Tricky Black Dot RIddle NEED HELP?

Question

OK, there are three men who are sentenced to death. One man has very high intelligence, the next man has average intelligence and the last man has low intelligence (this is importannt apparantly) The person who is incharge of hanging them says " OK because it is Friday and I am nice I will let one of you go, I have three black dots and two white dots, I am gong to blindefold you and put one dot on each of your heads. You are not allowed to talk or make any form of communictaion. Then you must guess which colour dot is on your head. Whoever gets it right first goes free" There are no mirrors and no one is allowed to help you. You are not allowed to remove the dot or swap dots. There is a logical answer. Then the man with high intelligence says, "I have a black dot on my head" How did he knoe? But I don't know it. HELP ME

All three men have black dots on their heads

Answer 1

It's a matter of double and triple logic.

Any of the 3 men (even the low intelligence man) should be able to count two white dots and determine they have a black dot. But nobody sees such an arrangement of dots.

The average intelligence man builds upon this knowledge. So if he were to see one white and one black, he would wait to see if anyone announced that they had black. But when no one does, he would then announce that he must have had black.

The high intelligence man builds further on this and says, if the average intelligence man didn't make an announcement, even after pondering the case above, then he must not have been looking at one white and one black. He must have been looking at two black dots.

Therefore the high-intelligence man announces that he has a black dot.

Answer 2

First, I am assuming that after the dots were placed on their heads, their blindfolds were removed so that they could see one another's dots but not their own. (If this is not the case, then it boils down to simple probability: With 3 black dots and 2 white dots and no other available information, the chances for having a black dot are simply greater at 60%.)

When the blindfolds are removed, we must consider three possibilities for the intelligent man:

First, he may have noticed 2 white dots on each of the other men's heads. Since there are 2 white dots total, then he would obviously have had a black one.

Second, he may have noticed 1 white dot and 1 black dot on each of the other men's heads. If this were the case, and he had a white dot on his own head, then one of the other men would have immediately seen two white dots and been able to claim right away that he had a black dot. Since none of the other two was able to claim this, then the intelligent man must have had a black dot.

Lastly, we come across the most complex possibility, that the intelligent man saw a black dot on each of the other men's heads. (And you later added a notation that this was in fact the case.) How could the intelligent man have known?

Consider what the other two men were to see. Each of them would see one man with a black dot, and one man (the intelligent man) with an unknown dot color. If the intelligent man's dot were white, then each of the other two would have seen one black dot and one white dot. The situation, then, would be exactly as it were in the second case above, except it would be so for one of the *other* men. Thus, either of the other men would have drawn the same conclusion as in the second case, above. Since neither of the other men came to that conclusion, then they must have seen two black dots themselves, and thus the intelligent man's dot must have been black.

(Of course, since he was the most intelligent of the three, then he was the one who came to this logical conclusion first.)

Answer 3

Well if they are blindfolded, they can't guess. If they are not, they can. Let's call them Man A, B and C.

Man A (the smart one) thinks:

'If i had a white dot, Man B would see a black and a white dot.

Then Man B would think: if he had a white dot, then Man C would see two white dots, and he knew he has a black. But Man C did not say 'I have black'.

So Man B knows he does not have white. In this case he knew he had black. But Man B did not say 'I have black'.

So the initial assumption that I has a white dot is false.

This way I must have a black dot on my head'

Answer 4

There are 3 possible situations for the wise one.

1.He can see 2 white dots. No comment on this one.
2.He can see a white dot and a black dot. For a white dot on his head, even the stupid one can give the answer above. Therefore it must be black.
3.He can see 2 black dots. In this case he can only hope that the “average” one would be able to give the correct answer in situation “2”, in case of a white dot on his head.


No offense, but… I was not sure about the importance of “smartness” assumption; considering the answers above I was enlighten.

Answer 5

But appearently, when answering the question, they can see each other (not oneself). So the man sees
1) 2 white dots. Means there are no more white. He has black thus, which is his answer.

2) 1 white dot. Then if he had WHITE, the person with black would have seen 2 white dots and could've thus be sure to have black! But as he doesn't, means the man has BLACK. And he can think of it, cause he's intelligent :)

But probably, I don't get something still... That is my logicial opinion, at least.

Answer 6

Because of his death being a possibility, he decided to make an educated guess or he caught on first. Because he was smart, the only clue he could get and know that his dot was black, the only thing he could say with certainty is that he saw the other two have white dots. Therefore he could only have a black dot.

Answer 7

3 black dots, 2 white dots. Apparently, the other 2 men have white dots on there foreheads, therefore the intelligent man knows he has a black dot.

Answer 8

The other 2 men went first and they both said white and they got it wrong, so he knew that he had a black dot, because it was only black dots left!

Answer 9

They were blindfolded, so they could not have seen what color dot the other men had.

The idea that the man with high-intelligence guessed black since statistically he had a higher probability of getting it right (3:2) seems to be the logical answer.

Answer 10

There is only one white dot. If it was on the clever mans head, the other two would see it. Even if they are very, very dim they would realise that if it was on his head it was not on theirs, so they would know that the dot on their head was black and would answer. As they did not answer, the dot cannot be white. So it must be black.