A King sends for 3 prisoners. HE has 3 black hats and 2 white hats. He blindfolds the prisoners & puts a hat on each. He then removes the blindfolds & allows them to look at each other. He tells them that if they can tell him the color of the hat they have on, he will set them free. If not, they will be killed. The 1st prisoner looks at the other 2 and says, "I don't know. I can not tell." The 2nd prisoner looks at the 1st & 3rd prisoner & says, "I don't know. I can not tell." The 3rd prisoner is blind, but says, "I have a black hat on." The blind prisoner is right!
Was the blind prisoner lucky, or did he really know what he was talking about?
-thanks for the helP!!
Since this is a classic logic problem, I Googled three hat black white logic and found these similar problems and their solutions.
http://www.google.com/search?hl=en&ie=ISO-8859-1&q=logic+three+black+white+hat
The blind prisoner was not lucky, but rather he was able to deduce the color of his hat. Here's how you can solve the puzzle to understand why the blind prisoner's answer was correct:
1. Start by considering the possibilities of hat combinations. The king has 3 black hats and 2 white hats, so the potential combinations for the prisoners are:
- Black, Black, Black
- Black, Black, White
- Black, White, Black
- White, Black, Black
- White, White, Black
2. The first prisoner, who can see the other two prisoners' hats, says, "I don't know. I can not tell." This means that he sees at least one white hat among the other prisoners. If all the other prisoners were wearing black hats, he would be able to deduce that he must be wearing a black hat. However, since he says he cannot tell the color of his own hat, we know that there must be at least one white hat among the remaining two prisoners.
3. The second prisoner, who can also observe the other two prisoners, says the same thing as the first prisoner, "I don't know. I can not tell." This means that after observing the first prisoner's hat and hearing his statement, the second prisoner still cannot determine the color of his own hat. Since the second prisoner was given additional information by observing the first prisoner, we can conclude that if the first prisoner saw a white hat, the second prisoner would have seen a black hat on the remaining prisoner and would be able to deduce the color of his own hat. However, if the first prisoner saw two black hats, the second prisoner would not be able to determine the color of his own hat, as there could be either two black hats or one white and one black hat left among the remaining two prisoners.
4. The third prisoner, who is blind and unable to observe any of the other prisoners' hats, then confidently states, "I have a black hat on." By analyzing the statements of the first and second prisoners and what we know from step 2 and 3, we can conclude that both the first and second prisoners saw at least one white hat among the remaining two prisoners. If the third prisoner were wearing a white hat, the first and second prisoners would have been able to deduce that they were both wearing black hats since the remaining two hats would be black. However, since both the first and second prisoners stated that they couldn't determine the color of their own hats, it means that the third prisoner must be wearing a black hat. Therefore, the blind prisoner's statement is correct.
In summary, the blind prisoner's answer was not based on luck but on a logical deduction from the statements of the other prisoners.