Empty Chairs
This is an interesting problem. But it is simple if one find the shortcut. I would not tell anything about the shortcut. It is fast to solve but you lose a lot to learn if you are only interested in the solution to be submitted.
I investigated the problem a little bit and then find a recurrent equation. It is routine to find the differential equation that needs to be solved. I asked "Mr. wolframalpha" to solve the equation for me, then the problem becomes easy and clear. When I got the final solution, I was surprised that the result is related to one of Euler's well known contribution to math. I hope everyone can enjoy the problem.
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