In a suburb three new houses all have to be connected to a gas (red), water (blue) and electricity (green) supply. All houses should get their own gas, water and electricity connection. Furthermore no connections may cross each other. Because of the danger of stealing, no connections are laid below a house. In the figure on the right-hand side the situation is sketched. The red squares are the houses, the circles the point from which the connections should go to the houses. Why is it impossible to lay down all connections in such a way that no connection crosses another connection?

The pieces with the same color in left figure have the same size as in the ones in the right figure. In the right image the pieces are only ordered differently. How to explain the hole in the right image?

Two fathers and two of their suns are going to fish. In total they catch three fishes. All of them take one complete fish at home. How is this possible?