Avon
Level: Delver
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Registered: 12-06-2003
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Make a pile of twenty coins and turn them over. If this pile had n tails before turning the coins over, now it has 20-n tails and the remaining coins contain 20-n tails.

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

Schik
Level: Legendary Smitemaster

Rank Points: 5383
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Very good - you're up again!

____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

The_Red_Hawk
Level: Smitemaster
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You have to ask the "someone" to tell you which are which.

If that fails, I could use my tongue to test what they feel like.

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Schik
Level: Legendary Smitemaster

Rank Points: 5383
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The_Red_Hawk wrote:
If that fails, I could use my tongue to test what they feel like.

Did I mention that you don't know where these coins have been? That's disgusting.

Anyways, Avon already solved it.


____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Avon
Level: Delver
Rank Points: 47
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This puzzle should not be a cruel as my last one.

A group of 20 men captured during a war. The enemy want to execute them, but are willing to grant a partial amnesty. Tommorow the prisoners will line up on the execution grounds facing north. A hat will be placed on each man's head so that no man can see his own hat or the hat of any man behind him but he can see the hats of all the men in front of him. Each hat is either red or white. Starting from the southernmost man (who can see the other 19 hats) and working north, each man will be asked the colour of his own hat. When all men have replied, those who answered incorrectly will be executed and the rest will be allowed to live.

The prisonsers can spend the night planning a strategy to ensure as many as possible survive. Unfortunately, they are unable to communicate without the enemy overhearing so the enemy will know their strategy and will distribute the hats to ensure as many as possible are executed.

What is the prisoners' best strategy?


[Edited by Avon on 01-01-2004 at 01:53 AM GMT]

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
Rank Points: 783
Registered: 09-02-2003
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They can simply take off their hats and look at them.

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

The_Red_Hawk
Level: Smitemaster
Rank Points: 783
Registered: 09-02-2003
IP: Logged

Wait - I know! I guess the previous answer won't be allowed, so.....

They agree for each second person to speak the colour hat of the person directly in front. So 10 will be assured of surviving, and the others have a 50% chance - so 15 will survive.

It doesn't matter if the enemy overhears, because no matter what colour hats they give, it won't make a difference.

[Edited by The_Red_Hawk on 01-01-2004 at 01:36 AM GMT]

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

agaricus5
Level: Smitemaster
Rank Points: 1838
Registered: 02-04-2003
IP: Logged

Avon wrote:
This puzzle should not be a cruel as my last one.

A group of 20 men captured during a war. The enemy want to execute them, but are willing to grant a partial amnesty. Tommorow the prisoners will line up on the execution grounds facing north. A hat will be placed on each man's head so that no man can see his own hat or the hat of any man behind him but he can see the hats of all the men in front of him. Each hat is either red or white. Starting from the southernmost man (who can see the other 19 hats) and working north, each man will be asked the colour of his hat. When all men have replied, those who answered incorrectly will be executed and the rest will be allowed to live.

The prisonsers can spend the night planning a strategy to ensure as many as possible survive. Unfortunately, they are unable to communicate without the enemy overhearing so the enemy will know their strategy and will distribute the hats to ensure as many as possible are executed.

What is the prisoners' best strategy?

I suppose it is to have each prisoner say the colour of the hat of the person in front. That way, 19 of the prisoners will be saved, and only the first one will die.

____________________________
Resident Medic/Mycologist

Oneiromancer
Level: Legendary Smitemaster

Rank Points: 2936
Registered: 03-29-2003
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The_Red_Hawk wrote:
They can simply take off their hats and look at them.

If you were going to be executed for guessing the wrong color of the hat you were wearing, don't you think they would execute you for "cheating" like that? A little common sense is necessary to solve these puzzles. If Avon says that no man can see the hat on his head or the ones behind him, then that's the way it is.

I have seen a very similar puzzle to this recently so I cannot post the answer though. But if it is the same answer then no one will die.

