First, a technicality: in this mathematical context, assume the light from the candle can travel through the room and bounce off the walls forever. If you have a regular rectangular room, a single candle that radiates in all directions will totally illuminate the room. Things get trickier when the room is not entirely convex—think of the shape of a five-point star as an example. In most cases, you'll find that the candle will bounce around enough to reach every corner to illuminate even the weirdest shaped rooms.

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This problem was initially posed in the 1950s by German-American mathematician Ernst Straus. Roger Penrose, an English mathematician and physicist, came up with a solution in 1958. He conceived of a room involving half-ellipses (semi-circles, basically) that would always have dark regions. This room is something like an oval with two sideways-lying, mushroom-shaped chunks taken out of opposite ends.

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