Hard Riddle

Platinum · 12-04-2007, 11:35 AM

Three prisoners know that the jailer has three white hats and two red hats. The Jailer gives one hat to each prisoner and says, "If you can deduce the color of your own hat, you will be freed." Each prisoner can see the hats of the other two prisoners, but not his own. The first prisoner says, "I cannot tell the color of my hat." And so does the Second prisoner. The third prisoner is blind, but he is freed. What color hat does the he have and how did he know?

Hint: Math

DK · 12-04-2007, 11:40 AM

Why the hell didn't they just guess? It's a 50/50 shot.

Wyborn · 12-04-2007, 11:41 AM

Well it seems fairly simple.

The only way to tell the color of your hat is if it's absolutely white - there aren't enough hats to tell if it's absolutely red.

Assumedly both of the sighted prisoners are wearing red hats and the blind man is wearing a white one, so when they look around they see red and white. So their own hats could be red or white - it is impossible to tell.

Since both of the other prisoners saw red/white, it means that....

wait.

The blind prisoner could also be wearing a red hat and both of the other prisoners could be wearing white hats, unable to tell the colors of their own hats for the same reason as before.

All right, I give up, somebody better explain it to me.

Platinum · 12-04-2007, 11:53 AM

^ just wait, untill more people go for it... your sort of on the right track.

Quote:

Originally Posted by DK

Why the hell didn't they just guess? It's a 50/50 shot.

They had to deduce the anwser.

DK · 12-04-2007, 12:14 PM

There are only two red hats, so as long as one of the prisoners could have seen two red hats on the others, he would have known his hat was white, as Wyborn said. So this is obviously not the case.

However, I don't understand how there is a definitive way to tell what color a hat is in any other scenario.

There is still the possibility that all three hats are white. If a sighted prisoner sees two white hats, there is still a possibility that he could be the third.

**Deku Trii** · 12-04-2007, 12:49 PM

If the first prisoner saw that both other prisoners had red hats, he'd have a white hat for sure. Since he could not deduce the color of his own hat, the remaining two prisoners know that both of their hats cannot be red.

Knowing that, if the second prisoner saw that the third prisoner's hat was red, he would know that his hat was not also red. But the second prisoner didn't know what color his hat was, so the third prisoner's hat could not have been red, and must have been white.

Wyborn · 12-04-2007, 01:01 PM

Quote:

Originally Posted by Deku Trii

If the first prisoner saw that both other prisoners had red hats, he'd have a white hat for sure. Since he could not deduce the color of his own hat, the remaining two prisoners know that both of their hats cannot be red.

Knowing that, if the second prisoner saw that the third prisoner's hat was red, he would know that his hat was not also red. But the second prisoner didn't know what color his hat was, so the third prisoner's hat could not have been red, and must have been white.

That only works assuming that the first prisoner is wearing a red hat, which is not necessarily true.

***Booyakasha*** · 12-04-2007, 01:06 PM

Uhhh...do the prisoners hear each others' answers? Because if so, I think I've got the answer.

**Deku Trii** · 12-04-2007, 01:13 PM

Quote:

Originally Posted by Wyborn

That only works assuming that the first prisoner is wearing a red hat, which is not necessarily true.

No, if the first prisoner is wearing a white hat, he would still have to say he doesn't know the color of his own hat if the other two prisoners aren't both weraring red hats.

If the first person sees the other prisoners wearing two white hats, his hat might be one of the two red hats, or the remaining white hat. If he sees one of the two other prisoners hats is red, his hat could be the other red hat, or one of the two remaining white hats. If he sees them both wearing red hats, he knows the color of his hat is white.

Given that the first prisoner didn't know the color of his hat, the two remaining prisoners have new information. If he had known the color of his hat, both prisoners could know their hats were red. He didn't, however, so the prisoners know that both of their hats cannot be red. That being true, if prisoner 2 looks at prisoner 3's hat and sees that it's red, he knows that his hat is white. Since he can't deduce the color of his own hat, prisoner 3's hat cannot be red.

Platinum · 12-04-2007, 01:20 PM

Quote:

Originally Posted by Booyakasha

Uhhh...do the prisoners hear each others' answers? Because if so, I think I've got the answer.

yes they do...

hint:
there is more than one answer, but all end in third having white.

Deku Trii is right

The secound prisoner saw a white hat on the third, but inorder for him to know his hat color, the third had to be waring a red hat, then he would know his hat was white.

