5 hats in a bag 3 red 2 blue
shi...@shell9.ba.best.com
There are 3 people in a room.
There is a bag with 5 hats in it, 3 red and 2 blue.
The 3 people are standing front-to-back in a line.
The 3 people know there are 5 hats in the bag, 3 red and 2 blue.
They can only see the person(s) in front of them, the first guy
sees no one.
One hat is placed randomly on each of there heads.
None of them knows what color his hat is.
The first guy (front of the line) says,
"I dont know what color my hat is."
The second guy (middle of the line) says,
"I dont know what color my hat is."
The third guy (last of the line) says,
"I KNOW what color my hat is."
Then the first guy says,
"OK, then I KNOW what color my hat is too."
Then the second guy says,
"OK, then I KNOW what color my hat is too."
What color was each of their hats and how could they know?
--Joe McCaughan | Great is the Lord, and greatly to be praised,
shi...@best.com | And His greatness is unsearchable! Psalm 145:3
STANG
The first two guys got the red hats. The last three guys in line could
see the color of the hats of the first two men. Through the process of
elimination, they could determine the color of thier own hats.
lwe...@nospam.cybertours.com
:<shi...@shell9.ba.best.com> wrote:
:
:
:There are 3 people in a room.
:There is a bag with 5 hats in it, 3 red and 2 blue.
:The 3 people are standing front-to-back in a line.
:The 3 people know there are 5 hats in the bag, 3 red and 2 blue.
:They can only see the person(s) in front of them, the first guy
: sees no one.
:One hat is placed randomly on each of there heads.
:None of them knows what color his hat is.
:
:The first guy (front of the line) says,
: "I dont know what color my hat is."
:
:The second guy (middle of the line) says,
: "I dont know what color my hat is."
:
:The third guy (last of the line) says,
: "I KNOW what color my hat is."
:
:Then the first guy says,
: "OK, then I KNOW what color my hat is too."
:
:Then the second guy says,
: "OK, then I KNOW what color my hat is too."
:
:
:What color was each of their hats and how could they know?
:
:
:--Joe McCaughan | Great is the Lord, and greatly to be praised,
:shi...@best.com | And His greatness is unsearchable! Psalm 145:3
first = blue
second = blue
third = red
The third guy saw the first two wearing blue so then he knew
he was wearing a red. The first and second guys, hearing that
the third guy knew what his was with only seeing two other
hats, figured out that theirs must both be blue.
Scott Morrow
Feroze Daud wrote:
> The third guy said that he doesnt know what color his hat his. This rules
> out the two people in from of him having both the blue hats ( coz that means
> that the third guy has a red hat ).
>
You've complicated your answer by misreading the story.. The third guy said he
DID know what color his hat was... The only way he could be sure of his hat
color would be if the first 2 had the two blue hats. Therefore: #1: Blue, #2:
Blue, #3: Red.
> Hearing this answer from the third guy, the first and second guy know that
> they both dont have blue hats, but red & blue. Which guy has which has to be
> found now,
>
> The truth table at this point looks as follows :
>
> 1 2 3
> R R R -->
> R R B
> R B R
> R B B
> B R R
> B R B
> B B R --> ruled out because 1 & 2 both dont have blue
> colored hats
>
> Now, if the first guy had a blue hat, this would mean that #2 had a red hat.
> Since #2 says that he doesnt know which color hat he has, that means that
> guy#1 has a red hat.
>
> WHen you ask guy #1 what color hat he has, he can give the answer now,
> because from the answers of #2 & #3 he can guess what color hat he got. #1
> has a red hat.
>
> Now, when #1 says that he has a red hat, that means that #2 can now guess
> his color to be blue.
>
> shi...@shell9.ba.best.com wrote in message
> <6ah6bg$1oc$1...@nntp1.ba.best.com>...
> >
> >
> >There are 3 people in a room.
> >There is a bag with 5 hats in it, 3 red and 2 blue.
> >The 3 people are standing front-to-back in a line.
> >The 3 people know there are 5 hats in the bag, 3 red and 2 blue.
> >They can only see the person(s) in front of them, the first guy
> > sees no one.
> >One hat is placed randomly on each of there heads.
> >None of them knows what color his hat is.
> >
> >The first guy (front of the line) says,
> > "I dont know what color my hat is."
> >
> >The second guy (middle of the line) says,
> > "I dont know what color my hat is."
> >
> >The third guy (last of the line) says,
> > "I KNOW what color my hat is."
> >
> >Then the first guy says,
> > "OK, then I KNOW what color my hat is too."
> >
> >Then the second guy says,
> > "OK, then I KNOW what color my hat is too."
> >
> >
> >What color was each of their hats and how could they know?
> >
> >
> >--Joe McCaughan | Great is the Lord, and greatly to be praised,
> >shi...@best.com | And His greatness is unsearchable! Psalm 145:3
--
Check out The Answer Dude at
http://www.geocities.com/SiliconValley/8728
shi...@shell9.ba.best.com
STANG <zt...@bellsouth.net> wrote:
: shi...@shell9.ba.best.com wrote:
: >
: > There are 3 people in a room.
