52! (52 factorial)

"If you had been shuffling a deck every single second since the universe began, 13.7 billion years a go. You still to this day, wouldn't have even come close to assembling every arrangement possible.."


52! (52 factorial) is equal to 8.0658 * 10^67, to put that in to perspective the observable universe is only 1*10^18 seconds old.


"Imagine setting a timer to count down 52! (52 factorial) seconds. While the timer runs 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, and so on. Once you have walked all the way around the earth, take a single drop of water out of the pacific ocean, that's 0.05ml (5 hundredths of a milliliter) and set it aside. Now, continue walking at a rate of one step every billion years removing one drop after every journey around the entire earth. And by the time the pacific ocean is completely empty, put a single sheet of paper on the ground. Refile the ocean and keep going until the stack of paper reaches the sun. At that point, how many seconds will be left on the timer? will it be 0? A few hundred? A few billion? No, there will still be 8 * 10^67 seconds left. If you start all over again and do that whole thing 1000 more times, you will only be 1/3 of the way done."

Another example is...

"Deal yourself 5 cards every billion years. When you finally deal yourself a royal flush, buy a lottery ticket. If the ticket wins the lottery. Throw a single grain of sand in to the grand canyon. As soon as the grand canyon is completely full of sand remove 1oz of rock (aprox. 28g) from mount Everest. By the time mount Everest is leveled. Take a look at the clock. You will be left with, '536,400,321,887,439,562,734,550,908,211,738,546,920,459,862,233,113,245,907,665,344,238,299'seconds. Do the royal flush, lottery ticket, grand canyon, mount Everest thing 256 times more times and then, and only then have reached, 0."

Truly amazing.

credit: http://listenonrepeat.com/watch/?v=ObiqJzfyACM&s=913&e=1171#Math_Magic (V-sauce)