Somebody would like to have a new garden with 10 trees which have to stand in 5 rows of 4 trees each. How can he or she achieve this? After the new garden has been layed out, neigbor Sym becomes enthousiastic. He says: "I also would like to have a new garden with trees. But it should have 12 trees which have to be planted in 6 rows of 4 trees each. Furthermore, my garden should be symmetric." How will his garden look like? And can you tell something more about Sym?

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?

Susan is in the final of a match at the olympic games. At the moment she reaches the finish, all the other contestants are behind her back. She did not play unfair and did also not use doping, but she does not get the gold medal? Why is that?