: > There is a bag with 5 hats in it, 3 red and 2 blue.
: > The 3 people are standing front-to-back in a line.
: > The 3 people know there are 5 hats in the bag, 3 red and 2 blue.
: > They can only see the person(s) in front of them, the first guy
: > sees no one.
: > One hat is placed randomly on each of there heads.
: > None of them knows what color his hat is.
: >
: > The first guy (front of the line) says,
: > "I dont know what color my hat is."
: >
: > The second guy (middle of the line) says,
: > "I dont know what color my hat is."
: >
: > The third guy (last of the line) says,
: > "I KNOW what color my hat is."
: >
: > Then the first guy says,
: > "OK, then I KNOW what color my hat is too."
: >
: > Then the second guy says,
: > "OK, then I KNOW what color my hat is too."
: >
: > What color was each of their hats and how could they know?
: >
: > --Joe McCaughan | Great is the Lord, and greatly to be praised,
: > shi...@best.com | And His greatness is unsearchable! Psalm 145:3
: The first two guys got the red hats. The last three guys in line could
: see the color of the hats of the first two men. Through the process of
: elimination, they could determine the color of thier own hats.
Nope - there are only (3) guys in line. Check the rules. Good try!
shi...@shell9.ba.best.com
lwe...@nospam.cyberTours.com wrote:
: :<shi...@shell9.ba.best.com> wrote:
: :
: :
: :There are 3 people in a room.
: :There is a bag with 5 hats in it, 3 red and 2 blue.
: :The 3 people are standing front-to-back in a line.
: :The 3 people know there are 5 hats in the bag, 3 red and 2 blue.
: :They can only see the person(s) in front of them, the first guy
: : sees no one.
: :One hat is placed randomly on each of there heads.
: :None of them knows what color his hat is.
: :
: :The first guy (front of the line) says,
: : "I dont know what color my hat is."
: :
: :The second guy (middle of the line) says,
: : "I dont know what color my hat is."
: :
: :The third guy (last of the line) says,
: : "I KNOW what color my hat is."
: :
: :Then the first guy says,
: : "OK, then I KNOW what color my hat is too."
: :
: :Then the second guy says,
: : "OK, then I KNOW what color my hat is too."
: :
: :
: :What color was each of their hats and how could they know?
: :
: :
: :--Joe McCaughan | Great is the Lord, and greatly to be praised,
: :shi...@best.com | And His greatness is unsearchable! Psalm 145:3
: first = blue
: second = blue
: third = red
: The third guy saw the first two wearing blue so then he knew
: he was wearing a red. The first and second guys, hearing that
: the third guy knew what his was with only seeing two other
: hats, figured out that theirs must both be blue.
YES! Could not have said it better... pure inductive reasoning...
--Joe McCaughan | He who heeds the word wisely will find good,
shi...@best.com | And whoever trusts in the Lord, happy is he. Proverbs 16:20
shi...@shell9.ba.best.com
Feroze Daud <fan...@opera.com> wrote:
: The third guy said that he doesnt know what color his hat his. This rules
: out the two people in from of him having both the blue hats ( coz that means
: that the third guy has a red hat ).
Nope - check the rules and the sequence of events. Here's the quote
from the third guy:
The third guy (last of the line) says,
"I KNOW what color my hat is."
Good try though...
--Joe McCaughan | He who diligently seeks good finds favor,
shi...@best.com | But trouble will come to him who seeks evil. Proverbs 11:27
: Hearing this answer from the third guy, the first and second guy know that
: they both dont have blue hats, but red & blue. Which guy has which has to be
: found now,
: The truth table at this point looks as follows :
: 1 2 3
: R R R -->
: R R B
: R B R
: R B B
: B R R
: B R B
: B B R --> ruled out because 1 & 2 both dont have blue
: colored hats
: Now, if the first guy had a blue hat, this would mean that #2 had a red hat.
: Since #2 says that he doesnt know which color hat he has, that means that
: guy#1 has a red hat.
: WHen you ask guy #1 what color hat he has, he can give the answer now,
: because from the answers of #2 & #3 he can guess what color hat he got. #1
: has a red hat.
: Now, when #1 says that he has a red hat, that means that #2 can now guess
: his color to be blue.
: shi...@shell9.ba.best.com wrote in message
: <6ah6bg$1oc$1...@nntp1.ba.best.com>...
: >
: >
: >There are 3 people in a room.
Mike
On Mon, 26 Jan 1998 11:32:25 -0800, "Feroze Daud" <fan...@opera.com>
fired up their news software and posted article
<6aiojg$u...@news.microsoft.com>, which said:
>The third guy said that he doesnt know what color his hat his. This rules
>out the two people in from of him having both the blue hats ( coz that means
>that the third guy has a red hat ).
Read it again. The third guy says he DOES know what color his hat is.
He saw two blue hats, so he know he had to have red. When they knew
the third guy knew, then that meant that they both had red.
---
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^A^
Mike Straw
http://www2.prestel.co.uk/thestraws
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