1. As everyone knows, Shahryar (the King of Kings), who seemed not to trust women, took a new wife each day and had her beheaded next morning. Scheherazade was the daughter of the King's vizier, and one day she volunteered to spend that night with the King. Scheherazade was a very clever lady, and postponed her execution each day by telling the King stories, ending each one at dawn with a cliffhanger. But after 1001 nights, she ran out of stories. She didn't really believe that the King would have her beheaded, but she decided that she had to make sure. She had ready a little problem for him, which turned out to be just as well, because he was looking for entertainment. And he was apt to turn nasty if he didn't get it. The little puzzle she offered him was this:
A certain sheik named Hassan had eight horses. Four of them were black, three were white, and one was brown. How many of Hassan's horses can each say that it is the same colour as another of Hassan's horses?
2. "Well," said the King the next night, "I solved that one all right. How's Hassan getting on with his horses?" "His horses are fine," replied Scheherazade. "And he also has a mule. One day he met three boys who asked him what was its colour. "The mule is either black, brown or gray," said Hassan. "You make some guesses, and when we've had enough, I'll tell you some things about the guesses, and we'll see if you can work it out."
The first boy said, "I'll guess it's not black."
"I'll guess that it's either brown or gray", said the second.
"And I'll guess that it's brown", said the third.
"Right," said Hassan, "that's enough guesses. Now then. At least one of you is right, and at least one of you is wrong."
What colour is Hassan's mule?
(Adapted from Raymond Smullyan's "The Riddle of Scheherazade".)