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### Math magic : shuffling cards

I've been watching a lot of YouTube videos about maths, especially Vsauce. I highly recommend it, it's fascinating and fun and simple to understand. This is entirely from one of his videos : https://youtu.be/ObiqJzfyACM

- •Do you know that every time you shuffle a deck of 52 cards, chances are you have put those playing cards into an order that they have never been in, in the entire history of cards!
- •The number of different ways 52 cards can be arranged is 52 factorialWhich means : 52x51x50x49x48x47x46x45x44.........
- •It is a HUGE number!!!!! Don't make the math, here it is :80658175170943878591660636856403766975289505440883277824000000000000
- •In fact, even if the cards were rearranged every seconds since the beginning of the earth, you still wouldn't have come close to assembling every arrangement possible!
- •Because 52 factorial is more than 8x10 to the 67thThe universe is only 10 to the 18th seconds old...!
- •Even that doesn't paint the whole picture of how big 52 factorial is :
- •Imagine sitting a timer to countdown 52 factorials seconds
- •Stand on the equator and wait 1 billion years
- •After a billion years have passed, take a single step forward and then wait another billion years before taking a second step.
- •So once you have walked all the way around the earth take a single drop of water out of the Pacific Ocean
- •now continue walking at a rate of 1 step every billion years removing one drop after every journey around the entire earth.
- •By the time the Pacific ocean is completely empty put a single sheet of paper on the ground.
- •Refill the ocean and keep going until the stack of paper reach the sun.
- •At that point there will still be 8x10 to the 67th seconds left on the timer!
- •You have barely made a dent!
- •If you start all over again and do that thing a thousand more times, you will only be a third of the way done!
- •The creator of this story has a great idea to pass the rest of the time left if you're bored :
- •Deal yourself Five cards every billion years, when you finally deal yourself a royal flush, buy a lottery ticket. Every time the ticket wins the lottery, throw a single grain of sand in the Grand Canyon.
- •As soon as the grand canyon is completely full of sand, remove one ounce of rock from Mount Everest at every winning lottery ticket until it's leveled.
- •Now do the five card/royal flush/lottery ticket/Grand Canyon/mount Everest thing 256 more times...
- •And then, and only then, will your timer have reached zero!
- •That is how big the possibilities of order in a deck of cards is!
- •The tiny deck of cards
- •I love maths
- •It's better than magic, because it's real !And not real simultaneously!

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