June 25, 2012 - A Penny for your Thoughts

[classicman]

You are going to be right against two walls and within the diameter of a penny from the other two. Thats what trim is for.
So back to my original question how many pennies fit in a 12"x12" space?

[Lamplighter]

Originally Posted by classicman

You are going to be right against two walls and within the diameter of a penny from the other two. Thats what trim is for.
So back to my original question how many pennies fit in a 12"x12" space?

Technically, I think you have changed the problem, but...
The simplest pattern to visualize is this:



If pennies are 0.75 inches in diameter, this pattern would hold 16 per linear foot.
16 x 16 = 256, or $2.56/sq ft.

But the pattern used in the OP was different, and more efficient.
So if you change the pattern towards a more "optimum" packing,
(or towards maximum number that will fit in a square foot)
the number or cost, obviously, would be higher.

The difficulty in calculating the optimum packing comes in selecting repeating "tiles" that fit the specific area efficiently.
Just as BigV said earlier. Circles fit hexagons very efficiently, but hexagons don't fit squares efficiently at the edges.