If you want more detail I can offer it... but i won't unless people need it.

Lady Bane · 12-04-2007, 01:29 PM

Quite the difficult puzzle.
Unfortunately, now that my brain is fried from playing that madness game, i cannot seem to deduce an answer.
I shall return when I can, do not fear.

-Lady
PS. Lol. Weird use of language. ^.^

Wyborn · 12-04-2007, 01:29 PM

Multiple answers? That's silly.

Now look here, if the first prisoner says he doesn't know his own hat color then yes it is true that both of theirs cannot be red, but it might also mean that both of theirs are white.

If prisoner 1 has a red hat, prisoner 2 has a white hat, and prisoner 3 has a white hat, there's no particular way for them to deduce who's wearing what hat.

If prisoner 1, 2, and 3 all have white hats, then the first two prisoners would not be able to deduce the colors of their own hats but prisoner 3 would be no more able.

Platinum · 12-04-2007, 01:32 PM

^ on the contrary my dear Wyborn... yes he would if all were wearing white hats.

**Deku Trii** · 12-04-2007, 01:33 PM

Ugh.

Yes, both of their hats might be white. The point is, the only way for prisoner 2 to know the color of his hat is for prisoner 3 to be wearing a red hat. If prisoner 3 were wearing a red hat, prisoner 2 would know the color of his hat is white. Prisoner 2 does not know the color of his own hat, so prisoner 3's hat cannot be red.

Wyborn · 12-04-2007, 01:41 PM

You can hear the gears grinding in my skull.

...Damn. I acquiesce the point, I will leave in shame.

Platinum · 12-04-2007, 03:32 PM

^ it can be confussing but not that much...

Microphone_Kirby · 12-04-2007, 04:19 PM

Maybe the two prisoners that are not blind saw a red cap AND a white cap on their fellow inmates!

Prisioner 1: Red Cap
Prisioner 2: Red Cap
Prisioner 3 (the blind one): White Cap

Prisioner 3 "put 2+2 together" and figures out that the other prisioners were wearing Both red caps and deduced he was wearing a White Cap. He MUST be smart.

***Ace Mercury*** · 12-04-2007, 05:14 PM

There's not much math in this riddle. Though I guess you can think of it as a matter of listing the possibilities (there are only eight different permutations, 2^3) and paring it down based on the riddle's premises.

***CaptHayfever*** · 12-05-2007, 05:42 PM

It's logic. For all practical purposes (& as far as I'm concerned), the same thing as math, but most non-mathematicians don't think of it that way.
It's also old. I first heard it with red & green hats, but yeah, basically, the 3rd guy is wearing the majority color.

And remember, "I'm-a Luigi, number one!"

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12-04-2007, 11:35 AM	#1
Platinum Member Join Date: Apr 2005 Location: Wv Gender: Posts: 1,369 Thanks: 48 Thanked 21 Times in 21 Posts	Hard Riddle Three prisoners know that the jailer has three white hats and two red hats. The Jailer gives one hat to each prisoner and says, "If you can deduce the color of your own hat, you will be freed." Each prisoner can see the hats of the other two prisoners, but not his own. The first prisoner says, "I cannot tell the color of my hat." And so does the Second prisoner. The third prisoner is blind, but he is freed. What color hat does the he have and how did he know? Hint: Math

12-04-2007, 12:14 PM	#5
DK Senior Member Join Date: Jul 1999 Gender: Posts: 3,003 Thanks: 43 Thanked 49 Times in 41 Posts	There are only two red hats, so as long as one of the prisoners could have seen two red hats on the others, he would have known his hat was white, as Wyborn said. So this is obviously not the case. However, I don't understand how there is a definitive way to tell what color a hat is in any other scenario. There is still the possibility that all three hats are white. If a sighted prisoner sees two white hats, there is still a possibility that he could be the third. Last edited by DK; 12-04-2007 at 12:22 PM.

12-04-2007, 11:40 AM	#2
DK Senior Member Join Date: Jul 1999 Gender: Posts: 3,003 Thanks: 43 Thanked 49 Times in 41 Posts	Why the hell didn't they just guess? It's a 50/50 shot.

