Along the beach are a number of poles standing at equal distance from each other. The poles are numbered 1, 2, 3, 4, ..... Alice is walking from the first pole to the last one and back, Bob is doing that in the opposite direction. They start at the same time and walk with constant, but different velocity. Their first encounter is at pole number 10, their second (when they're both on the way back) at pole number 20. How many poles are standing along the beach?

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?