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One for the mathematicians:

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Community Veteran
Posts: 7,391
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Registered: ‎30-08-2007

One for the mathematicians:

I expect most users of Windows have at some time indulged in Microsoft Solitaire, or one of the many other versions. Some (like me) may have actually played using old fashioned playing cards.

And yes, the original MS Solitaire can be installed on W10, much better than the version included in W10. I know, I've been playing it for ages.

But my question for the mathematicians:among you is:

How many combinations of openings - 7 across with the top each of each descending column face up, but before any other cards are played) are there - ?. 

Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
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All Star
Posts: 1,204
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Registered: ‎25-07-2007

Re: One for the mathematicians:

Face up or face up + face down ?

Face up = A good Euromillions jackpot win............

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Community Veteran
Posts: 7,391
Thanks: 93
Fixes: 2
Registered: ‎30-08-2007

Re: One for the mathematicians:

Yes probably...

All column cards face down, except the first card dealt, and top card of each column, as in standard Solitaire opening deal.

Or to give it its traditional name: the tableau.

Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
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Grafter
Posts: 165
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Registered: ‎13-01-2011

Re: One for the mathematicians:

All together there are Factorial 52 combinations of the game 52!  If only the 7 face up cards are considered and the order of the face down cards does not matter then there are 52x51x50x49x48x47x46 combinations. More of a question for a statistician!

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Aspiring Pro
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Re: One for the mathematicians:

According to St Stephen of Fry in his temple of QI, the number of combinations and permutations of a shuffled deck of cards is so large, that essentially each each shuffled deck could be considered unique; but a previous answer is correct, and to save you doing the multiplication, there are 674,274,182,400 potential combinations of any 7 cards taken at random from a thoroughly shuffled deck.

 

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All Star
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Registered: ‎25-07-2007

Re: One for the mathematicians:

Perm 7 from 52

I reckon the previous answer (52*51*50*49*48*47*46) needs to be divided by (7*6*5*4*3*2*1)

I don’t mind being corrected.......

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Grafter
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Registered: ‎13-01-2011

Re: One for the mathematicians:

I assumed that the order of the face up cards is significant as it is in a game of patience. If not the you could divide by 7!

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Aspiring Hero
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Re: One for the mathematicians:

FreeCell has become more difficult in Win10.  I can still win every game but it usually takes longer than it used to.  A few versions ago you could choose a game number, and a colleague tried a negative number.  He still got a game but it proved impossible to win.

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Community Veteran
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Registered: ‎30-08-2007

Re: One for the mathematicians:

Umm! I suppose then when as happens occasionally, I get a nagging suspicion that I have seen the opening I have before me before...

I probably haven't.

I wonder how well Microsoft shuffles the cards...Huh

Experience; is something you gain, just after you needed it most.

When faced with two choices, simply toss a coin. It works not because it settles the question for you. But because in that brief moment while the coin is in the air. You suddenly know what you are hoping for.
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Anonymous
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Re: One for the mathematicians:

Quite possibly using the Fisher Yates Algorithm @petlew

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All Star
Posts: 1,204
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Registered: ‎25-07-2007

Re: One for the mathematicians:

An interesting read, reminds me of a project we worked on back in the early 90’s.

we found there was no such thing as a random number generator.

No matter how you started the pattern would eventually repeat itself.

so, yes, you’ve probably seen the dealt deck before.......