Induction puzzles mental1-1c-ans.html

...... Induction puzzles: The King's Wise Men ......

3 black & 2 white hats


All three wise men were wearing black hats.

1) Suppose that you are one of the wise men. Looking at the other wise men, you see they are both wearing white hats. Since there were only two white hats, you would immediately know that your own hat must be black.

2) Now suppose that you see the other wise men, and one is wearing a white hat and the other is wearing a black hat. If your own hat was white, then the man you can see wearing the black hat would be himself seeing two white hats and would - by the logic above - have immediately declared his hat color. If he doesn't do this, it can only be because your hat isn't white, therefore it must be black.

3) In this particular puzzle, you see the other wise men and both are wearing black hats. You can't work anything out from this. However, if your own hat was white, then two other wise men would be seeing a black and a white hat, and the wiser one would have declared his hat color by the rule above. Thus, if none of them has done so, they must also be seeing two black hats and thus your hat must be black.

"This is also the reason why a lot of intelectuals wear black hats."