12-04-2007, 11:41 AM	#3
Wyborn Zelda Join Date: Jun 2000 Location: All over the place Gender: Posts: 12,388 Thanks: 87 Thanked 469 Times in 281 Posts	Well it seems fairly simple. The only way to tell the color of your hat is if it's absolutely white - there aren't enough hats to tell if it's absolutely red. Assumedly both of the sighted prisoners are wearing red hats and the blind man is wearing a white one, so when they look around they see red and white. So their own hats could be red or white - it is impossible to tell. Since both of the other prisoners saw red/white, it means that.... wait. The blind prisoner could also be wearing a red hat and both of the other prisoners could be wearing white hats, unable to tell the colors of their own hats for the same reason as before. All right, I give up, somebody better explain it to me.

12-04-2007, 12:49 PM	#6
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 9,031 Thanks: 521 Thanked 1,099 Times in 583 Posts	If the first prisoner saw that both other prisoners had red hats, he'd have a white hat for sure. Since he could not deduce the color of his own hat, the remaining two prisoners know that both of their hats cannot be red. Knowing that, if the second prisoner saw that the third prisoner's hat was red, he would know that his hat was not also red. But the second prisoner didn't know what color his hat was, so the third prisoner's hat could not have been red, and must have been white.

12-04-2007, 01:06 PM	#8
*Booyakasha* SuperMod of War Join Date: Nov 2000 Location: Wisconsinland Gender: Posts: 9,945 Thanks: 157 Thanked 1,481 Times in 763 Posts	Uhhh...do the prisoners hear each others' answers? Because if so, I think I've got the answer.

12-04-2007, 01:29 PM	#11
Lady Bane Junior Member Join Date: Jul 2007 Location: Hell. Gender: Posts: 301 Thanks: 8 Thanked 6 Times in 6 Posts	Quite the difficult puzzle. Unfortunately, now that my brain is fried from playing that madness game, i cannot seem to deduce an answer. I shall return when I can, do not fear. -Lady PS. Lol. Weird use of language. ^.^

12-04-2007, 01:32 PM	#13
Platinum Member Join Date: Apr 2005 Location: Wv Gender: Posts: 1,369 Thanks: 48 Thanked 21 Times in 21 Posts	^ on the contrary my dear Wyborn... yes he would if all were wearing white hats.

12-04-2007, 01:33 PM	#14
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 9,031 Thanks: 521 Thanked 1,099 Times in 583 Posts	Ugh. Yes, both of their hats might be white. The point is, the only way for prisoner 2 to know the color of his hat is for prisoner 3 to be wearing a red hat. If prisoner 3 were wearing a red hat, prisoner 2 would know the color of his hat is white. Prisoner 2 does not know the color of his own hat, so prisoner 3's hat cannot be red.

12-04-2007, 01:41 PM	#15
Wyborn Zelda Join Date: Jun 2000 Location: All over the place Gender: Posts: 12,388 Thanks: 87 Thanked 469 Times in 281 Posts	You can hear the gears grinding in my skull. ...Damn. I acquiesce the point, I will leave in shame.

12-04-2007, 03:32 PM	#16
Platinum Member Join Date: Apr 2005 Location: Wv Gender: Posts: 1,369 Thanks: 48 Thanked 21 Times in 21 Posts	^ it can be confussing but not that much...

12-04-2007, 04:19 PM	#17
Microphone_Kirby Senior Member Join Date: Apr 2003 Location: None of your business. Gender: Posts: 7,155 Thanks: 559 Thanked 225 Times in 181 Posts Blog Entries: 6	Maybe the two prisoners that are not blind saw a red cap AND a white cap on their fellow inmates! Prisioner 1: Red Cap Prisioner 2: Red Cap Prisioner 3 (the blind one): White Cap Prisioner 3 "put 2+2 together" and figures out that the other prisioners were wearing Both red caps and deduced he was wearing a White Cap. He MUST be smart.

12-04-2007, 05:14 PM	#18
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 23,274 Thanks: 568 Thanked 3,297 Times in 1,582 Posts Blog Entries: 1	There's not much math in this riddle. Though I guess you can think of it as a matter of listing the possibilities (there are only eight different permutations, 2^3) and paring it down based on the riddle's premises.

12-05-2007, 05:42 PM	#19
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,659 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	It's logic. For all practical purposes (& as far as I'm concerned), the same thing as math, but most non-mathematicians don't think of it that way. It's also old. I first heard it with red & green hats, but yeah, basically, the 3rd guy is wearing the majority color. And remember, "I'm-a Luigi, number one!"