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| Hobby Forum Index » Puzzles » rainbow hat/ rainbow game puzzle |
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| Mariya |
 Posted: Tue Feb 06, 2007 2:52 am |
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I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat on
their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
:) |
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| Simon Tatham |
| Posted: Tue Feb 06, 2007 2:52 am |
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Quote: Mariya wrote:
Without communication, each man guesses the color of the hat
on their head.
CBFalconer <cbfalconer@maineline.net> wrote:
Quote: Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
That's not `without communication'.
--
Simon Tatham What do we want? ROT13!
<anakin@pobox.com> When do we want it? ABJ! |
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| dgates |
| Posted: Tue Feb 06, 2007 3:20 am |
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On 5 Feb 2007 22:52:09 -0800, "Mariya" <mariya.sf@gmail.com> wrote:
Quote: I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat on
their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
:)
I know the solution, but it's hard to explain without using the word
"modulo."
Beforehand, they agree to add up the total of all the colors they see.
They score the colors as R = 1, O = 2, Y = 3, G = 4, B = 5, I = 6, V =
7.
Guy #1 guesses that his own hat color is whatever color would produce
a total for all the hats such that the total modulo 7 is equal to 1.
(If you can understand that sentence, you're home free!)
Guy #2 guesses as though total modulo 7 = 2.
Guy #3 guesses as though total modulo 7 = 3.
And so on, with Guy #7 guessing as though total modulo 7 = 0.
That should win them the game, assuming that all the rest of my
assumptions match yours. |
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| CBFalconer |
| Posted: Tue Feb 06, 2007 4:28 am |
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Mariya wrote:
Quote:
I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat
on their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
--
<http://www.cs.auckland.ac.nz/~pgut001/pubs/vista_cost.txt>
<http://www.securityfocus.com/columnists/423>
"A man who is right every time is not likely to do very much."
-- Francis Crick, co-discover of DNA
"There is nothing more amazing than stupidity in action."
-- Thomas Matthews |
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| Phil Carmody |
| Posted: Tue Feb 06, 2007 6:58 am |
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CBFalconer <cbfalconer@yahoo.com> writes:
Quote: Mariya wrote:
I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat
on their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
The first person could simply say the colour of the second
person's hat and end the procedure even more quickly.
A twist to avoid this would be that the 'someone' points at
the individuals in a, to them, unpredictable order. But even
that fails, as they just have to agree to parrot what the
first person says, and the first person guesses any colour
of any other hat.
However, I think we're not reading enough into the "without
communication". Of course, you can't guess without communication,
so the above assumes that they can communicate their guesses but
nothing else, but I suspect the OP meant to imply that the 7 men
are unable to communicate their guesses to each other. This could
be effected by having them guess simultaniously, for example.
In which case, dgates' answer appears to be the solution. Well found!
Phil
--
"Home taping is killing big business profits. We left this side blank
so you can help." -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./. |
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| dgates |
| Posted: Tue Feb 06, 2007 11:25 am |
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On 06 Feb 2007 12:58:20 +0200, Phil Carmody
<thefatphil_demunged@yahoo.co.uk> wrote:
Quote: CBFalconer <cbfalconer@yahoo.com> writes:
Mariya wrote:
I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat
on their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
The first person could simply say the colour of the second
person's hat and end the procedure even more quickly.
A twist to avoid this would be that the 'someone' points at
the individuals in a, to them, unpredictable order. But even
that fails, as they just have to agree to parrot what the
first person says, and the first person guesses any colour
of any other hat.
However, I think we're not reading enough into the "without
communication". Of course, you can't guess without communication,
so the above assumes that they can communicate their guesses but
nothing else, but I suspect the OP meant to imply that the 7 men
are unable to communicate their guesses to each other. This could
be effected by having them guess simultaniously, for example.
In which case, dgates' answer appears to be the solution. Well found!
Well, well-remembered anyway.
http://groups.google.com/group/rec.puzzles/browse_frm/thread/594bd22ab7003b07
Plus my ability to convert the 4-man answer into the new 7-man answer.
Reminder: If you're telling this out loud to anyone resembling a
normal person, make it TWO men, each of whom has a coin taped to his
forehead!  |
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| Mariya |
| Posted: Tue Feb 06, 2007 12:22 pm |
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good job...!!!
it works...
thnx
On Feb 6, 7:25 am, dgates <dga...@somedomain.com> wrote:
Quote: On 06 Feb 2007 12:58:20 +0200, Phil Carmody
thefatphil_demun...@yahoo.co.uk> wrote:
CBFalconer <cbfalco...@yahoo.com> writes:
Mariya wrote:
I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat
on their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
The first person could simply say the colour of the second
person's hat and end the procedure even more quickly.
A twist to avoid this would be that the 'someone' points at
the individuals in a, to them, unpredictable order. But even
that fails, as they just have to agree to parrot what the
first person says, and the first person guesses any colour
of any other hat.
However, I think we're not reading enough into the "without
communication". Of course, you can't guess without communication,
so the above assumes that they can communicate their guesses but
nothing else, but I suspect the OP meant to imply that the 7 men
are unable to communicate their guesses to each other. This could
be effected by having them guess simultaniously, for example.
In which case, dgates' answer appears to be the solution. Well found!
Well, well-remembered anyway.
http://groups.google.com/group/rec.puzzles/browse_frm/thread/594bd22a...
Plus my ability to convert the 4-man answer into the new 7-man answer.
Reminder: If you're telling this out loud to anyone resembling a
normal person, make it TWO men, each of whom has a coin taped to his
forehead! |
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| Mark P |
| Posted: Tue Feb 06, 2007 2:58 pm |
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Guest
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Phil Carmody wrote:
Quote: CBFalconer <cbfalconer@yahoo.com> writes:
Mariya wrote:
I have a similar problem to this
Problem: Rainbow Hats
7 men are sitting in a room. Someone puts a hat on the head of each
man. Each hat has an equal probability of being one of the seven
colors of the rainbow. It is okay for 2 men to have hats of the same
color. Without communication, each man guesses the color of the hat
on their head. If at least one of them guesses right, they win this
little game of theirs. If they are allowed to make a strategy
beforehand, how can they be assured of winning.
does anyone know the solution?
Each looks at the seventh man, and guesses the color on his head.
The seventh man echoes the same guess.
The first person could simply say the colour of the second
person's hat and end the procedure even more quickly.
A twist to avoid this would be that the 'someone' points at
the individuals in a, to them, unpredictable order. But even
that fails, as they just have to agree to parrot what the
first person says, and the first person guesses any colour
of any other hat.
However, I think we're not reading enough into the "without
communication". Of course, you can't guess without communication,
so the above assumes that they can communicate their guesses but
nothing else, but I suspect the OP meant to imply that the 7 men
are unable to communicate their guesses to each other. This could
be effected by having them guess simultaniously, for example.
In which case, dgates' answer appears to be the solution. Well found!
Phil
This is a pretty famous puzzle, but the way it's usually told is that
the men have to guess *simultaneously* and without communication.
Possibly redundant, but this makes it clear that no one can base his
guess on an overheard previous guess. |
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