Eight logicians stand one behind the other facing an opaque wall such that 3 are on one side and 5 are on the other. None of the logicians can turn around or see beyond the wall.
Each wears a black or white hat as shown below; '|' represents the wall; capital letters are used to identify the logicians; b and w refer to black and white respectively:
w b w | b w b w b A B C | D E F G H
Each knows the location of the others and the quantity of each colour of hat. They also know that all hats of same colour are not on the same side. Logician should announce the colour of owned hat once sure.
Considering that all logicians think at the same speed, who will be the first to declare having which colour? How many can come to know the colour of owned hat and in what order?
Considering that all logicians think at the same speed, who will be the first to declare having which colour? How many can come to know the colour of owned hat and in what order?
| See The Solution | Submitted by Salil |
| Rating: 2.8000 (5 votes) |
re: First to declare
|
 | Comment 7 of 8 |  |
You are essentially right. But I would add one clarification.
B and G will both be first to declare simultaneously. B knows he is black because A did not announce he was white. If A had seen two whites in front of him he woud have declared black because he knows that "all hats of the same colour can not be on same side. Since A didn't announce black, then B "knows" he is black.
Then C (he knows he can't be black like B) and F will both be second to declare simultaneously.
Then E is third.
Then D is fourth.
A and H will never declare because they do not have enough information.
| Posted by Don Cleland on 2006-07-16 23:21:53 |
