# Four hats

Natural Science
Posers and Puzzles 06 Oct '06 12:38
1. Natural Science
blunderer of pawns
06 Oct '06 12:384 edits
Here's the situation:

Four men are tied to chairs in this configuration: (the arrows denote which way the men are facing.)

Man ---) Man ---) Man ---) (Wall) (--- Man

These are the instructions the men have been given:

1. Each of you is wearing a hat. Two of you are wearing a blue hat, two of you are wearing a red hat.
2. In order to save yourselves, one of you must correctly identify the color of your own hat.
3. You are not allowed to tell anyone else what color their hat is.
4. You have 10 minutes for one of you to positively identify the color of his own hat. After 10 minutes, or after a wrong guess, a bomb will go off. The bomb will also go off if anyone cheats.

Because of the manner in which they are tied, none of the men can see what's behind them; they can only see forward. The lone man on the one side of the wall, obviously, cannot see any of the other men. Also, none of the men can take off their hat to identify it. Obviously, any of the 4 of them can take a guess and have a 50% chance of being right. But how can one of them deduce, with 100% certainty, the color of his own hat, given the rules laid out?
2. 06 Oct '06 12:59
Originally posted by Natural Science
Man ---) Man ---) Man ---) (Wall) (--- Man
call them A,B,C,D from left to right

either B and C are wearing the same colour, in which case A can tell he is wearing the other colour,

or B and C are wearing different colours, so A says nothing.
B then knows C has a different colour to B,
so B knows what he is wearing the other colour than C is wearing.
3. 07 Oct '06 15:21
Originally posted by aging blitzer
call them A,B,C,D from left to right

either B and C are wearing the same colour, in which case A can tell he is wearing the other colour,

or B and C are wearing different colours, so A says nothing.
B then knows C has a different colour to B,
so B knows what he is wearing the other colour than C is wearing.
if B and C are different, they can figure it out, but how does A and D determine what they have?
4. AThousandYoung
08 Oct '06 08:14
Only one person needs to figure it out.
5. Natural Science
blunderer of pawns
08 Oct '06 12:12
Againg Blitzer has the correct solution.
6. 10 Oct '06 20:462 edits
The middle person on the left side of the wall can say with 100% certainity. If the first two persons are wearing the same hat then definelty the last person has the answer but if doesnt then the middle one is wearing the opposite color cap from the guy who is sitting in front of him.
7. 10 Oct '06 21:17
You can still do this if you add a third hat of one colour (and discard it after shuffling them and 'dealing' them onto people's heads).
8. 10 Oct '06 22:32
Well if one man has to identify the colour of their own hat and each man can take their hat off and look at it then surely te rest follows?
Am i missing something, again. ðŸ™‚ðŸ˜•
9. XanthosNZ
Cancerous Bus Crash
11 Oct '06 01:00
Originally posted by jimslyp69
Well if one man has to identify the colour of their own hat and each man can take their hat off and look at it then surely te rest follows?
Am i missing something, again. ðŸ™‚ðŸ˜•
"Also, none of the men can take off their hat to identify it."
10. 11 Oct '06 01:01
That they are tied to the chairs including their arms (and therefore cannot reach up to grab their hats).

Also, it is important to note that these are the most intelligent people on the planet (all Guttersnipes) and for the purposes of this riddle, they don't tell each other anything - knowing that they are all brainy enough by themselves.
11. 11 Oct '06 01:041 edit
Grrrr....
12. CalJust
It is what it is
11 Oct '06 10:49
Originally posted by Gastel
Grrrr....
What do you have to edit if you just say Grrrr....???
13. sonhouse
Fast and Curious
11 Oct '06 11:58
Originally posted by CalJust
What do you have to edit if you just say Grrrr....???
Figuring out if it's supposed to be Grrr or Grrrr......
14. CalJust
It is what it is
11 Oct '06 12:08
Originally posted by sonhouse
Figuring out if it's supposed to be Grrr or Grrrr......
In that case, your edit definitely improved it!
15. 11 Oct '06 21:14
Originally posted by XanthosNZ
"Also, none of the men can take off their hat to identify it."
Not what what it said last time I read it. 4 edits?