Game on,

[Edited by Oneiromancer on 01-01-2004 at 01:39 AM GMT]

____________________________
"He who is certain he knows the ending of things when he is only beginning them is either extremely wise or extremely foolish; no matter which is true, he is certainly an unhappy man, for he has put a knife in the heart of wonder." -- Tad Williams

The_Red_Hawk
Level: Smitemaster
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agaricus5 wrote:

I suppose it is to have each prisoner say the colour of the hat of the person in front. That way, 19 of the prisoners will be saved, and only the first one will die.

That won't work, because though the second person will know what colour his hat is, he has to say the colour of the one in front. So if they are different, one of the two will die.

My solution should work though (I think).

[Edited by The_Red_Hawk on 01-01-2004 at 01:40 AM GMT]

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

agaricus5
Level: Smitemaster
Rank Points: 1838
Registered: 02-04-2003
IP: Logged

Oneiromancer wrote:
If you were going to be executed for guessing the wrong color of the hat you were wearing, don't you think they would execute you for "cheating" like that?

Well, since the number of red and white hats appears to be variable, as no-one has made a mention about how many of each there are, then all the men would have to guess if they weren't cheating because they cannot work it out logically.

____________________________
Resident Medic/Mycologist

Avon
Level: Delver
Rank Points: 47
Registered: 12-06-2003
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The_Red_Hawk wrote:
Wait - I know! I guess the previous answer won't be allowed, so.....

They agree for each second person to speak the colour hat of the person directly in front. So 10 will be assured of surviving, and the others have a 50% chance - so 15 will survive.

It doesn't matter if the enemy overhears, because no matter what colour hats they give, it won't make a difference.

[Edited by The_Red_Hawk on 01-01-2004 at 01:36 AM GMT]

Yes, they are forbidden to take off their hats, and also to speak apart from saying either "red" or "white".

Also you second strategy only guarantees 10 people survive. The enemy knowing this plan can ensure the other 10 die.

But you can do better than 10 surviving.

I guess a few people got in before me.

[Edited by Avon on 01-01-2004 at 01:42 AM GMT]

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
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All right then, the first one guesses, then taps the next guy on the shoulder. The right shoulder means "red" and the left "white" or vice versa.

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Avon
Level: Delver
Rank Points: 47
Registered: 12-06-2003
IP: Logged

agaricus5 wrote:
Well, since the number of red and white hats appears to be variable, as no-one has made a mention about how many of each there are, then all the men would have to guess if they weren't cheating because they cannot work it out logically.

They can work it out logically, most of them anyway.

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

Avon
Level: Delver
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Registered: 12-06-2003
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The_Red_Hawk wrote:
All right then, the first one guesses, then taps the next guy on the shoulder. The right shoulder means "red" and the left "white" or vice versa.

They're standing too far apart for that or the guards chopped off their arms, whichever you think is more realistic.

And their legs too, if you like.

[Edited by Avon on 01-01-2004 at 01:46 AM GMT: make it more violent]

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
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I just noticed something! With the way you worded the question, it can also be interpreted as "they will be asked the colour of the southernmost man's hat. So he guesses. If he guesses right, all survive, and if he's wrong, 19 survive.

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Avon
Level: Delver
Rank Points: 47
Registered: 12-06-2003
IP: Logged

The_Red_Hawk wrote:
I just noticed something! With the way you worded the question, it can also be interpreted as "they will be asked the colour of the southernmost man's hat. So he guesses. If he guesses right, all survive, and if he's wrong, 19 survive.

I changed it to "each man will be asked the colour of his own hat" even though I thought it was clear enough already.

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
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Registered: 09-02-2003
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All right then, they all get to sneak a glimpse at their hat before it is put on.

How many exactly can be saved?

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Mattcrampy
Level: Smitemaster

Rank Points: 2388
Registered: 05-29-2003
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I know an answer to this puzzle that guarantees all but one survives. Seeing as I knew it before-hand, I'll let you all have some fun.

