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 
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My genius is well hidden. 
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Is it longer than since the Big Bang?
Yes, I think it is.
Who’s for a game of poker ?
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
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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
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!
Yep, column width limited. I could have increased the width and retained more sig figs.
Apologies.
I goofed when I drafted the second “Road from X to Y” teaser. I’ll correct it and re-post tomorrow.
The Road from X to Y. (2nd attempt !)
Our Local Council is building a new road from Village X to Village Y but hasn’t made much progress to date. In fact, they have only completed a few sections as shown on the plan below.
The numbers along the top of the plan and down the side of the plan show how many sections of road will be built in each column and each row. The planned road will not cross itself at any point.
Each cell on the Plan can only contain :-
a straight length of road either horizontally or vertically on the plan or
a turn to the right or a turn to the left (or up/down)
Can you complete the Plan ? (hopefully, this time you can !)
I’ll post my solution to the above X to Y road scheme tomorrow.
Meanwhile, a few simple bits of arithmetic to get the old grey cells working …
A) 3 children can eat 3 ice creams in 9 minutes. How long will it take 5 children to eat 5 ice creams ?
B) 4 lumberjacks chop down 12 trees in a day. How many trees could 13 lumberjacks chop down in a day ?
C) 5 mathematicians take 20 hours to solve a problem. How long would it take 25 mathematicians ?
Usual maths rules apply. ie the situations are hypothetical and “fair” eg with the mathematicians, you could argue that if the problem has already been solved by the first 5 mathematicians, any old maths teacher could subsequently solve it in a couple of minutes !!! Let’s just stick with the hypothetical ratios.