Four smart gnomes are standing in line with all faces pointed in the same direction. They all carry a hat, but they do not know their color. They only know that there are two red and two green hats. The first gnome stands behind a wall and does not see the others. The second gnome is able to see the hats of the third and the fourth. The third only sees the hat of the fourth, and the fourth gnome does not see any hat at all. The gnomes would like to know which hat they wear without checking their own. When a gnome has figured out which hat he carries, he will immediately tell the others. Suppose that the first gnome wears a red hat, the second a green one, the third a red one and the fourth a green one. Which gnome will be the first to figure out?

How can you put (without using glue or something like that) ten nails on the head of a standing nail? The final construction should be stable.

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?