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© Copyright 1999, Jim Loy
FreeCell is a solitaire card game (see your Windows start/programs/accessories/games for the rules) that comes with Windows. In the help messages, it says, "It is believed (although not proven) that every game is winnable." I told a friend of mine that it would be easier to prove that not every game is winnable (if that were true), than it would be to prove that every game is winnable (if that were true). The reason for this is that to prove that not every game is winnable, all you need is an example which is not winnable. The above opening situation is my example. It is easy to show that this is not winnable. Now we know why the FreeCell programmers were not able to prove that every game is winnable.
Addendum:
I received email that suggested that maybe the programmers of FreeCell have somehow prevented oddball hands like above, and so maybe all hands that the program can deal are indeed winnable. Could be, but I think the quoted statement in the help messages implies (mildly) that it means all 52! (52 factorial) possible deals.
OK, there is a lot of FreeCell info out there. Above is the famous game 11982, which is known to be unwinnable. FreeCell's random number generator deals any of 32,000 random deals, way short of the 52! deals that I assumed. And game 11982 is the only deal of those 32,000 which is unwinnable. This was deduced by having an army of people (over 100 of them) test all 32,000 deals. Then, when game 11982 eluded solution by humans, it was tested exhaustively by computer. See FreeCell - Frequently Asked Questions (FAQ) - by Michael Keller.