Shuffle a Deck

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There are 52! (factorial) ways to shuffle a deck of cards. That means:

 

80658175170943878571660636856403766975289505440883277824000000000000 ways.

How big is that number? Start by picking your favourite spot on the equator. You shuffle the deck of cards once every second. Walk around the world along the equator, but take a very leisurely pace of one step every billion years.

After you complete your round the world trip, remove one drop of water from the Pacific Ocean.

Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe.

Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.

Do this until the stack of paper reaches from Earth to the Sun (149,597,870.691 kilometres). You still have this many seconds and card shuffles to go: 

80630000000000000000000000000000000000000000000000000000000000000000

So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. You’re just about a third of the way done.

 

THATS, how many possibilities there are of shuffling a deck of cards.

 

Next time a magician wows you, maybe wow him back with your knowledge of card shuffle possibilities.