The number of possible ways where, 3,
teams can play Soccer with each other, and each team had exactly, r,
Goals For
and exactly, r, Goals against, is given by the following POLYNOMIAL of degree,
1
r + 1
and in Maple input form:
r+1
-------------------------------
The number of possible ways where, 4,
teams can play Soccer with each other, and each team had exactly, r,
Goals For
and exactly, r, Goals against, is given by the following POLYNOMIAL of degree,
5
2
(2 r + 3) (r + 2) (r + 1) (r + 3 r + 5)
----------------------------------------
30
and in Maple input form:
1/30*(2*r+3)*(r+2)*(r+1)*(r^2+3*r+5)
-------------------------------
The number of possible ways where, 5,
teams can play Soccer with each other, and each team had exactly, r,
Goals For
and exactly, r, Goals against, is given by the following POLYNOMIAL of degree,
11
8 7 6 5 4
(r + 3) (r + 2) (r + 1) (43 r + 688 r + 4934 r + 20680 r + 55907 r
3 2
+ 101272 r + 123436 r + 96240 r + 40320)/241920
and in Maple input form:
1/241920*(r+3)*(r+2)*(r+1)*(43*r^8+688*r^7+4934*r^6+20680*r^5+55907*r^4+101272*
r^3+123436*r^2+96240*r+40320)
-------------------------------
The number of possible ways where, 6,
teams can play Soccer with each other, and each team had exactly, r,
Goals For
and exactly, r, Goals against, is given by the following POLYNOMIAL of degree,
19
14 13
(2 r + 5) (r + 4) (r + 3) (r + 2) (r + 1) (55156451 r + 1930475785 r
12 11 10
+ 31426751500 r + 315397914875 r + 2181374421522 r
9 8 7
+ 11011717259925 r + 41921602480600 r + 122633173357625 r
6 5 4
+ 278241144318203 r + 490506924963670 r + 667964358905100 r
3 2
+ 691864584471000 r + 528464246017824 r + 278397371589120 r
+ 84475764172800)/10137091700736000
and in Maple input form:
1/10137091700736000*(2*r+5)*(r+4)*(r+3)*(r+2)*(r+1)*(55156451*r^14+1930475785*r
^13+31426751500*r^12+315397914875*r^11+2181374421522*r^10+11011717259925*r^9+
41921602480600*r^8+122633173357625*r^7+278241144318203*r^6+490506924963670*r^5+
667964358905100*r^4+691864584471000*r^3+528464246017824*r^2+278397371589120*r+
84475764172800)
This took, 372.130, seconds.