1 and 3 are math questions. It does matter and you should switch because when you have three answers you have a 33.3% chance of getting it right. When one is eliminated, you then have a 50% chance, thus a greater chance. I'll have to think on the guys with the dotted hats.
Here's one that's probably been done before, but it's worth a shot. Please don't look the answer up!
A king announces he'll give a golden apple to any man who can tell him an outrageous lie. Man after man comes, but the king is unimpressed by all of their boasts and deceit. Finally an old man walks in. A few minutes later he leaves with the golden apple. What lie did he tell to the king?
The wise men are ordered to not communicate or touch the hats. However, by closely examining the hats that were put on each of them, he perceptively saw that none of the 2 mens' hats had dots on each of them, so by process of elimination, he should be the one with the dotted hat.
Yes they did. All of them had dots, maybe you should read.
Fine.
So assuming that, the wise man noticed that no other wise man had answered that he had a dot on his hat, so AGAIN, by process of elimination, he figured out that he himself had a dot on his hat and went right away.
And when you say not at all, I was at least close when I said 50% chance. I'd heard this before but forgot the complete answer.
As for the dots, I think it goes like this...
One of the wisemen thought that if he were they other wisemen and he saw that no one had dots, he would declare himself the winner. But because they were silent and said nothing, he knew it must because everyone had dots, so he won.
So assuming that, the wise man noticed that no other wise man had answered that he had a dot on his hat, so AGAIN, by process of elimination, he figured out that he himself had a dot on his hat and went right away.
lets call them a,b and c
no because pretend A had no dot then B would see a dot on C and A with no dot since he doesn't know if there is more then two dots he stays quiet the same for C
