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Spots before our eyes

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While traveling through the Middle East, you and three (logical and intelligent) friends are seized, accused of espionage, and sentenced to ten years hard labor and torture. The warden of the prison, an honest man, enjoys logic puzzles and agrees to a game for your freedom. If you win the game by answering correctly, you gain your freedom. If you lose the game, you will be immediately executed. If you say nothing (i.e. you refuse to play), you will serve out your sentence. You and your friends all agree to answer only if you are sure that you are right.

The game is as follows:

Your three friends are led into one room and you are led into an adjoining room, where you can hear but not see your friends. You are sitting in front of a mirror; your friends are sitting in a circle with no mirrors, but where they can see each other. The prison warden shows you five small stickers, three black and two white. All four of you are blindfolded. He puts one sticker on your forehead and one on each of your friends' foreheads. Then he announces the rules:

"Absolutely no speaking or other communication is allowed, except to answer 'black' or 'white'. You are not allowed to move, except as much as required to speak the answer. I will remove the blindfolds from the three who are together. Any one of the three who tells me the color of the sticker on his own forehead wins, and you all go free. If any one says the wrong color, you will be executed. The three have five seconds for one of them to tell me the color of his (or her) own forehead sticker."

"If the three say nothing for five seconds, then I will remove the blindfold from the fourth [which is you]. The fourth then has thirty seconds to tell me the color of the sticker I kept."

The blindfolds of the three are removed. You hear nothing for five seconds. Then your own blindfold is removed, and you see in the mirror that you have a black sticker on your own forehead.

What do you say?

You say 'white'.

Clearly, if two of your three friends had been given white stickers, the third would have realized that his own sticker must be black, and would have said so. Since your friends said nothing, at least two of them must have black stickers. Since you also have a black sticker, your third friend and the prison warden must each have a white sticker.

[Edited for clarity]

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White.

If both white stickers were visible to one of your friends, he would have known his sticker was black.

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While traveling through the Middle East, you and three (logical and intelligent) friends are seized, accused of espionage, and sentenced to ten years hard labor and torture. The warden of the prison, an honest man, enjoys logic puzzles and agrees to a game for your freedom. If you win the game by answering correctly, you gain your freedom. If you lose the game, you will be immediately executed. If you say nothing (i.e. you refuse to play), you will serve out your sentence. You and your friends all agree to answer only if you are sure that you are right.

The game is as follows:

Your three friends are led into one room and you are led into an adjoining room, where you can hear but not see your friends. You are sitting in front of a mirror; your friends are sitting in a circle with no mirrors, but where they can see each other. The prison warden shows you five small stickers, three black and two white. All four of you are blindfolded. He puts one sticker on your forehead and one on each of your friends' foreheads. Then he announces the rules:

"Absolutely no speaking or other communication is allowed, except to answer 'black' or 'white'. You are not allowed to move, except as much as required to speak the answer. I will remove the blindfolds from the three who are together. Any one of the three who tells me the color of the sticker on his own forehead wins, and you all go free. If any one says the wrong color, you will be executed. The three have five seconds for one of them to tell me the color of his (or her) own forehead sticker."

"If the three say nothing for five seconds, then I will remove the blindfold from the fourth [which is you]. The fourth then has thirty seconds to tell me the color of the sticker I kept."

The blindfolds of the three are removed. You hear nothing for five seconds. Then your own blindfold is removed, and you see in the mirror that you have a black sticker on your own forehead.

What do you say?

when the three people see each other, they know that there are three blacks and two whites total. If they see two whites then they know that they must be black and they would say 'black' right away. So they each saw at least one black. Meaning either 2 are black and 1 is white or all 3 are black. Since they can deduce that this is so, and thus if they see a white, they know that they are black since there can only be 1 white, max, but 5 seconds isn't enough to think this and to wait enough for the other people to get past the first logic phase, etc. So nobody says anything, thus it is either 2b-1w or all blacks. If given a few more seconds and nobody said anything, it would be all blacks, but they didn't have enough time, so they didnt say anything, so it could be either.

You, who have already deduced this, see that you have a black and know there is only 3 blacks so it must have 2-1 in your three friends, and you have the third black. Meaning the warden has the final white.

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