LOGIC RIDDLE: A jailer has 5 hats...

...3 white, 2 red.

There are three inmates, one can see perfectly, one has the use of only one eye, and one is blind.

The jailer puts a hat on each inmates and tells them if they can tell him the color of the hat on their head with absolute certainty, they will go free. If not, they die.

The inmates are not allowed to tell the other inmates what color hat they have on.

The man with two good eyes looks at the other inmates and tells the jailer he does not know the color of the hat on his head.

Then the man with one eye looks at the other inmates and tells the jailer he does not know the color of the hat on his head.

lastly the blind man tells the jailer with absolute certainty the color of the hat on his head. He is correct and goes free.

How did the blind man know the color of the hat on his head?

he's a good guesser!!

I give up.

I have no idea. :?

sighted guy sees white and white... so he does not know if his is white or red 1 eye guy sees white and white.. so he does not know if his is white or red. blind guy knows that both sighted guys see white and white... so he must be wearing white.

3 hats are white, 2 are red. There are three inmates, so only three hats are used.

If the inmate with the good eye cannot know what hat he has on, then on other inmate has a white hat, and one other inmate has a red hat. The inmate with the good eyes has an equal chance of having a red or white hat, and so cannot know the color of the hat on his head.

The same principal applies to the man with the one good eye. One of the other inmates has a red hat and the other has a white hat, and so he cannot know what he has on.

The blind man, after hearing the other two inmates guess incorrectly, knows that there are only two red hats, and one is in use. If both of the other men saw red hats on one of the other inmates then the blind man must be wearing a red hat.

By the way, do the inmates know what color and how many hats there are in the first place?

3 hats are white, 2 are red. There are three inmates, so only three hats are used.

If the inmate with the good eye cannot know what hat he has on, then on other inmate has a white hat, and one other inmate has a red hat. The inmate with the good eyes has an equal chance of having a red or white hat, and so cannot know the color of the hat on his head.

The same principal applies to the man with the one good eye. One of the other inmates has a red hat and the other has a white hat, and so he cannot know what he has on.

The blind man, after hearing the other two inmates guess incorrectly, knows that there are only two red hats, and both are in use. If both of the other men saw red hats on the other inmates then the blind man must be wearing a red hat.

[QUOTE="comp_atkins"]sighted guy sees white and white... so he does not know if its white or red 1 eye guy sees white and white.. so he does not know if its white or red. blind guy knows that both sighted guys see white and white... so he must be wearing white.rcignoni

We shouldn't assume things we do not know for certain. That is logic. After all, logic is reasoning.

sighted guy sees white and white... so he does not know if his is white or red 1 eye guy sees white and white.. so he does not know if his is white or red. blind guy knows that both sighted guys see white and white... so he must be wearing white.

comp_atkins

[QUOTE="DrSponge"]What? I read both explanations and they don't make sense. They could all have white hats, there could be 2 red and 1 white, there could be 2 white and 1 red...etc. There's no way of him knowing which combination it is.unholymight

[QUOTE="Theokhoth"]

3 hats are white, 2 are red. There are three inmates, so only three hats are used.

If the inmate with the good eye cannot know what hat he has on, then on other inmate has a white hat, and one other inmate has a red hat. The inmate with the good eyes has an equal chance of having a red or white hat, and so cannot know the color of the hat on his head.

The same principal applies to the man with the one good eye. One of the other inmates has a red hat and the other has a white hat, and so he cannot know what he has on.

The blind man, after hearing the other two inmates guess incorrectly, knows that there are only two red hats, and both are in use. If both of the other men saw red hats on the other inmates then the blind man must be wearing a red hat.

MetalGear_Ninty

For the blind inmate to know without a doubt what hat he has on, the other two inmates need white hats and he needs to have a red hat.

The inmate with good eyes has a white hat, and the other two inmates have a white hat and a red hat. So he could have a white hat or a red hat--he doesn't know.

The inmate with one good eye (also with a white hat) sees one white hat (the hat on the inmate with two good eyes) and one red hat (the hat on the blind inmate), and faces the same predicament as the other guy.

Now the blind man knows there are two people with a white hat and one with a red hat, because if two people had a red hat then one of the previous inmates would have guessed that his hat was white, since there are only two red hats. If an inmate that could see was wearing a red hat, then the other two inmates would be wearing either both white or one red and one white. However, if BOTH men see a white hat and red hat, then the only logical conclusion is that the blind man has the red hat, since for both men to see a red hat would have to mean they see it on the same person; otherwise one of them would have correctly guessed that he had a white hat.

[QUOTE="unholymight"][QUOTE="DrSponge"]What? I read both explanations and they don't make sense. They could all have white hats, there could be 2 red and 1 white, there could be 2 white and 1 red...etc. There's no way of him knowing which combination it is.MetalGear_Ninty

[QUOTE="MetalGear_Ninty"][QUOTE="Theokhoth"]

3 hats are white, 2 are red. There are three inmates, so only three hats are used.

