Hi, As you may be aware the Louis Vitton Cup is taking place in Hauraki Bay, New-Zealand. Nine challengers take part. The winner of the LV Cup will face the New Zealand holder of the America's Cup at the beginning of 2003. Each team races each other once. One point per win. Thus the preliminary stage totalize 72 races (9*8/2), hence 36 points to be shared by 9 boats. I would like to determine how many scenarii are likely to happen. I have tried to answer this problem by considering 3 boats only (3 races: A vs B, A vs C, B vs C), then 4 boats (6 races: A vs B, C and D, B vs C,D and finally C vs D) and so on for 5 and 6 boats (cf. below). Unfortunately I have not understood the logic behind my first findings.
I will appreciate if you see a "probalistic" way to solve the problem or a solution that does not involve the enumeration of all the solutions. Tanguy Arzel Considering 3 boats (A,B,C) yields 2 scenarii to share 3 points at stake: boat identity. A B C points........ 2 1 0 .............. 1 1 1 Considering 4 boats yields 4 scenarii to share 6 points at stake: A B C D 3 2 1 0 3 1 1 1 2 2 2 0 2 2 1 1 Considering 5 boats yields 7 scenarii to share 10 points at stake: A B C D E 4 3 2 1 0 4 3 1 1 1 4 2 2 2 0 4 2 2 1 1 3 3 2 1 1 3 2 2 2 1 2 2 2 2 2 Considering 6 boats yields 18 scenarii to share 15 points at stake: A B C D E F 5 4 3 2 1 0 5 4 3 1 1 1 5 4 2 2 2 0 5 4 2 2 1 1 5 3 3 2 1 1 5 3 2 2 2 1 5 2 2 2 2 2 4 4 4 2 1 0 4 4 4 1 1 1 4 4 3 2 1 1 4 4 2 2 2 1 4 3 3 3 2 0 4 3 3 3 1 1 4 3 3 2 2 1 4 3 2 2 2 2 3 3 3 3 3 0 3 3 3 3 2 1 3 3 3 2 2 2 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
