What is the minimum number of pennies that can be placed upon a table so that each penny touches three, and only three, others?

(All the pennies must lie flat on the table.)

(In reply to solution by SilverKnight)

If we assume (or could prove) that any solution must be n of your tight diamonds put together, then we still need to show n=4 is minimal. With my pennies, it isn't utterly clear that n=3 won't work. The centers of the pennies of the diamond are vertices of a rhombus made up of two equilateral triangles that share a side. This rhombus can be scaled up to just circumscribe the pennies of the diamond. Maybe these observations will help to rule n=3 in or out.

Edited on December 18, 2003, 3:48 pm

Posted by Richard on 2003-12-18 01:24:20