There are more ways to shuffle a deck of cards than atoms on Earth


Is that sentence true?

Poll closed May 11, 2015.
  1. YES

  2. NO

  1. Jael Pendragon
    KitKat May 9, 2015

    Jael Pendragon , May 9, 2015 :
    Assuming mass made up only by lighter elements actually gives higher atom numbers ;)

    If it were all hydrogen it would be 10^51 atoms. For the sun we get up to 10^57 atoms. You need one 100th of the milky way to get enough atoms to compare to 52! number wise

    T3STY and LifelessLewis like this.
  2. LifelessLewis
    Jelly Bean May 9, 2015

    LifelessLewis , May 9, 2015 :
    Good point haha, but yeah even 10^51 atoms is small compared to 52! Crazy!

    Jael Pendragon likes this.
  3. Jael Pendragon
    KitKat May 9, 2015

    Jael Pendragon , May 9, 2015 :
    8x10^67 is way bigger yes. People don't get that 15/16 orders of magnitude of difference is simply enormous. The Sun is "only" 1 million times the earth ....

    LifelessLewis likes this.
  4. B-Rad
    KitKat May 9, 2015

    B-Rad , May 9, 2015 :
    I poop more atoms than that.

    LifelessLewis likes this.
  5. dsmonteiro
    Community Consultant Staff Member May 9, 2015

    dsmonteiro , May 9, 2015 :
    But that's precisely the other way around. 1kg of water has way more atoms than a kilogram of plutonium. And lighter elements are more common than heavier ones.

    Jael Pendragon and LifelessLewis like this.
  6. dsmonteiro
    Community Consultant Staff Member May 9, 2015

    dsmonteiro , May 9, 2015 :
    I stand corrected.

    Jael Pendragon and LifelessLewis like this.
  7. mmrbest
    Jelly Bean May 9, 2015

    mmrbest , May 9, 2015 :
    Dayum,I was gonna consider that(was gonna take lithium) but I checked uranium's atomic number and poof,my brain melted. Anyways,if we consider all mass as water,we have 1.9980*10^50atoms.,still not even close...
    Edit: that's for 55.55 mole,and for hydrogen with a whooping 400+mole,we still have some value around 10^51..lol!
    Last edited: May 9, 2015

  8. T3STY
    Honeycomb May 10, 2015

    T3STY , May 10, 2015 :
    It looks like some people got really interested into these numbers... keep goin'!!!

  9. Aayan99
    Cupcake May 10, 2015

  10. mashranga
    Gingerbread May 11, 2015

    mashranga , May 11, 2015 :
    A correction on my idea:
    1. Card Suffel:
    i. 52 cards. so total possible suffel 52! = 8.065817517 E+67
    Each card has two way to draw a) upside down b) upside. So 52 cards has 2^52 way to place in the dack of 52 cards.
    Total possible way of suffel : 52! x 2^52 = 8.0658175e+67 x 2^52 = 3.6325213e+83

    2. Total atom in world :
    Estimated total : 1.33 e+50 [Ref]

    Hypothesis: "
    There are more ways to shuffle a deck of cards than atoms on Earth
    Decision : "TRUE"

    Interesting :)

    T3STY likes this.
  11. T3STY
    Honeycomb May 11, 2015

    T3STY , May 11, 2015 :
    Congratulations to @LifelessLewis, @mashranga, @Jael Pendragon and @mmrbest, your replies are correct! Congratulations to @Slyther1 as well, even though your initial answer was wrong :)
    YES, this fact is totally true! But let's dig a bit into some simple math, and science :)

    Very neat comparison!
    The numbers between right and wrong are what we call an estimate. So let's say that we get a wrong estimate, by excess: just like Jael above, let's consider that the whole Earth was made of the lightest atoms known: Hydrogen atoms. In this case we will get a very huge error by excess in our calculations. In this case the number of atoms is somewhere around 10^51 (ten to the power of 51).