If the inmate with the good eye cannot know what hat he has on, then on other inmate has a white hat, and one other inmate has a red hat. The inmate with the good eyes has an equal chance of having a red or white hat, and so cannot know the color of the hat on his head.

The same principal applies to the man with the one good eye. One of the other inmates has a red hat and the other has a white hat, and so he cannot know what he has on.

The blind man, after hearing the other two inmates guess incorrectly, knows that there are only two red hats, and both are in use. If both of the other men saw red hats on the other inmates then the blind man must be wearing a red hat.

For the blind inmate to know without a doubt what hat he has on, the other two inmates need white hats and he needs to have a red hat.

The inmate with good eyes has a white hate, and the other two inmates have a white hat and a red hat. So he could have a white hat or a red hat--he doesn't know.

The inmate with one good eye (also with a white hat) sees one white hat (the hat on the inmate with two good eyes) and one red hat (the hat on the blind inmate), and faces the same predicament as the other guy.

Now the blind man knows there are two people with a white hat and one with a red hat, because if two people had a red hat then one of the previous inmates would have guessed that his hat was white, since there are only two red hats. If an inmate that could see was wearing a red hat, then the other two inmates would be wearing either both white or one red and one white. However, if BOTH men see a white hat and red hat, then the only logical conclusion is that the blind man has the red hat, since for both men to see a red hat would have to mean they see it on the same person; otherwise one of them would have correctly guessed that he had a white hat.

[QUOTE="MetalGear_Ninty"][QUOTE="Theokhoth"]

3 hats are white, 2 are red. There are three inmates, so only three hats are used.

If the inmate with the good eye cannot know what hat he has on, then on other inmate has a white hat, and one other inmate has a red hat. The inmate with the good eyes has an equal chance of having a red or white hat, and so cannot know the color of the hat on his head.

The same principal applies to the man with the one good eye. One of the other inmates has a red hat and the other has a white hat, and so he cannot know what he has on.

The blind man, after hearing the other two inmates guess incorrectly, knows that there are only two red hats, and both are in use. If both of the other men saw red hats on the other inmates then the blind man must be wearing a red hat.

Theokhoth

For the blind inmate to know without a doubt what hat he has on, the other two inmates need white hats and he needs to have a red hat.

The inmate with good eyes has a white hat, and the other two inmates have a white hat and a red hat. So he could have a white hat or a red hat--he doesn't know.

The inmate with one good eye (also with a white hat) sees one white hat (the hat on the inmate with two good eyes) and one red hat (the hat on the blind inmate), and faces the same predicament as the other guy.

Now the blind man knows there are two people with a white hat and one with a red hat, because if two people had a red hat then one of the previous inmates would have guessed that his hat was white, since there are only two red hats. If an inmate that could see was wearing a red hat, then the other two inmates would be wearing either both white or one red and one white. However, if BOTH men see a white hat and red hat, then the only logical conclusion is that the blind man has the red hat, since for both men to see a red hat would have to mean they see it on the same person; otherwise one of them would have correctly guessed that he had a white hat.

The inmate with perfect vision sees a white and a red hat, so he doesn't know for sure. The same thing applies to the inmate with one good eye. These two men are wearing the 2 red hats, so the blind man knows that he must be wearing one of the white hats.

But all three could have been wearing white hats. MetalGear_Ninty

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

[QUOTE="Theokhoth"]

[QUOTE="MetalGear_Ninty"] No, the inmate with the good eyes could see that both men have white hats. Same with the man with one good eye. Also, even if that were not true, then the blind man could have been detected twice with a red hat by both men negating the neccesitation of two red hats in play. I think this riddle is a nonsense to be honest.unholymight

For the blind inmate to know without a doubt what hat he has on, the other two inmates need white hats and he needs to have a red hat.

The inmate with good eyes has a white hat, and the other two inmates have a white hat and a red hat. So he could have a white hat or a red hat--he doesn't know.

The inmate with one good eye (also with a white hat) sees one white hat (the hat on the inmate with two good eyes) and one red hat (the hat on the blind inmate), and faces the same predicament as the other guy.

Now the blind man knows there are two people with a white hat and one with a red hat, because if two people had a red hat then one of the previous inmates would have guessed that his hat was white, since there are only two red hats. If an inmate that could see was wearing a red hat, then the other two inmates would be wearing either both white or one red and one white. However, if BOTH men see a white hat and red hat, then the only logical conclusion is that the blind man has the red hat, since for both men to see a red hat would have to mean they see it on the same person; otherwise one of them would have correctly guessed that he had a white hat.

Your post makes no sense.

[QUOTE="unholymight"][QUOTE="Theokhoth"]

For the blind inmate to know without a doubt what hat he has on, the other two inmates need white hats and he needs to have a red hat.

The inmate with good eyes has a white hat, and the other two inmates have a white hat and a red hat. So he could have a white hat or a red hat--he doesn't know.

