the intelligence of the prisoners and would give them the information they needed to succeed. Otherwise, there would not be much point in the exercise.
Another possible solution would be for all three prisoners to state that they had white headbands. The instructions simply state that "If somebody said the colour of his head-band, they all would be free." Nothing says that an incorrect guess deems them to imprisonment. So, since they all know there are only two red headbands, at most only two of them could be wrong, making at least one of them correct. In the same light, one of the prisoners could claim to have a white headband and then if he is incorrect immediately state that he has a red headband. Again, this does not violate the instructions. I think both of these are cheesy solutions, though, and can both be eliminated by simply adding a condition to the puzzle stating that only one guess can be made by the group.
Posted 30 June 2007 - 09:46 PM
Posted 30 June 2007 - 09:50 PM
Posted 01 July 2007 - 11:28 PM
Assuming they saw the headbands before the darkness:
The 2 unused headbands were red and the third man saw two white headbands.
Posted 02 July 2007 - 06:55 AM
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