Hi all,

I would like if someone could provide a very brief independent mathematical proof of something. I know it to be true, but others won't accept it, even with my proof.

Imagine a sports league. League A has 12 teams and League B has 16 teams. Each year, the top four teams from each league get promoted to a higher league, League X (so that's eight teams in total).

Now let's imagine that the two leagues merge. We now have a League C, which has two levels, I and II. You get promoted from League C II to League C I, and from League C I to League X. I've tried to describe this pictorially at the end.

Four teams from League C I get promoted to League X, and none from League C II get promoted to League X (they go up to League C I instead).

Problem - show that there is less chance of getting promoted under this new format (probability seems the easiest way of doing this).

Code:Old formatLeague X| | -------------------------- | | 4 teams 4 teams | |League ALeague BNew format

League X

l

4 teams

l

League C I

l

4 teams

l

League C II

Ultimately, the proof required is that 4 does not equal 8; I'm aware of that and apologise for wasting your collective times here! However, there is someone in cyberland who is making the following argument (and I paraphrase) -

(Side note - I suggested to him being in a group of 12 people, four of whom were to be shot. A second group of 16 people came along, of whom also four were to be shot. If they merged, four of the merged group would be shot. Would you merge? QED I thought. Nope. We're dealing with some serious ignorance here. Any help appreciated!)You're just not getting this.

I'm not talking about thenumber of promotions across the two leagues, for one very simple reason - no club can qualify for more than one space.total

As the league currently stands, Team A can strive for only one of the League A's 4 promotion slots. The fact there are also currently 4 promotion slots in the League B is irrelevant, as Team A can only strive for one of League A's four.

Under the new format - Guess what ? Team A could still only strive for one promotion slot from the combined league's four. Competiton for those slots may possibly be stiffer.

In summary :

Under the old format: 4 promotion slots available to each individual team

Under the new format: 4 promotion slots available to each individual team.

Iin an abstract '4+4=8' fashion, slots have been lost. But in terms of thethey haven't been. You can't lose out on something you never had/weren't entitled to in the first place, and no team in League A has ever been entitled to more than one promotion slot from a sum total of four.actual impact on each individual club