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?

Eric has a perfect spherical shaped apple. With a cilindrically shaped drill bit he removes the core of the apple. A cilindrically shaped hole remains, the center of this hole is exactly at the center of the apple. Eric measures the length of the hole with a piece of rope. It turns out to be exactly 8 cm. What is the volume of the remaining apple?

I lived in a city that held as much as it could,
So I moved to another that repaid what it should.
The third had very little, with not much to be found,
The fourth was very boring, with no change in the sound.
The fifth was a jungle; wild beasts roamed the in street,
The sixth was so foggy you could not see past your feet.
The seventh was on the move; I could barely keep the pace,
The eighth was so evil; a whole city in disgrace.
The ninth was off-center; the people were bizarre,
The tenth was quite truthful; where honesty is par.
The eleventh was so wise; the acumen hurt my brain,
So I settled in a twelfth, because it was so plain.