Current Events > RIDDLE: 4 men walk into the desert

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Suddenly all four are simultaneously knocked out. They awake buried to their heads in the sand unable to look anywhere but straight ahead. They are positioned so that each man sees another's head before him. However between the first and second man there is a separating wall. So the first man sees only desert. The second man sees only wall. The third man sees another's head and a wall. The fourth man sees two heads and a wall. On top of each mans head is a hat. The underside of each cap is black, but the outside of each cap is either blue or white. Before any of the men can speak, their captors tell them if they speak, they die.

However, if any of them can guess the color of their cap on the first try they go free. The captors tell them that there are two blue caps and two white caps. Being an omniscient observer of the situation, we know that the order of the caps are: blue, white, blue, white. So knowing the perspective of each man in the sand, and that they can only see the color of caps/wall/desert in front of them, which of the four men knows for certain the color of his own cap? More importantly: why?

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When the person in the back doesn't say anything, the person second from back knows that their hat is the opposite color from the person in front of them.

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Pretty sure no one can know for sure without guessing until another man guesses.

The guy in the back can see a blue and white hat, so, hed still have a 50/50 guess without the guy isolated by the wall saying anything.

Everyone else has worse odds.

Assuming there arent any reflection shenanigans.

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I just Googled it and the riddle itself does not give enough information to answer. Apparently post 2 is correct, but the riddle does not say the men know where each other are. It only states they are told how many color hats there are.

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old

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The man is a planet and the desert is a room outside

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Assuming they already know where everyone is in relation to each other: the third man. The fact that the fourth man does not speak up indicates that he sees a blue and white cap on those he can see in front of him (i.e. the second and third man). Therefore if the 2nd person is wearing a white cap then #3 is wearing blue or vice versa.
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Aliens come down and kill everyone

End of riddle

Paragon21XX posted...

Assuming they already know where everyone is in relation to each other: the third man. The fact that the fourth man does not speak up indicates that he sees a blue and white cap on those he can see in front of him (i.e. the second and third man). Therefore if the 2nd person is wearing a white cap then #3 is wearing blue or vice versa.

Wouldnt person 2 also get out then since they would infer the same as 3, that if they were the same, 4 would have called it out. But as they were different, they would know to be opposite of 3.

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Shablagoo posted...

They are positioned so that each man sees another's head before him.

Shablagoo posted...

the first man sees only desert. The second man sees only wall

The riddle has no internal consistency.

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KILBOTz posted...

Paragon21XX posted...

Assuming they already know where everyone is in relation to each other: the third man. The fact that the fourth man does not speak up indicates that he sees a blue and white cap on those he can see in front of him (i.e. the second and third man). Therefore if the 2nd person is wearing a white cap then #3 is wearing blue or vice versa.

Wouldnt person 2 also get out then since they would infer the same as 3, that if they were the same, 4 would have called it out. But as they were different, they would know to be opposite of 3.

2 doesn't know what color 3's hat is, though. They might know the color is different, but they don't know exactly which color it is
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UnholyMudcrab posted...

2 doesn't know what color 3's hat is, though. They might know the color is different, but they don't know exactly which color it is

I guess I was imagining them shouting out the color of their hat once they figure it out.

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KILBOTz posted...

Wouldnt person 2 also get out then since they would infer the same as 3, that if they were the same, 4 would have called it out. But as they were different, they would know to be opposite of 3.

#2 has no reference point to infer his own color with. He can rely only upon the 3rd man to get free (riddle says they are released if any of them can guess his own color correctly).
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Let's see...

The person in front has no information.

The second person who only sees a wall has no information.

The third person knows the second person is wearing a blue hat and knows he also has no information.

The person in the back knows what everybody knows and sees one blue cap and one white cap.

If the third person were wearing a blue cap like the man in front of him is, then the person in the back would immediately know he must be wearing a white cap since there are two of each color. But he isn't, so he doesn't.

By not hearing the person in the back exclaim the color of his cap, the third person knows the color of his cap is different from the person in front of him.

Seems about right.

masterbarf posted...

Let's see...

The person in front has no information.

The second person who only sees a wall has no information.

The third person knows the second person is wearing a blue hat and knows he also has no information.

The person in the back knows what everybody knows and sees one blue cap and one white cap.

If the third person were wearing a blue cap like the man in front of him is, then the person in the back would immediately know he must be wearing a white cap since there are two of each color. But he isn't, so he doesn't.

By not hearing the person in the back exclaim the color of his cap, the third person knows the color of his cap is different from the person in front of him.

Seems about right.

How does person 3 know person 4 is behind him?

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cuttin_in_farm posted...

How does person 3 know person 4 is behind him?

Good question. My best guess is due to the implication that one of them can know the color of their cap. Not hearing anybody behind him also rules out the possibility of there being two people behind him.