Last night a friend of mine and I were having a debate over the armor combos in Halo 3. It ended with him saying there couldn't possibly be more than a couple hundred armor combos, and me saying he was blatantly wrong.
Me being the dude I am, decided to use the overpowering abilities of math to prove him wrong. So I did the math.
It was a simple permutation problem.
NOTE: I excluded colors for the sake of sanity, and the fact we were discussing armor, not color.
For every SPARTAN, there are 11 Head Pieces:
Mark VI
Mark V
ODST
Rogue
Security
Recon
CQC
EVA
EOD
Hayabusa
Scout
8 Shoulder pieces, x2 shoulders:
Mark VI
Security
Recon
CQC
EVA
EOD
Hayabusa
Scout
And 8 chest pieces:
Mark VI
CQC
Recon
EVA
EOD
Hayabusa
Katana
Scout
So it becomes 11x8x8x8= 5,632 different SPARTANS. For Elites, itsthe much simpler 5x5x5x5 (Assualt, Combat, Flight, Asetic, Commando) = 625. 5,632+625= 6,257.
So there are 6,257 different player combinations, thus proving him wrong. But the I decided to carry it into the land of excess. I asked the question: "How many armor combos can there be in an MM game?" So I took the basic amounts of players total n each list, and come up with games of 4, 6, 8, 10, 12 and 16 players.
So how many combos is that? Each one can be repersented by 6,257^X, where is the number of players. So it came to this:
4 Player Games:
1.532726337e15, or 1,532,726,337,000,000
6 Player Games:
6.000631119e22, or 60,006,311,190,000,000,000,000
8 Player Games:
2.349250023e30, or 2,349,250,023,000,000,000,000,000,000,000
10 Player Games:
9.19732532e37, or 9,197,325,532,000,000,000,000,000,000,000,000,000
12 Player Games:
3.600757382e45, or 3,600,757,382,000,000,000,000,000,000,000,000,000,000,000,000
16 Player Games:
5.518975672e60, or 5,518,975,672,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000
Thats possible combinations every game people, with each combination representing 1 unique game.
But I decided to take it one step further. What if you wanted to play 1 sinlge player game with every possible combination? How long would that take you?
Assuming 1 game every second, thats 60 games a second, 3,600 ames an hour, 86,400 games a day. Playing every day, non-stop, it would take you 63,877,033,240,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000 days to do it.
That translates into 17,500,557,050,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000 years to do it.
Math is awesome. And long.
But it begs the question....with so many different possible combinations, why is it we see like 25 or so repeated over and over and over and over?
Me being the dude I am, decided to use the overpowering abilities of math to prove him wrong. So I did the math.
It was a simple permutation problem.
NOTE: I excluded colors for the sake of sanity, and the fact we were discussing armor, not color.
For every SPARTAN, there are 11 Head Pieces:
Mark VI
Mark V
ODST
Rogue
Security
Recon
CQC
EVA
EOD
Hayabusa
Scout
8 Shoulder pieces, x2 shoulders:
Mark VI
Security
Recon
CQC
EVA
EOD
Hayabusa
Scout
And 8 chest pieces:
Mark VI
CQC
Recon
EVA
EOD
Hayabusa
Katana
Scout
So it becomes 11x8x8x8= 5,632 different SPARTANS. For Elites, itsthe much simpler 5x5x5x5 (Assualt, Combat, Flight, Asetic, Commando) = 625. 5,632+625= 6,257.
So there are 6,257 different player combinations, thus proving him wrong. But the I decided to carry it into the land of excess. I asked the question: "How many armor combos can there be in an MM game?" So I took the basic amounts of players total n each list, and come up with games of 4, 6, 8, 10, 12 and 16 players.
So how many combos is that? Each one can be repersented by 6,257^X, where is the number of players. So it came to this:
4 Player Games:
1.532726337e15, or 1,532,726,337,000,000
6 Player Games:
6.000631119e22, or 60,006,311,190,000,000,000,000
8 Player Games:
2.349250023e30, or 2,349,250,023,000,000,000,000,000,000,000
10 Player Games:
9.19732532e37, or 9,197,325,532,000,000,000,000,000,000,000,000,000
12 Player Games:
3.600757382e45, or 3,600,757,382,000,000,000,000,000,000,000,000,000,000,000,000
16 Player Games:
5.518975672e60, or 5,518,975,672,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000
Thats possible combinations every game people, with each combination representing 1 unique game.
But I decided to take it one step further. What if you wanted to play 1 sinlge player game with every possible combination? How long would that take you?
Assuming 1 game every second, thats 60 games a second, 3,600 ames an hour, 86,400 games a day. Playing every day, non-stop, it would take you 63,877,033,240,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000 days to do it.
That translates into 17,500,557,050,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000 years to do it.
Math is awesome. And long.
But it begs the question....with so many different possible combinations, why is it we see like 25 or so repeated over and over and over and over?