    But, how many ways to shuffle a deck of (52) cards are there?
    Wow, mashranga, really wanted to make sure you didn't get it wrong, huh? ;)
    The logic behind of this is: choose the first card from the initial 52, then choose another one from the remaining 51, and keep going until you're left with no more cards to choose from. That is (52-0)*(52-1)*(52-2) ... *(52-51) = 52! (read as: 52 factorial). By rounding this number we get 8.07*10^67.

    If you were to do by hand all those shuffles... you'd need to be immortal, or at least a vampire to finish them all :D
    You can judge by yourselves that a 1 followed by 67 zeros is way out of reach for a 1 followed by 51 zeros. If you think that the 51 is even a wrong estimate, then both Earth and the Sun are nowhere near that number of shuffles :)

    Guys, I hope you had a little bit of fun with this, and I hope I blew your mind with outstanding numbers. See you next time! :)

    EDIT - interesting twist by mashranga
    In the calculations before I have considered each card as a unique card. But if you do like mashranga and consider that a card can be extracted upside or upside down, then you get a mighty unthinkable number!! Fortunately, our brains don't crash with a "out of memory" exception when we try to imagine that number :D

    This is how you read that number...
    Last edited: May 11, 2015

  12. Rocco214
    Eclair May 11, 2015

    Rocco214 , May 11, 2015 :
    I am always telling people about this! Whenever I'm playing cards with someone and they say I dont shuffle good or something I always tell them that chances are that any deck of cards has never been shuffled in this order. I shuffle it again and say or like this. And keep doing that. If everyone on earth shuffle a deck of cards every second for a billion years we wouldnt even be close to the amount of combination. I'm talking not even .000000001% of the combinations.

    LifelessLewis likes this.
  13. T3STY
    Honeycomb May 11, 2015

    T3STY , May 11, 2015 :
    I'm not sure about that billion years and 0.0000....1%, but I'm not going to put that to a practical test either :D
    However, the whole thing is amazing ;)

  14. Rocco214
    Eclair May 11, 2015

    Rocco214 , May 11, 2015 :
    Seconds in a year- 365 days X 24 hours X 60 minutes X 60 seconds= 31,536,000

    31,536,000 in a year X 1,000,000,000 years= 3.15x10^16

    3.15x10^16 Seconds in a billion years X 7,000,000,000 people on earth= 2.20752x10^26 combinations

    2.20752x10^26 Combinations in a billion years divided by total combinations 8.065818x10^67 = 2.736883x10^-42 or .000000000000000000000000000000000000000001% of the combinations

    T3STY likes this.
  15. T3STY
    Honeycomb May 11, 2015

    T3STY , May 11, 2015 :
    You're awesome, @Rocco214! These numbers simply blow me out!

    By the way, believe me, but I didn't do it on purpose to make my answer post #51, just like the power of the estimated Hydrogen atoms in the calculations :D

  16. Rocco214
    Eclair May 11, 2015

    T3STY likes this.
  17. jcb4200
    Cupcake Oct 19, 2016

    jcb4200 , Oct 19, 2016 :
    Well, I'm way late to this thread, but here is how I calculated it for a worst case (most exaggerated) situation:

    I assume the entire earth, by volume, was filled with hydrogen atoms.
    I also assume that a hydrogen atom is spherical and thus its volume can be calculated by using simple equation for calculating the volume of a sphere:
    hydrogen atom which as a radius of 53 picometers:
    volume of the atom = 4/3*PI*(53pm^3) =about 623,600 cubic picometers
    A similar calculation puts the volume of the earth at 1.6x10^11 cubic km
    So a simple rudimentary calculation to get the number of hydrogen atoms that can fit inside the volume of the earth. This is very similar to how you would calculate the number of marbles that would fit inside of a ball:
    (1 hydrogen atom / 623600 cubic picom) * (1 cubic picom / 1x10^-45 cubic km) * (1.6x10^11 cubic km) = approximately 2.57x10^50 hydrogen atoms that could fit inside of the earth.

    While this is large it is not even .0000000000000025% of the number of iterations of a 52 card deck. Pretty amazing.