I can only try-
Take seven Nickels (or any coin for that matter but preferably without ridges), put one in the center and the other six around it. Look closely and you will see a space between two of the coins. That space is twice the decimal of PI (multiplied by a constant).
Let’s say Mr. Director starts a pattern that is a family of concentric circles centered at the center of the table. In each subsequent circle the little space will get bigger and bigger until there is room for another quarter. Once there is an odd amount of quarters in a circle there will be a space for Mr. Director to place a quarter without a corresponding spot on the “other” side of the table.
QED