How many possible ways can the 2010 World Cup tournament unfold?

If you are filling out a bracket for the 2010 World Cup , here are the number of ways a bracket can go:

8 groups of 4 teams each. Top 2 move on, and the order is important. So that is 4 teams choose 2 teams or 6 ways to pick the two teams. Then, those 6 pairs of teams can be ordered 2 diff. ways, so 12 possibilities per group. There are 8 groups, so 12^8 possible ways to pick the top 2 teams in order from the 8 groups. Then, these 16 teams play a single elim tourney which is 15 games, so 2^15 possible ways that can go.

This gives 12^8 * 2^15 which is 14089640214528 (14 trillion or 1.4 x 10^13) ways for the tournament to go. Which of these ways do you hope or expect it to go? :)

(Btw, for comparison purposes, the NCAA basketball tournament with 64 teams has 2^63 or 9223372036854775808  (9 quintillion or 9.22 x 10^18 ) possibilities. )

Now, given the way the knockout stage works, you could have symmetries with respect to which teams play which. We don’t have to worry about those if we define our problem to also take into consideration the days and stadiums in which the teams play.

Good luck to all 32 teams!

Wretched Hives of Scum and Villainy, part VI

For Part V of Wretched Hives of Scum and Villainy, click here.

One of the casinos that I play at in the Reno area has a tropical rainforest theme. Now, I’m used to seeing all sorts of garish decor around casinos, but this one is pretty bad even by casino standards.

They have a “Storm Bar” or something which is supposed to remind people of rainforest storms. Every half hour or so, thunder plays over the loudspeakers, the lights around the bar flash, and water comes pouring down into a large(maybe 10′ by 20′), flat rectangular pool a few inches deep. Unfortunately, the water nozzles are all off of a single long pipe running the length of the pool, suspended seven feet above. This makes the entire array look like a giant stadium-style urinal, which I’m sure is the kind of image that encourage people to order expensive fruity drinks.

Far more annoying, however, is the presence of a supposed “bird of paradise” that zooms around the casino regularly. This mechanical contraption(which looks more like a badly painted flying chicken) is suspended from a rail track on the ceiling and emits ear-piercing squawks. The bird also drops chips and cash every so often, giving the impression that the bird is shitting money. I put in play only because it has a pretty good comps and cashback deal, but after a couple hours of listening to that infernal machine, I wanted to ask the casino staff whether I could spend some comps for the use of a 12-gauge shotgun and a box of shells. Blowing that thing out of the sky would’ve been as good as hitting four of a kind.