I can only try-
Change is good: II
I’ve been racking my brain all day on this one but can’t come up with the correct answer. I think this is probably the one you are looking for (although it is wrong).
I would go first.
To decide where to put the first quarter I would draw two straight, non-parallel lines on the table (with my trusty pencil of course) where each end of the line touches the circumference of the table. I’d then rip out my protractor that I always carry in my pocket protector and use it to find the midpoint of each line. Next I would draw a perpendicular bisector for each line towards the other end of the table. The point where the two lines meet is the exact center of the table.
The center of the first quarter is placed on the center of the table.
After Mr. Director places a quarter I would place a quarter on the exact opposite side of the table. Therefore if he has an empty spot to place a quarter there should be an empty spot on the exact opposite side. Hence I will be the last on to place a quarter on the table.
This will not work once the diameter of the table reaches a certain length which I can definitely not calculate while in the state of mind I am currently in. (It has to do with my favorite constant.)