Hi Markus,
Welcome back!
There are very few combinations where everyone can compete against each other the same number of times. For example 25 people in heats of 9 will work if you can do 25 heats (rows):
1 2 3 4 5 6 7 8 9
2 4 9 10 24 17 15 22 12
3 24 8 23 18 21 13 4 10
4 22 25 8 20 12 11 3 19
5 15 17 18 8 11 2 13 20
6 8 12 13 1 14 24 25 15
7 16 5 22 3 10 25 15 13
8 10 11 16 6 22 23 1 17
9 13 20 5 12 23 1 21 22
10 19 14 12 16 2 8 5 21
11 18 19 24 10 1 5 9 25
12 6 10 25 7 18 20 2 23
13 11 4 9 23 25 14 16 2
14 3 7 17 11 5 12 23 24
15 20 21 1 14 7 10 11 4
16 17 18 7 13 19 4 12 1
17 14 13 20 19 3 9 10 6
18 9 22 14 25 8 21 17 7
19 7 23 15 9 20 16 24 8
20 5 16 6 4 24 22 14 18
21 12 6 11 15 9 3 18 16
22 21 24 19 2 13 6 7 11
23 1 2 3 22 15 18 19 14
24 25 1 2 21 16 17 20 3
25 23 15 21 17 4 19 6 5
Above everyone has exactly 9 heats and sails together with every other competitor exactly 3 times.
This is one of only 11 possible scenarios within the parameters you have set and with 30 heats or less. The options are:
n k h
15 7 15
16 6 16
19 9 19
12 6 22
16 6 24
25 9 25
13 6 26
14 7 26
21 7 30
15 7 30
16 8 30
where n is the number of competitors, k the number in one heat, and h the total number of heats. I could supply the others if you wish, but note there are no options with n>25. Can you say what is the maximum number of heats?
Regards
Ian
