Riddle 02

A) Three masters of logic wanted to find out who was the wisest one. So they invited the grand master, who took them into a dark room and said: "I will paint each one of you a red or a blue dot on your forehead. When you walk out and you see at least one red point, raise your hands. The one who says what colour is the dot on his own forehead first, wins." Then he painted only red dots on every one. When they went out everybody had their hands up and after a while one of them said: "I have a red dot on my head." How could he be so sure?

B) There are 3 prisoners and a sheriff. Sheriff says, "The one who solves my riddle will be set free". He puts 5 hats, 3 white and 2 black, into a bag. Then he said: "I will turn off the light and put a hat on each of your heads and hide the other hats. When I turn on the light you will have equal chances to win. Each of you will see the hats of the two others, however not your own. If you guess the colour of your hat then you win." He did so. The first guy thought for some time but couldn't answer. The second one thought and couldn't answer either. When it was the turn of the third guy, the sheriff said: "Ahh, ou have lesss chances as you are blind." The reply was: "I know the color of my hat." He names the color, explains how he guessed and is set free. What is the clor of his hat and why?

C) The grand master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn if they know the colors of their own stamps:

A: "No."
B: "No."
C: "No."
A: "No."
B: "Yes."
What are the colors of her stamps, and what is the situation?