World Cup combinatorics again

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] At the end of yesterday’s post about the combinatorics of the World Cup group stage, I said “this is good enough for me.” Turns out that was a lie. Today I rewrote some of the code to come up with a slightly more detailed result. The last bit of work in that post was to generate the 40 unique point totals that can come from a group. These are the possible totals, with no regard for which team gets which total: 9 6 3 0 7 6 3 1 7 3 2 2 5 5 3 2 9 6 1 1 7 6 2 1 6 6 6 0 5 5 3 1 9 4 4 0 7 5 4 0 6 6 4 1 5 5 2 2 9 4 3 1 7 5 3 1 6 6 3 3 5 4 4 3 9 4 2 1 7 5 2 1 6 5 4 1 5 4 4 2 9 3 3 3 7 4 4 1 6 5 2 2 5 4 3 2 9 2 2 2 7 4 3 3 6 4 4 3 5 3 3 2 7 7 3 0 7 4 3 2 6 4 4 2 4 4 4 4 7 7 1 1 7 4 3 1 5 5 5 0 4 4 4 3 7 6 4 0 7 4 2 2 5 5 4 1 3 3 3 3 As discussed early in yesterday’s post, there are 36=729 ways the six games of a group can turn out, so today’s script…