Hidddy_ wrote:Sum from 1 to 14 is easiest that's a nice equation you found there, how'd you see that?
If you pick a civ A, it will have 14 different match ups. Then pick another one B, it will have only 13 different match ups left, because one was already counted (A vs B). And so on, until you reach 0, so the sum is 14 + 13 + ... + 1. And the sum from 1 to n is equal to n(n+1)/2 (can be easily proven by induction reasoning or w/e it's called in english), so in this case 14*15/2 = 105, or 13*14/2 = 91 if you don't count the mirrors.
LoOk_tOm wrote:I have something in particular against Kaisar (GERMANY NOOB mercenary LAMME FOREVER) And the other people (noobs) like suck kaiser ... just this ..
Hidddy_ wrote:Sum from 1 to 14 is easiest that's a nice equation you found there, how'd you see that?
If you pick a civ A, it will have 14 different match ups. Then pick another one B, it will have only 13 different match ups left, because one was already counted (A vs B). And so on, until you reach 0, so the sum is 14 + 13 + ... + 1. And the sum from 1 to n is equal to n(n+1)/2 (can be easily proven by induction reasoning or w/e it's called in english), so in this case 14*15/2 = 105, or 13*14/2 = 91 if you don't count the mirrors.
Hidddy_ wrote:Sum from 1 to 14 is easiest that's a nice equation you found there, how'd you see that?
If you pick a civ A, it will have 14 different match ups. Then pick another one B, it will have only 13 different match ups left, because one was already counted (A vs B). And so on, until you reach 0, so the sum is 14 + 13 + ... + 1. And the sum from 1 to n is equal to n(n+1)/2 (can be easily proven by induction reasoning or w/e it's called in english), so in this case 14*15/2 = 105, or 13*14/2 = 91 if you don't count the mirrors.
Yeah this is the correct version of my post lol.
You guys did it 2 different ways but both are good yea
Hidddy_ wrote:Sum from 1 to 14 is easiest that's a nice equation you found there, how'd you see that?
If you pick a civ A, it will have 14 different match ups. Then pick another one B, it will have only 13 different match ups left, because one was already counted (A vs B). And so on, until you reach 0, so the sum is 14 + 13 + ... + 1. And the sum from 1 to n is equal to n(n+1)/2 (can be easily proven by induction reasoning or w/e it's called in english), so in this case 14*15/2 = 105, or 13*14/2 = 91 if you don't count the mirrors.
Thanks for the explanation and all, and yes the term you're looking for is induction. But I was referring to h2o's equation 91*2 + 14 = 14* 14 = 196?
Hidddy_ wrote:Sum from 1 to 14 is easiest that's a nice equation you found there, how'd you see that?
If you pick a civ A, it will have 14 different match ups. Then pick another one B, it will have only 13 different match ups left, because one was already counted (A vs B). And so on, until you reach 0, so the sum is 14 + 13 + ... + 1. And the sum from 1 to n is equal to n(n+1)/2 (can be easily proven by induction reasoning or w/e it's called in english), so in this case 14*15/2 = 105, or 13*14/2 = 91 if you don't count the mirrors.
Thanks for the explanation and all, and yes the term you're looking for is induction. But I was referring to h2o's equation 91*2 + 14 = 14* 14 = 196?
< ,> mean less than/greater than or equal to here
Assign each civ a number between 1 and 14. 14x14 is the number of ordered pairs (x, y) you can have with 1 < x, y < 14. But each matchup that is not a mirror is represented at two ordered pairs, (x, y) and (y, x). To calculate the total number of matchups subtract 14 from 196, and divide the result by 2 to get 91, because each matchup is represented twice. Now add back the 14 mirrors and you get 105. The equation we did is (196-14)/2 = 91, and if you rearrange this you get h2o's equation.
I think the question about rarest matchups would've been more interesting before EP. Since RE is more unbalanced some matchups were so broken that they would almost never be played.
Hidddy_ wrote:Thanks for the explanation and all, and yes the term you're looking for is induction. But I was referring to h2o's equation 91*2 + 14 = 14* 14 = 196?
Ah ok. Well then, he just took the amount of non-mirror match ups (that we calculated to be 91), multiplied it by 2 because there's 2 sides for those match ups, and then added the amount of mirror match ups (14). So it's 91*2 + 14 = 196. But that's also equal to 14*14, because that's the amount of pairs you can do with integers from 1 to 14.
LoOk_tOm wrote:I have something in particular against Kaisar (GERMANY NOOB mercenary LAMME FOREVER) And the other people (noobs) like suck kaiser ... just this ..