Think of this:
The number of ways a common deck of cards can be arranged is 52! The exclamation mark is mathematical shorthand for “factorial” which means, 1 x 2 x 3 x 4 x 5 etc., etc., on up to …….x 52.
For instance 3! = 6 (1 x 2 x 3). There are 6 ways to arrange 3 letters:
ABC
ACB
BAC
BCA
CAB
CBA
4! = 1 x 2 x 3 x 4 which equals 24 different ways to arrange 4 letters. (Try it!)
52! makes a big number—approximately 8 x 10^67—or 8 with 67 zeroes behind it.
Here’s a way to think about that number:
Start a timer that runs in seconds.
1. Stand at the equator then take one step forward. (One step = 1 foot.)
2. Pause for 1 billion years.
3. Take another step. Pause for 1 billion years.
4. Continue like this until you’ve gone all the way around the earth.
5. Reach down and remove one drop of water from the ocean.
6. Go around the earth again at this pace (one step every billion years). When you get all the way around the earth again, take another drop out of the ocean.
7. Repeat step #6 until the ocean is empty. (About 26 septillion laps)
8. Now, set a sheet of paper on the ground.
9. Repeat steps 1-8.
10. When you’ve repeated steps 1-9 enough times that you have a stack of paper reaching to the moon (about 3.3 trillion repetitions) then start back at #1 again.
Repeat steps 1-10 about 216,000* more times, and your timer will have reached a number equal to 8 x 10^67 seconds.
*216,485 to be exact
Yep. That’s a big number, and a completely useless fact unless, on a moment’s reflection, you realize that if you have
2 pairs of shoes
2 jackets
3 pairs of pants
7 shirts and
7 neckties or scarves
You can wear a different outfit every single day for over 1.6 years!
(2 x 2 x 3 x 7 x 7 = 588)
Numbers I used for this calculation:
Number of card combinations: 52!
Gallons in the ocean: 3.52670*10^20 (from NOAA)
Water drops in a U.S. gallon: 75,708.2 (From online conversion page)
Distance around Earth at equator: 24,902 miles. (From encyclopedia)
Number of days in a year: 365.25
Average distance to the moon: 238,855 miles. (From NASA)
Thickness of a ream of 20 lb. copy paper: 2.25 inches
Thickness of one sheet of copy paper: 2.25/500=0.0045 inches
Sounds a bit like my explanation of why it is impossible to use brute force to break the 256 bit AES encryption by trying every possible key to Apple's iPhone encryption. . . not when they use a 144 character key made up from a potential pool of 226 possible characters. . . trying 50,000 possible keys per second a super computer, testing to see if you got any sensible results, using a super computer, would only take 5.62195 YEARS to try them all.