Maths isn't my strong point. I could probably work this out with enough time to think about it, but I know there are folk clever enough on here to sort this out in their head in under a minute.

My 6-a-side football team has 8 regular players. Normally, at least one guy has something better to do so we have 1 substitute. Subs are roll-on/roll-off whenever you like and with 1 sub it's easy to work out fair timings so that everyone gets an equal amount of game time.

However, tonight everyone is available so we have 2 subs.

The goalie doesn't get subbed so I have 7 outfield players who all need equal game time. Only 5 can be on the pitch at the same time.

The game is 36 minutes long (2 halves of 18).

How can I arrange the substitutions so that its equal?

You don't. You put the strongest side out ..... and sub as players tire..

Sub every 4.5 minutes
1.) jim bob julie ann john jane
2.) ted millicent jim bob julie ann
3.) john jane ted millicent jim bob
4.) julie ann john jane ted millicent
5.) jim bob julie ann john jane
6.) ted millicent jim bob julie ann
7.) john jane ted millicent jim bob
8.) julie ann john jane ted millicent

cheated ... http://www.playingtimecalculator.com/

If you can field five of seven players, each needs to be out there for five sevenths of the time. That's 5 sevenths of 18 minutes (twice)... one seventh of 18 mins is 2.57 minutes, so pop one bod off and one on every 2.57 minutes and it will all work out fine.

Richard, I think you assumed there were 8 people on the team, but only seven of them count.

You might have cheated but how the hell did you know their names

That sounds the best idea

more haste less speed me thinks lol - nice explanation

much easier using the link

But I'd never get a game!

To be fair it's a bunch of mid thirties blokes having a bit of a kick about. We don't take it very seriously and hence like to make sure everyone gets a fair crack at kicking the youngsters we play against scoring a 30 yarder panting and cursing as we get nutmegged yet again.


Neil; thanks for the explanation.

That's one shit team right there

Oi oi :-P