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.)

I don't have a proof of it... but I can come up with a 16-penny solution...

Make a diamond with 4 of them... (like two equilateral triangles against each other), and use that as a base.

Then put 4 diamonds together (for a total of 16) at the 4 compass points, oriented perpendicular to their direction.

rough ascii art view:


         O
     O       O
  O      O      O

O   O         O   O

  O      O      O
     O       O
         O

Edited on December 17, 2003, 2:33 pm

Posted by SilverKnight on 2003-12-17 14:23:36