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?
| Submitted by Salil | |
| Rating: 2.8000 (5 votes) | |
| Solution: | (Hide) |
|
Except the two logicians at the ends all will be able to guess their colours. First one to guess will be G since H is not able to guess his hats colour ( This is possible only with 3:1 colour combination ) Second to guess would be F. By which time B would have waited for A to makeup his mind. Then simultaneously B & E would guess their colour followed by C & D. A & H will not be able to guess their colour. |
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| Subject | Author | Date | |
 | Puzzle Thoughts | K Sengupta | 2023-05-20 02:12:53 |
| re: First to declare | Don Cleland | 2006-07-16 23:21:53 |
| hat problem | samantha | 2006-07-14 08:29:42 |
 | hat problem | scott | 2006-07-14 00:39:33 |
| re(2): i think i got it.....? | trey | 2006-07-10 00:28:49 |
| re: i think i got it.....? | a | 2006-07-07 05:15:29 |
| i think i got it.....? | a | 2006-07-07 05:09:49 |
 | First to declare | Jyqm | 2006-07-02 11:34:55 |
