How many possible FreeCell deals are there?   Strictly speaking
there are 52! different deals, about 8x10^67. However, deals can
be transformed in several ways which make no mathematical
difference, which cuts down the number a bit. The four left-hand
(7 card) columns can be interchanged in 4! (24) ways, as can the
four right-hand (6 card) columns. Also, suits can be
interchanged in certain ways. If you swap suits so that all the
black cards become red and vice versa (there are 4 ways to do
this: SHCD can become HCDS, HSDC, DCHS, or DSHC respectively),
the mathematical properties of the deal do not change; you can
also maintain colors, but swap spades for clubs, diamonds for
hearts, or both (3 more ways). So there are 576 permutations of
columns (including no swaps) and 8 permutations of suits
(including no swaps), which reduces the number of essentially
different FreeCell deals to roughly 1.75x10^64 (a few rare deals
will be identical under one of the 4608 transformations). The
32-bit integers used in FreeCe