Brain Teasers are Back!

Want to do something right now that nobody else has ever done since the start of the Universe, and nobody else will ever be able do……ever ?

It’s very simple.

Shuffle a standard deck of 52 cards and deal them out one at a time.

That sequence has (probably) never been dealt before and (probably) never will again.

why (probably) ? There are 52 x 51 x 50 x 49 ……… ways of dealing out those cards. That’s 52!

That’s more than the number of atoms that make up the Earth. Chances are, it’s never been done before, and never will be done again !

Anyone want to quote an approximate figure for the number of different ways ? Ie put a number on for 52!

PS the cards do need to be well and truly shuffled to be considered random.

I’ll take 25% on the coins and I found a great You Tube video about the cards.

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I assume that means there is a neat approximation that I’m not aware of.

I didn’t have a calculator to hand, nor pencil and paper for that matter so I’m going with old school ballpark mental arithmetic.

My first stab was to pair up 1x52, 2x51… 26x27, suggesting 26.5^52 which is both heroic and a bit challenging to progress to an actual number.

How about: 7! x (8x52) x (9x51) x… (29x31) x 30?

7! = 720 x 7 = 5000 (approx).

Replace brackets with fairly heroic 22.5 pairs of 30x30, giving 30^45 = 3^45 x 10^45.

As 3^5 = 243, use approx 250 = 1000/4. So, 3^45 = 1000^9 / 4^9.

4^10 = 1 megabyte = 10^6 approx.

Bringing it all together: 5000 x 10^45 x 10^27 x 4 / 10^6

Gives: 2 x 10^70

Likely to be quite an overestimate from using 30x30 instead of 8x52 etc.

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I thought the answer was 42.

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Well done Mike.

I haven’t found any neat approximations, despite a quick search on Google.
Best estimate I have seen is 8x10^67
Approximations are often turned into time lines assuming you shuffle&deal the pack once every second !

I knew somebody would come up with the right answer - and I wasn’t disappointed :sunglasses:

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My genius is well hidden. :rofl::rofl::rofl:

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Is it longer than since the Big Bang?

Yes, I think it is.

Who’s for a game of poker ? :sunglasses:

Just looked up that there are 1.33x10^50 atoms in the Earth. Age of universe is 13.8bn years. So if there was a deck of playing cards for every atom on Earth each being dealt every second since the Big Bang, it would still take another 5bn years to reach 52! deals. Even then there’s a good chance that any particular deal would not have occurred.

Paraphrasing Douglas Adams:

“Dealing cards is big, really big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way across space, but that’s just peanuts to dealing cards.”

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Nice development Ravvie.

52! is such an easy number to quote, and in the context of a deck of cards so easy to grasp the concept of shuffling and dealing - but so difficult to imagine just how big the number of permutations there are.

I’m going to stick with Pete’s answer of 42 :sunglasses:

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A pack of cards with the words “Don’t Panic” written in large, friendly letters on the front. Sign me up.

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Just popped the numbers into Excel to check …
…8.06582^67
So pretty close to the approximation I quoted above.

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This is the video I watched:

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Neat video Mike.

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I carefully explained this visualisation of dealing 52 cards in all their different ways to Mrs D.

I had to take it slowly, especially the concept of how many atoms there are in the Earth - she could visualise the back garden (1/3 acre) - but was struggling a bit with the Earth.

She didn’t feel that atoms could shuffle and deal a deck of cards every second- they would need at least a minute ! and what had the Big Bang to do with it - nobody was around at that point in time :sunglasses:

But eventually, I thought i’d managed to deliver a reasonable concept of how vastly, hugely, mind-bogglingly big it is until she concluded with “so not really worth trying, I suppose ?”

Bless ! It did make me smile.

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My ballpark estimate of 2x10^70 was disappointingly 250 times too high.

Stirling’s approximation (I cheated by looking it up) is (sqrt(2n x pi)) x (n/e)^n, giving 8.0529x10^67. I’m not sure that’s any easier than multiplying out all the numbers. Maybe it was designed for larger n than 52.

If anyone needs an exact answer, I got this from Xnumbers (a free 3rd party add-in for Excel):

80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

I then started to wonder if a pen and paper approach could get there, until I saw your comment from Mrs D:

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In Excel I did both the

52 x 51 x 50 x 49 … x 2 x 1 arithmetic. Took about 2 minutes to set up.

and also used the FACT() function (Factorial 52)

Of course, in both cases, Excel rounded off to half a dozen significant figures.

That’s likely Excel’s default formatting. The calculations should be good for 15 or 16 figures if reformatted.

Xnumbers (powerful but clunky to use) can in theory correctly maintain anything up to about 30,000 significant figures, though it’s rather meaningless to try and see them all!