The Illumination Problem

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This isn’t your average mini-golf course. There is something special about this room and it took almost 50 years to come up with this design.

If Satan plays miniature golf, this is his favorite hole. A ball struck at A, in any direction, will never find the hole at B — even if it bounces forever.

The idea arose in the 1950s, when Ernst Straus wondered whether a room lined with mirrors would always be illuminated completely by a single match.

Straus’ question went unanswered until 1995, when George Tokarsky found a 26-sided room with a “dark” spot; two years later D. Castro offered the 24-sided improvement above. If a candle is placed at A, and you’re standing at B, you won’t see its reflection anywhere around you — even though you’re surrounded by mirrors.


6 thoughts on “The Illumination Problem”

  1. Maybe if A and B are point-sized this is true. If A and B are golf ball sized then just hit A off the corner that is down and to the right. Corners let you bounce is many directions based on where you hit. One bounce brings you to B.

  2. Surely the Devil knows how to apply English (a slight spin) when striking a ball, which, with a few practice strokes, would make this hole an easy ace for the POD (Prince of Darkness). 😈
    The candle reflection example is more interesting.

  3. I’m not sure about the com between a forever bouncing golf ball & candle light is correct. The light will dissipate after a number of reflections.

    1. The light wouldn’t dissipate if you’re assuming perfect reflections (no absorption or transmission). The lit match would continually pump the entire room (or a 2D slice of it depending on the floor and ceiling) with more and more photons except for at that one spot.

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