Editing FreeCell (section)

== Solver complexity ==
The FreeCell game has a constant number of cards. This implies that in constant time, a person or computer could list all of the possible moves from a given start configuration and discover a winning set of moves or, assuming the game cannot be solved, the lack thereof. To perform an interesting complexity analysis, one must construct a generalized version of the FreeCell game with {{nowrap|4 × ''n''}} cards. This generalized version of the game is [[NP-complete]];<ref>{{cite journal |title=Complexity results for standard benchmark domains in planning |journal=Artificial Intelligence |first=Malte |last=Helmert |date=March 2003 |volume=143 |issue=2 |pages=219–262 |doi=10.1016/S0004-3702(02)00364-8|doi-access= }}</ref> it is unlikely that any algorithm more efficient than a [[brute-force search]] exists which can find solutions for arbitrary generalized FreeCell configurations.

There are 52! (i.e., 52 [[factorial]]), or approximately 8{{X10^|67}}, distinct deals. However, some games are effectively [[isomorphism|identical]] to others because suits assigned to cards are arbitrary or columns can be swapped. After taking these factors into account, there are approximately 1.75{{X10^|64}} distinct games.<ref name="FCFAQ" />