Free Cell combinations.

[Snowy Owl]

FreeCell has 1,000,000 games. There are 52 cards laid out as 4 columns of 7 and 4 columns of 6 cards. How many different combinations of this are there?

[auntflo]

would it be 52 x 51 x 50 x 49 x48....... x 3 x 2 x1?

[gen2]

That might be what is wanted auntflo, but I read the question slightly differently.

The four columns of 7 cards could appear in any sequence and still be the same game, likewise the 4 columns of 6 cards.

That will give you (factorial 52)/(2*factorial 4) different games.

[Snowy Owl]

I guess that means a lot more than 1,000,000 then?!!!

Thanks for the help.

[factor-fiction]

Yes! A few trillion trillions- more than 1 with 65 noughts on the end!

[Snowy Owl]

No wonder I have yet to come up against the lay out that has all the kings at the tops of their columns, followed by the queens etc.,etc.!

[dundurn]

From a practical point of view there will be a number of card layouts that wouldn't be included because they wouldn't make a challenging enough game, so you'd never get the layout you specified. In addition there will be layouts which will be replicas of others, apart from the fact that the suits will change places so I would think they might be missing also. Another issue is that Microsoft advertise that all their published games are capable of solution and a large number of the possible layouts must be impossible so those too will be omitted.