An optimization problem in geometry — RMO and INMO

An exerciser wants to twirl a 1 meter long baton in a horizontal plane through 360 degrees as he moves around in a room without hitting the walls. He does not mind any shape but wants to minimize the area of the room. Note that a circular room of 1 meter diameter (with an area of pi/4 square meters) is far from the minimum area possible.

Pick up this challenge for yourself! Victory is ours when we have strength and courage to run our own race!

Nalin Pithwa.

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