We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
In the 1950's, Ernst Straus asked a seemingly simple problem. Imagine a dark room with lots of turns and side-passages, where all the walls are covered in mirrors - just like the Hall of Mirrors in an old-fashioned fun-fair. Is it true that if someone lights a match somewhere in the room, then wherever you stand in the rest of the room (even down a side-passage) you can see a reflection of the match?