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Topic: Are there more ways to arrange a deck of cards than the number of atoms in the universe? 


I've told people that there are more ways to arrange a deck of 52 cards than there are number of atoms in the universe. Few believe me, but I believe it's true. The conditions I use for counting are (1) a face up card is different than a face down card (cards can be face up or face down), and (2) the order of face down cards matters (i.e., a different order of face down cards is a different arrangement). I calculate that the number of ways to arrange the cards under these conditions is (2^52) * (52!) = 3.63 x 10^83. According to a Google search, the upper limit for the number of atoms in the observable universe is 10^82. I find it remarkable that when you allow cards to be mixed face up and face down, the number of possibilities is so immense. I am hoping that someone can confirm my calculation. David M. 


You should post this in the puzzle section. The smart math guys hang out there. I have heard that when a deck is well shuffled it is likely that no other deck has ever been in that same order. 


Here's an incredible way to visualize 52! https://czep.net/weblog/52cards.html 


It is not really necessary to add face up and face down. 52 factorial is large enough to dazzle. 


If you google "the number of atoms in our galaxy" you'll find that it's about 1/3 of the way to 52! which is the number of ways to arrange the 52 cards in a deck. I used the reference Steven Keyl pointed to above in TESSSERACT to dazzle the reader with the incredible size of 52!. SO 52! is not bigger than the number of atoms in the UNIVERSE. It's bigger than the number of atoms in our galaxy of two to four hundred billion stars. Our star, the sun, is about a million times the size of the earth. But check out Steven's reference. It's a mind blower. Mike 


This is usually true, unless you see a Nine of Diamonds on the bottom. Then chances are they've been in that order before :D //Dan 


Good one Dan! 


Dan’s quote usually goes over my head. I definitely think Juan Tamariz is smiling😀 


Both Juan and Simon are smiling! Mike 


No! More ways to arrange a deck than there are atoms on EARTH. 


Scott  do a google search on 52! and also on "number of atoms in the milky way galaxy." You'll see that there are more ways to arrange the cards in a deck (52!) than there are atoms in the entire galaxy of 200 to 400 million stars and all their planets etc. Mike 


E.C.R.P.: https://www.themagiccafe.com/forums/viewtopic.php?forum=37&topic=676750 


The reference above just says that 52! is bigger than the number of atoms in our solar system. Just do a google search on "the number of atoms in the milky way galaxy." The estimate is less than 52! This is an estimate. So it's correct to say that 52! is "in the vicinity of" the number of atoms in our 200 to 400 billion star galaxy. It's not the number of atoms in our sun or the earth or the solar system. That's not even close. It's off by a factor of hundreds of billions. Mike 