If I was smart enough, I'd be able to say how many different stat builds there are. It is too hard for me to try to figure out since 6 volleyball players and 6 lab geeks = 12 foreign exchange students and there's too much overlap and over counting. Blockey you didn't take into account that you can have geeks and volleyball players at the same time or the fact that you could have all 3 at the same time. I computed the amount of ways to arrange crew where order doesn't matter. I got 561.
I basically put the three types of crew side by side, for example, take the left most number to be the amount of volleyball captains you can have, the middle to be the foreign exchange student, and the right to be a lab geek. You can have 0-32 of each but each must all 3 add to 32. 32 0 0 31 1 0 31 0 1 30 2 0 30 0 2 30 1 1 29 3 0 29 0 3 29 2 1 29 1 2 ........ ........ ........ Notice the pattern. With 32 volleyball players there are 1 possible ways to have your crew, with 31 of them, there's 2 possible ways to arrange, with 30, there's 3 ways to arrange them. So you can see there is one more arrangement for each volleyball player you take away. Therefore the total number of arrangements is 1 2 3 4 5 6 ... 33 which equals 561. The reason why it stops at 33 and not 32 is because you can put 0-32 volleyball players which is 33 different arrangements. (1-32 would be 32 arrangements) I am not saying that I am right. But this is what I did and it is my guess for the amount of ways to arrange your crew where order doesn't matter. Again, I have no clue for the amount of different stat builds that can be made but it would most certainly be a number lower than this since it would be basically this number and then subtracting how many you over counted.
If that is what you meant then I dunno if you are right or wrong as I do not know the answer to that.
I stated specifically that you could have 1lab geek and one volleyball or two exchange but they're equal. Gonzo said the whole point of the thread was about the t5 builds, and I doubt he cares about who he has in dorms 15 19 and 31. So I interpreted that he was looking for how many different stat builds there are for a t5bc.
Yes exactly, I was saying that by doing your number of 561 you're over counting the kcs results. I think it's correct for what you're saying though, number of ways to organize crew where order doesn't matter. But 16 volleyball and 16 geeks= 32 exchange, so that was my point. What you did for number of ways to arrange where order doesn't matter isn't the same as how many different kcs results there are.
I think the appropriate way to do this is what blockey did which is by starting off with the most strength skewed and becoming slightly less strength skewed each time. So get the most strength skewed build then the second most then the third most etc. I think what you did blockey was almost right. For example. Take 32 muscles and then slowly replace with exchange student to (supposedly) get the next biggest strength skewed set up. Now, lets say that you stop when you get 30 muscles and 2 foreign exchange student which would be your 3rd iteration. The question to ask is, is this the 3rd highest strength set up? If the answer is yes, then your logic is perfect. Compare this with 31 muscles and 1 lab geek. This has higher strength than 30 muscles and 2 exchange students. This means there are more than 65 stat set ups and there's more work to be done
The key is to manually try everything out with low amounts of dorms and see if you can find the pattern with over counting (for the occasions where you get the same stats with different arrangements, example: 2 exchange students = 1 volleyball player and 1 lab geek) and then you can make a general formula where you can plug in any number which would work for high numbers. I went back to my method of total arrangements when order doesn't matter. I made a table in this order, number of dorms, number of arrangements, number of over counting 1 3 0 2 6 1 3 10 3 4 15 5 5 21 7 6 28 11 I know the pattern for number of arrangements but not for amount of over counting so I give up