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Guest Message by DevFuse
 

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Hats on a death row!! One of my favorites puzzles!


Best Answer bonanova, 08 January 2008 - 06:25 PM

Spoiler for Here's my idea
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#1 roolstar

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Posted 28 December 2007 - 02:35 PM

If you don't already know this one, I'm sure you will find it very interesting and fun to solve! And if you do find the answer (or already know it) please put it under a spoiler tab so that you don't take the fun from the rest of the intelligent people in this forum....

Here we go....

You are one of 20 prisoners on death row with the execution date set for tomorrow.

Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:

“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)

(The prisoner in the back will be able to see the 19 prisoners in front of him
The one in front of him will be able to see 18…)

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…

Well, good luck tomorrow, HA HA HA HA HA HA!”

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many?



Remark of Site Admin:
Note that solution for this puzzle is already given in the following post by bonanova.
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#2 stwalk

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Posted 28 December 2007 - 03:29 PM

19 Prisoners can be guaranteed a stay of exicution and the 20th prisoner has a 50% chance of survival.
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#3 roolstar

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Posted 28 December 2007 - 03:48 PM

Sounds good....

Is your method bullet proof for all possibilities?

Does it work for 19 prisoners?
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#4 stwalk

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Posted 28 December 2007 - 03:51 PM

yes.

hint:
the prisoner at the end of the row (#20) has to be willing to sacrifice himself, or at leats risk sacrifice for the good of the group. (being in the military I can assure you all 20 would be willing to do that for comrads in prison together)
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#5 Bidonet

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Posted 28 December 2007 - 04:16 PM

yes.

hint:
the prisoner at the end of the row (#20) has to be willing to sacrifice himself, or at leats risk sacrifice for the good of the group. (being in the military I can assure you all 20 would be willing to do that for comrads in prison together)



I assume you think prisonner #20 will tell the next prisonner the color of his hat but if all prisonners do the same, only prisonner #1 will be able to tell his own hat color. all others will have 50% chance.

To guarantee the freedom of 10 prisonners, #20 will tell #19's color, #18 will tell #17's color, etc.
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#6 stwalk

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Posted 28 December 2007 - 04:36 PM

bidonet: you are wrong in your assumption of the rest of my answer... good luck
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#7 Bidonet

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Posted 28 December 2007 - 04:47 PM

bidonet: you are wrong in your assumption of the rest of my answer... good luck



A funny solution to guarantee 19 prisonners free is to tell the color of your hat loud or normally, loud meaning the color is red and normally, the color is black. That way, you meet all criteria, 19 prisonners are safe and the 20th has 50% chance.
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#8 roolstar

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Posted 28 December 2007 - 08:46 PM

A funny solution to guarantee 19 prisonners free is to tell the color of your hat loud or normally, loud meaning the color of the hat in front of you is red and normally, the color of the hat in front of you is black. That way, you meet all criteria, 19 prisonners are safe and the 20th has 50% chance.



This technique would work (I suppose you meant the amended solution Bidonet)

stwalk technique may also work, provided it was very well rehearsed...

Now can you find a bullet proof technique, in case the king does not allow us to change the intonation of our voice, or makes us click on the right answer on a giant screen in front of everybody, or makes us push either one of two buttons where the computer says the choice we made.....

I'm just adding these handicaps because this is what I meant by saying: no communication is tolerated (touch, words...). Communication means no message to be sent by voive or touch or noise or light...

HINT: The words RED or BLACK from the first person asked will give all the info for the rest of the prisoners!

Can you find other solutions while respecting these new complications? (and there are more than one)

PS: This is not a latheral thinking puzzle. Common sense and logic can get you safe from being executed in this case.
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#9 unreality

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Posted 29 December 2007 - 05:30 AM

It seems like that's impossible- the person at the very front, who goes first, who can see the 19 people in front of him, has no idea what color his own hat is. It seems like he would always have a 50/50 chance, so there can never be a 100% sucessful outcome. Or is my reasoning wrong?
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#10 spoxjox

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Posted 29 December 2007 - 06:04 PM

It seems like that's impossible- the person at the very front, who goes first, who can see the 19 people in front of him, has no idea what color his own hat is. It seems like he would always have a 50/50 chance, so there can never be a 100% sucessful outcome. Or is my reasoning wrong?


Your reasoning is correct. It was stated that a correct strategy would guarantee the safety of 19 of the 20, with the 20th (first to guess) having a 50% chance.

With no other information present, I don't see how this is solvable. What strategy would allow you to say the word "red" or the word "black" and tell nineteen people which of two colors each was wearing? I believe it is impossible; you cannot convey that much information in a simple binary choice.

I can see a method to save at least 13 of the 20 people:
Spoiler for solution

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