Quote:
Originally Posted by Mathgod
I agree that your approach is much more precise, direct, and succinct than mine. However, I think there may be a problem with both your solution and mine (and really, the entire premise of the question). The problem is the corners. The center of the closest coin to the corner could be more than 2r away from the corner, yet no new coin could fit in the corner space there becuase it couldn't fit within the edges of the table. Hence, the contradiction you pointed out is not entirely true.
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I think the edge case is taken care of by the fact that a coin doesn't have to be fully on a table. As long as the centre of a coin is on the table (even if it overhangs the edge) it is considered on the table.
The question could be more precisely stated that 100 coin centres are on the table.