The twelve signs of the horoscope (AQUARIUS, ARIES, and so on) run a race along the Zodiac. In how many different ways can the race end, if ties are possible?

(In reply to re: Smaller Zodiacs by tomarken)

Yes, that is what I got.

f(n) = # of ways race can go for n racers =

  sum from i = 1 to n of (n choose i) * f(n-i)

i.e. for each number of racers than could have tied for first the number of ways to choose that many racers times the ways to resolve the rest.

Then, f(0) = 1 (one way to resolve a race with no one in it)

creating a spreadsheet in excel I got f(12)=28091567595

1
1
3
13
75
541
4683
47293
545835
7087261
102247563
1622632573
28091567595
 

Posted by Joel on 2006-11-28 16:03:33