[psyang]

Originally Posted by bizaro86

Spoiler!

The table is 100 identical squares of side length D the diameter of the coins.

You have 4 coins per square. If you line them up such that each coin has a diameter on the edge of the square it covers the whole square because a semi circle is concave out (more than the isosceles triangle that would exactly cover)

Then do the same for all the other squares.

Hmm. Not quite.

Spoiler!

You will have to prove that every table for which you can arrange a maximum of 100 coins without overlapping is smaller than or equal to your 100 square table (which I don't think is the case).

What you've proven is that there exists a table for which 400 coins will cover given the initial conditions. But the problem is about any rectangular table that satisfies the initial conditions.

For example, I think it would be possible to arrange a maximum 100 coins non-overlapped on a table composed of 100 squares of side length D+k where D is the diameter of the coin, and k is an infinitely small value.

In such a table, the initial conditions would still be satisfied, but your procedure would not work as there would be an infinitely small uncovered area in the center of each square.