13000 pennies? hmm… I see only about $64 worth of pennies!! here is a slightly different take on the problem:
– Note that the rows and columns across the length and breadth of the floor are constant; that is, any two columns of pennies have the same number of pennies, as do any two rows.
– each bright and dark diamond of the center pattern is made from 16 pennies, four pennies from bottom point to top point and four from left point to right point
– there are 22 dark diamonds going back (length), and 12 dark diamonds going across (width)
– on the sides, there are only five pennies which are added from each point of a dark diamond to get to the wall
– the far and near ends are a problem; where the pattern meets the wall at the front of the picture is obscured; the back is so far back, it’s hard to see the individual rows; i count 11 pennies from the point of any dark diamond to the far wall. maybe 12? maybe 10?
From the above, we can calculate exactly the length and width of the room in pennies:
– width (from side to side) = 5 cents + (12 * 4 cents) + 5 cents = 58 cents
– length (from front to back) = 11 cents + (22 * 4 cents) + 11 cents = 110 cents
Or, total number of pennies in the room = 53 * 110 = 6380, or $63.80
The width of the room is directly observable; this number is correct. As I mentioned, i’m not sure about the number of pennies at the border of the front and back of the room, so we could be off by 100 pennies, plus or minus. Still a far cry from 13,000 pennies!
We’ve made two assumptions here:
a) the pennies are most efficiently packed
b) the room is perfectly rectangular
As an aside, a careful measurement of a sixteen penny diamond shows that pennies directly on top of one another (top of the diamond to the bottom) are 7.5 cm long, and when they are staggered (from one side of the diamond to the other) are 11.7 cm long. The difference is due to the way round objects pack.
So, the dimensions of the room are:
58 cents * 11.7 cm by 110 cents * 11.7 cm, or
678.6cm by 825vm, or
about 22 ft by 27 ft