Matt

____________________________
What do you call an elephant at the North Pole?

The_Red_Hawk
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How about this? If the next person is red, the first person hesitates 5 seconds before saying his guess. If white, he says it immediately. This would continue down the line, except the rest of the people would know their colour.

[Edited by The_Red_Hawk on 01-01-2004 at 02:07 AM GMT: Just when I'm sure I'm right, Avon leaves the forum! ]

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Avon
Level: Delver
Rank Points: 47
Registered: 12-06-2003
IP: Logged

The_Red_Hawk wrote:
How about this? If the next person is red, the first person hesitates 5 seconds before saying his guess. If white, he says it immediately. This would continue down the line, except the rest of the people would know their colour.

[Edited by The_Red_Hawk on 01-01-2004 at 02:07 AM GMT: Just when I'm sure I'm right, Avon leaves the forum! ]

Sorry, I had to go and get something to eat.

The guards then chop out the prisoner's tongues and each man nods his head for "white" and shakes his head for "red". Then the guard calls out the guess.

[Edited by Avon on 01-01-2004 at 02:12 AM GMT]

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
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Without a tongue, you can still make sounds. So the person says "Uuuhhhhhh" before his guess if the next is red, and nothing if the next is white.

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Avon
Level: Delver
Rank Points: 47
Registered: 12-06-2003
IP: Logged

The_Red_Hawk wrote:
Without a tongue, you can still make sounds. So the person says "Uuuhhhhhh" before his guess if the next is red, and nothing if the next is white.

The guards are fairly nice fellows. They could have executed the prisoners straight away. If the guards believe that any prisoner tried to communicate anything other than a guess of his own hat colour, all the prisoners will be executed.

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
Level: Smitemaster
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Is the number of colours important? i.e. if there were green hats too, would the solution be the same?

And does the fact they are facing north have anything to do with it?

Do they have anything with them other than their clothes?

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

levelthirteen
Level: Master Delver
Rank Points: 109
Registered: 02-20-2003
IP: Logged

Red Hawk; there are no side channels in the solution. They all state the night before that they will say that they have a white hat on. The next day, when asked the color of their hat, they all say red and live.

Avon
Level: Delver
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The_Red_Hawk wrote:
Is the number of colours important? i.e. if there were green hats too, would the solution be the same?

And does the fact they are facing north have anything to do with it?

Do they have anything with them other than their clothes?

A some point I said the prisoners were forbidden from saying anything other than "red" or "white", so if we add green hats, the guards would maximise the number of executions by giving everyone a green hat.

They're facing north. The sun rises in the east. In the morning they should cast a pretty long shadow. But when they arrive at the execution grounds, alas, the eastern wall is too high for the shadows to be of any use.

Who said they were wearing clothes? I always imagined the prisoners were naked.



____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

Avon
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levelthirteen wrote:
Red Hawk; there are no side channels in the solution. They all state the night before that they will say that they have a white hat on. The next day, when asked the color of their hat, they all say red and live.

How do they plan this without the guards knowing?

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

The_Red_Hawk
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levelthirteen wrote: there are no side channels in the solution.

I am only trying to find the answer.

Avon wrote: At some point I said the prisoners were forbidden from saying anything other than "red" or "white", so if we add green hats, the guards would maximise the number of executions by giving everyone a green hat.

No - I mean if the prisoners knew there were green hats as well, would the solution be any different?

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

zex20913
Level: Smitemaster

Rank Points: 1723
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Darn. I thought that something would work, but it only works for a red-white-red-white orientation, and not for too many others.

____________________________

Avon
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The_Red_Hawk wrote:

Avon wrote: At some point I said the prisoners were forbidden from saying anything other than "red" or "white", so if we add green hats, the guards would maximise the number of executions by giving everyone a green hat.

No - I mean if the prisoners knew there were green hats as well, would the solution be any different?

Yes, I was only joking. I'm fairly sure you couldn't save as many with three hat colours. You can save at half no matter how many colours there are, but I'm not sure if you could do better.

[Edited by Avon on 01-01-2004 at 03:06 AM GMT]

____________________________
"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz