[bizaro86]

Originally Posted by psyang

Ok, one more coin question (for now). This one might be tricky, we'll see. The solution is very elegant.

You have 100 perfectly round and identical quarters on a rectangular table arranged such that none of them overlap (ie. all quarters are flat on the table) and it is impossible to add another quarter to the table without requiring an overlap.

Show that you can always cover the table completely with 400 coins (where, by "cover", I mean that for every point on the table, there is at least one coin directly above it). Obviously, the covering would allow for overlaps.

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.