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?

Matthew leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, Matthew cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that Matthew saw on the clock at home.

At what time did he reach school?

Suppose you would like to boil an egg for exactly 15 minutes. But you only have two hourglasses, one of zeven and one of eleven minutes. What is the the fastest way to do this?