Three horses are standing in a triangular field, which is exactly 100 yards on each side. One horse stands at each corner; and simultaneously all three set off running. Each horse runs after the horse in the adjacent corner on his left, thus following a curved course, which terminates in the middle of the field, all three horses arriving there together. The horses obviously ran at the same speed, but just how far did they run?

King Kreso had decided that one of his daughters, princess Ikani had to marry the mean grave Gwenn. When Ikani did hear of this she started crying for days and she did not want to eat anything anymore. The king became a little bit uncomfortable with this situation, so he decided that she should take a small stone from a hat. If Ikani would take the white stone, she would have to marry grave Gwenn, if she takes the black one she would not have to. Some days later, grave Gwenn, King Kreso and Ikani are together on the lane to the castle which is paved with small black and with stones. The king asks grave Gwenn to take two stones and put it in his hat. Princess Ikani sees that the mean grave puts in two white stones. She thinks of saying this, but then most likely the procedure has to start over. Suddenly she gets a great idea. Some minutes later it is decided that princess Ikani does not have to marry grave Gwenn. What did princess Ikani do?

What is the maximal height a pole vaulter could theoretically jump? Would it ever be possible that a pole vaulter passes the height of 10 meter?