20 racers, heats of 10...

[skyywalker]

Hi,

I am looking for a solution for this scenario:

In a racing competition I have 20 competitors, and I have 2 starts of 10 racers each. So Round 1 could look like
Start 1: racers 1-10
Start 2: racers 11-20

Is there a schedule that mixes the racers so that in the end everyone is racing against everyone ?

An alternative solution could be that for example seed 1 and 2 never meet etc, so we could have 10 groups that then all play each other ?

Group 1: 1-2
Group 2: 3-4
etc

But ideally everyone races everyone (if thats not too many rounds...)

Thanks for any help available !

Cheers,
Markus

[Ian Wakeling]

Hi Markus,

In general there will not be useful solutions for your scenario.  With n=20 and 2 starts per round, you would need 19 rounds to get a balanced solution - at which point the competitors would have raced against each other 9 times.   If you want a shorter schedule it would start to get messy,  for example in 6 rounds you might be able to have everyone against each other at least once, but some pairs would have raced 5 times.

My feeling is that the seeds idea will makes things even harder, but I have nothing that could generate such a schedule to test my theory out.

Essentially the problem is that you want half the competitors in each race.  If this fraction were smaller then there are options.   Say 16 competitors with 4 starts of 4 per round.

Best,

Ian.

[skyywalker]

Hi Ian,

19 rounds is actually fine - races are very short so that is manageable.

Could you give me an idea of that schedule ?

Cheers,
Markus

[Ian Wakeling]

Hi Markus,

There is an example schedule attached as an Excel file.

Best,

Ian