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Three brave clever soldiers are held captive by the enemy forces. They are given a chance and are tied to stakes which are pushed into into the ground one after the other. The soldiers are tied to the the first three stakes. There are two more stakes behind. They are told that two of the stakes out of five is green and three of them is red. None of the soldiers are able to see the colours of the stakes which they are tied to. The third soldier is able to see the colours of the stakes which the first two soldiers are tied to. The second soldier is able to see the colour of the stake which the first soldier is tied to. The first soldier is able to see no stakes, but just the hills. They are told that if one of them knew the color of the stake he is tied to, all of them would be free, or else they would be killed. Can they know it? How? There are four possibilities. You have to explain in each possibility which soldier knows and how if it is at all possible.

1- The first possibility: Something like this. The esasiest one. If the possibility is like this, which soldier knows and how? it is forbidden for the soldiers to speak.

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2- the second possiblity:

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the third one is either red or green. you can regard either one as true. actually it is not really important. this is a little tricky. It is strictly forbidden for the soldiers to speak. Who can know?

3- the third possiblity:

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the third one is either red or green. you can regard either one as true.

4- the fourth possiblity:

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the third one is either red or green. you can regard either one as true
Comments  
Hi Diamondrg

If the third soldier ( who can see the other two in front of him) had seen two green stakes in front of him then he could of said for certain that his was red.( only two green stakes).

But he didn't say anything . Given this fact if the second soldier had seen a green stake in front of him , then he would of been able to tell that his stake was red.

But he too didn't say a word.

So from this the man in front can deduce that his stake his red.!!! Emotion: smile [Y]
Eargasms
If the third soldier ( who can see the other two in front of him) had seen two green stakes in front of him then he could of said for certain that his was red.( only two green stakes).

Yes. You are right.
EargasmsBut he didn't say anything .

No. He certainly speaks. He says that his is red and they are let go. This is the first possibility.

What do you think of the second possibility? (I think you misundersood something. If one of them finds out his color, he can say it. Speaking is forbidden lest the soldiers help each other.)

Yes, about the second possiblity, the third man can see that there are two stakes in front of him. One is green and the other is red. Given this, can he know his? If not, who can know it? How? Anyway, actually Eargasms was really close. In the second possiblity the third man can't know it. But he acts with tact and keeps silent. After a while the second man, noticing that the third man keeping silent, begins to think. The stake in front of his is red. If his were green too, the third man would know that his is red. But he keeps silent."Then," thinks the second man, "I am not green. So I am red." and they are let go.

About the third and the fouth possibilities: The answer is the same. Let's look at the 3rd possibility.

The third man can see one green and one red stake. So he may be either red or green. He keeps silent. The second one, noticing that the third man keeping silent, begins to think. he can see one red stake. He thinks he may be either green or red. He keeps silen too. After a while the first man who cannot see any stakes notices that the third and the second man will not come up with an answer. He begins to think. "If, " he thinks, "the first two stakes were green, the third man would know, and if the first stake were green and the second stake red, then the second man would know it. (considering the steps explained above. as I said they are so clever.Emotion: wink) Finally he thinks that his were not green, otherwise the others would know it. And says: "I am red!" They are let go. The End.