Just found this riddle, I don't know the answer, but I have a few ideas, see what you think;

You are one of 100 prisoners to be subjected to the ritual of the hats. All the prisoners are blindfolded and buried up to their necks in the sand in a long straight line.

Each one has a hat put on his head, either a black hat or a white hat. The blindfolds are then removed and each man can see only the heads of the men ahead of him.

He can therefore see the colour of the hat each man is wearing in the queue in front of him, but he cannot see whether his own hat is black or white, nor can he see the whiteness or blackness of the hats on the heads of the people behind.

The despot then starts at the rearmost man and asks him to state the colour of the hat he is wearing. If he gets the colour right he is freed, if he gets it wrong he is doomed!

Now the man at the back, Rearsby, is a cricketer and a gentleman, and he happens to be an expert on the ritual of the hats. He has come up with a scheme to save as many of the prisoners as possible, which he has explained to the others before the ritual began. How many can be saved, who shall be saved and how?

Heh, the rules of the riddle aren't strict enough cos you can come up with loads of dodgy schemes to save everyone except the man right at the back. The man at the back coughs before he says his answer if the man in front has a black hat and no cough if he has a white hat. Then he guesses his own colour so he might even escape, but the man in front will already know what colour hat he is wearing and he can communicate to the man in front of him and so on, up to the man at the front.

similar answer here, dude

left wink for black and right wink for white I was thinking [img]smile.gif[/img]

<blockquote>quote:</font><hr>Originally posted by Lord Shield:
similar answer here, dude

left wink for black and right wink for white I was thinking [img]smile.gif[/img] <hr></blockquote>

Hehe. They cant see the person behind. ;) [img]tongue.gif[/img] ;)

<blockquote>quote:</font><hr>Originally posted by Lucre:


Hehe. They cant see the person behind. ;) [img]tongue.gif[/img] ;) <hr></blockquote>

what person behind? you mean they're in a line, not a circle? ****'s sake. Oh well, will have to go for vocal signals then

It's simple...I think

The last man in line is the only one who will not be saved...you could use coughs, as was said...the last man can say the color of the man in front of him, but that only works once...but you could have some voice signals I guess

If he counts the number of hats that are black (or white), he can also be saved

Ah, yes. But noone said there were as many black hats as there were whites. Not this time, at least.

But I'm afraid the answer is not as simple as that. If it was, why then would you be given the information that Rearsby plays cricket and is a gentleman? Eh? ;) [img]tongue.gif[/img]

So my guess is that he politely requests one final game of cricket wiht his fellow prisoners. Black team versus white team. Then, when the captors put all the blackhatted men in one half of the field, and the whitehatted men on the other, everyone would know the colour of his own hat, have a nice game to play and not die ;)

<blockquote>quote:</font><hr>Originally posted by Legolas:
Ah, yes. But noone said there were as many black hats as there were whites. Not this time, at least.

But I'm afraid the answer is not as simple as that. If it was, why then would you be given the information that Rearsby plays cricket and is a gentleman? Eh? ;) [img]tongue.gif[/img]

So my guess is that he politely requests one final game of cricket wiht his fellow prisoners. Black team versus white team. Then, when the captors put all the blackhatted men in one half of the field, and the whitehatted men on the other, everyone would know the colour of his own hat, have a nice game to play and not die ;) <hr></blockquote>

LOL - I cut and pasted it from the radio 4 website, so I suspect that is just part of the wording.

My theory is that every other man states the color of the hat infront of him. That way at least 50% are saved. There is also the chance that his hat will be that color aswell, so without really looking at the maths too much, maybe 75% are saved. Having said that I don't know if it is that sort of puzzle, and I'm not sure where to find the answer. :(

<blockquote>quote:</font><hr>Originally posted by Lioness:
It's simple...I think

The last man in line is the only one who will not be saved...you could use coughs, as was said...the last man can say the color of the man in front of him, but that only works once...but you could have some voice signals I guess<hr></blockquote>

I think that only saves 50% Lioness. If you tell the man in front of you the colour of his hat he has to say the colour of his own hat to save himself and he can't help the man in front of him. So 50% can be saved and 50% of the rest hav a 50/50 chance - so that's approximately 75% saved.

<blockquote>quote:</font><hr>Originally posted by Donut:


I think that only saves 50% Lioness. If you tell the man in front of you the colour of his hat he has to say the colour of his own hat to save himself and he can't help the man in front of him. So 50% can be saved and 50% of the rest hav a 50/50 chance - so that's approximately 75% saved.<hr></blockquote>

That's why I said that'll only work for the first guy...I think coughing is the best idea so far...

Okay, I have it. He looks at the shiny, polished boots of the despot from the corner of his eye so he can see his reflection...

Or, he asks the despot if he's colourblind or something, because he needs to ask. Then when the despot says he's not, the prisoner dares him to prove it by telling him the colour of his hat. ;)

Or he can just agree with each prisnoer to say the following for every 'other' prisoner, "Black, White, Black, White, Black, White, Black, White".

75% of prisoners may be saved.

And these things vary, so there are many more solutions in my head hehe.

<font color="darkblue"> I can do this easily if we take the number of people down to 3.
They are in a Line as Follows-
<Person 1 <Person 2 <Person 3

We will say that person 3 has a black hat on. He can see the hats of both person 1 and person 2. If he sees 2 white hats, he knows that his must be black because there is at least 1 black hat in the lineup. If however, he sees 1 Black and 1 White hat, he says nothing.
If person 3 doesnt say anything, Person 2 knows that his hat must be different to person 1's, so he knows the colour of his hat.

Then, out of the remaining 2, 1 further can be saved. If person 3 calls out that he has a Black hat, Person 2 knows his must be the same as person 1s ie. White.

If person 2 figured his out, person 3 cant do a thing.


So the maximum which can be saved is 2/3. And this riddle is not mathematical, but rather scientific. It is a control experiment- the results are recorder twice, the seond time after changing 1 variable. </font>

Yes, but every prisoner can only see the hat on the one person directly in front of him. So person number three can only see the hat on person number two. Not the one on person number one, not the one on person number four, not his own, only that of number two.

Plus, you don't know how the hats are divided. For all we know there's one black hat on person 1 and all the other 99 have whites. Or, it could be the other way around. Or, more likely, somehting inbetween.

I still like my cricket solution best ;) [img]tongue.gif[/img]