Teaser 2513

[Peter Noll]

Hello All,

If n is the number of balls along one side and n+m the number of balls
along the longer side then the size of the base layer is

B = n*(n+m)

and the number of balls in the pile is

T = n*(n+1)*(2n+1+3m)/6 = 10000

The largest B is obtained when m is the smallest number giving an
integer solution for T. I found

Bmax = 24*(24+17) = 984

Incidentally, the tightest packing of the pile is for a base layer
with 60 degree inclination between the sides of the layers --> smaller
area than for rectangular shape. The number of balls in the base layer
remains of course unchaged.

Peter