Re: Packing problem

You might want to read some essays on Ramanujan.  The partition of an
integer is:

3 = 3
3 = 1 + 2
3 = 1 + 1 + 1

when you partition the integer 20, well, have lunch first as there are
about 1 billion ways.  Ramanujan had formula he developed that unlike
many theorems in number theory that assert "The behavior is ~o(N))^2"
his theorem was exact!  So obscure was his notation (he was self-taught
in India) that when he sent his papers to GH Hardy, Hardy was about to
toss them, believing them to be the work of a fool (as we find too
often on this site).  Luckily Hardy took the time to work his way
through and invited Ramanujan to England where they collaborated.
Sadly the food and the weather caused an early death (I've been to
England and I can believe it!  :-) )

Ramanujan's work may not help you but could be an interesting read.

.

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