10 competitors, 5 against each other per game, round robin

[skyywalker]

Hi,

I have 10 competitors and I want 5 of them compete against each other at a time. I need a round robin where everyone competes against everyone in the end.

First flight would be:
Race 1: 1 2 3 4 5
Race 2: 6 7 8 9 10

etc.

Is there something simple for that ?

Cheers,
Markus

[Ian Wakeling]

Hi Markus,

Unfortunately there is no good solution to this problem.  I believe you need 5 flights before you can make sure that everyone competes against everyone else at least once.  For example:

 5  4  8  7  2
10  1  3  6  9

 6  4  1  2  8
 9  5  3  7 10

 3  4  7  8  9
 6 10  1  5  2

 1 10  9  4  8
 6  3  2  7  5

 6  4  2  9  3
 5 10  8  1  7

However some pairs of competitors meet 4 times, these are (1 10), (2 6), (3 9), (4 8) & (5 7), while other pairs meet only once, such as (1 3).  It is possible to have a balanced schedule, but you would need 18 flights, with all pairs of competitors sailing against each other exactly 8 times each, but I imagine this is far too big.

Regards,  Ian