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.
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.