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King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there will be area inside the room without light.

How to build such room?

Note: Of course columns in this room don't have holes ( you can not just put candle inside the column) and can't touch each other.

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Is a column a point? And are there other conditions on the room? Just make two circles, connect them with a U-shaped tube smoothly, and stick the candle in one circle. No columns needed. –  Robert Mastragostino Apr 26 '13 at 4:35
    
@Robert, unfortunately your solution in general won't work, because all the walls reflect so no matter where you put the candle the light will reflect into the tube and from there to the other circle. –  vadim123 Apr 26 '13 at 4:38

1 Answer 1

This is actually a well-known problem, see Mathworld, or Wikipedia. Roger Penrose made the first solution in 1958, with curved walls, and Tokarsky made a solution in 1995 with straight walls. Although Penrose's solution is not smooth, I believe if you smooth out the corners it will still answer the question posed.

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