The inmate with one good eye (also with a white hat) sees one white hat (the hat on the inmate with two good eyes) and one red hat (the hat on the blind inmate), and faces the same predicament as the other guy.

Now the blind man knows there are two people with a white hat and one with a red hat, because if two people had a red hat then one of the previous inmates would have guessed that his hat was white, since there are only two red hats. If an inmate that could see was wearing a red hat, then the other two inmates would be wearing either both white or one red and one white. However, if BOTH men see a white hat and red hat, then the only logical conclusion is that the blind man has the red hat, since for both men to see a red hat would have to mean they see it on the same person; otherwise one of them would have correctly guessed that he had a white hat.

Theokhoth

Your post makes no sense.

[QUOTE="MetalGear_Ninty"] But all three could have been wearing white hats. Theokhoth

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

[QUOTE="Theokhoth"]

[QUOTE="unholymight"] Theokoth, I think you're overthinking this a bit, did you read my post?unholymight

Your post makes no sense.

You don't explain anything in your post. "By the first guy the second one knows that both himself and blind man can't both be red."

This alone makes absolutely zero sense.

[QUOTE="unholymight"][QUOTE="Theokhoth"]

Your post makes no sense.

Theokhoth

You don't explain anything in your post. "By the first guy the second one knows that both himself and blind man can't both be red."

This alone makes absolutely zero sense.

I still think the blind guy is just a good guesser. -_-XDXDXDXDXDXDXD

[QUOTE="Theokhoth"]

[QUOTE="MetalGear_Ninty"] But all three could have been wearing white hats. MetalGear_Ninty

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

The jailer felt sorry for the blind guy so he just let him go. Once the blind guy left he stepped out into the middle of the road and was hit by a transport

[QUOTE="MetalGear_Ninty"][QUOTE="Theokhoth"]

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

Funky_Llama

[QUOTE="rcignoni"][QUOTE="comp_atkins"]sighted guy sees white and white... so he does not know if its white or red 1 eye guy sees white and white.. so he does not know if its white or red. blind guy knows that both sighted guys see white and white... so he must be wearing white.MetalGear_Ninty

[QUOTE="MetalGear_Ninty"][QUOTE="rcignoni"] This right here.comp_atkins

[QUOTE="MetalGear_Ninty"][QUOTE="rcignoni"] This right here.comp_atkins

[QUOTE="Theokhoth"]

[QUOTE="MetalGear_Ninty"] But all three could have been wearing white hats. MetalGear_Ninty

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hat.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

[QUOTE="MetalGear_Ninty"][QUOTE="Theokhoth"]

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

Theokhoth

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hate.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

[QUOTE="MetalGear_Ninty"][QUOTE="Theokhoth"]

If that's the case, then the blind man can know for a fact that his hat is white, because the other two men would only see white hats. They would be unsure if their hat was red or white, but the blind man would know based on the previous two peoples' observations that all three men wear white hats, and so his must be white.

Theokhoth

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hat.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

[QUOTE="Theokhoth"]

[QUOTE="MetalGear_Ninty"] But it is stated in the riddle that the prisoners are not allowed to tell each other what colour hats they have on.DrSponge

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hate.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

Are you being serious or sarcastic? >_>

[QUOTE="DrSponge"][QUOTE="Theokhoth"]

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hate.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

Theokhoth

Are you being serious or sarcastic? >_>

Two eyed inmate: He see the one eyed inmate wearing a red hat, and the blind inmate wearing a white hat. He doesn't know what he's wearing. One eyed inmate: He sees the two eyed inmate wearing a red hat and the blind inmate wearing a white hat. He doesn't know what he's wearing. The blind inmate solves this puzzle exactly the same way we just did.

Neat riddle! I love these.

What stupid inmates. At least guess what hat you have on, don't just say you don't know. >_>JC346

[QUOTE="Theokhoth"]

[QUOTE="MetalGear_Ninty"] But it is stated in the riddle that the prisoners are not allowed to tell each other what colour hats they have on.unholymight

I just figured out where I've gone wrong. The blind man must have a white hat, not a red one.

There are five hats: three white, two red. There are three inmates. That means that any of the following combinations are possible:

All three get white hats. If this is true then the first two inmates would see two white hats and not know whether they have red hats or not, so they get uncertain, leaving the blind man to conclude he must be wearing a white hat.

One gets a white hat, and two get red hats. If this is true then the first two inmates would have to see one white and one red, because if they saw two reds then they would know their hats were white. Since they are uncertain, the blind man knows he must have the white hat.

Two get white hats, and one gets a red hat. If this is true then one of the first two men would see two white hats and one would see one white and one red; their uncertainty of their own hats would lead the blind man to conclude that he has a white hat.

I said, the blind man must be wearing a white hat.

Your logic is also incorrect: if the first man sees red (on the blind man) and white (on the one-eyed man), then the second one would see one white and one red; the uncertainty of the first man would lead the second man to believe that he could be wearing either white or red.