The riddle
I Have Cities but No Houses. What Am I?
The full riddle
The whole riddle has three parts: "I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?" The answer is a map. Other versions swap in forests, rivers or roads, and the answer stays the same.
Adding lines of your own
The pattern is easy to extend, and a map supports plenty of new lines: roads but no cars, rivers but no water, borders but no fences. Asking a group to add a line of their own is a good test of whether they have really understood why the first three work.
What a map leaves out
The riddle works because a map is a picture of a place, not the place. A dot with a name beside it is a city without a single house. A patch of blue is water without a fish, and shading or a symbol for a peak is a mountain without a tree. Each line of the riddle names something the map shows and then removes what would normally go with it.
A flat map of a round world
Gerardus Mercator made his famous world map in 1569 for sailors, because on it a line of constant compass direction comes out straight. The price is size: shapes near the poles are stretched. On a Mercator map Greenland looks about as big as Africa. In fact Africa, at roughly 30.2 million square kilometers, is about 14 times the size of Greenland, at roughly 2.17 million.