Need Help Generating a List of all Possible Tournament Rounds

I have what at first glance appears to be a trivial task, but I've found it to be a bear to figure out.

Given an arbitrary even number of participants between 2 and 32 (lets call that number "n"), generate a listing of all possible tournament rounds consisting of n/2 games. Each match should appear in an separate cell and each round should appear on a separate line.

For example, given 4 players, numbered 1 through 4, here is what it would generate:

(1,2), (3,4)
(1,3), (2,4)
(1,4), (2,3)

Here is a start to what it would look like for 6 players:

(1,2), (3,4), (5,6)
(1,2), (3,5), (4,6)
(1,2), (3,6), (4,5)
(1,3), (2,4), (5,6)
(1,3), (2,5), (4,6)
(1,3), (2,6), (4,5)
(1,4), [...]

Obviously, the higher the number of players, the more games in each round and the more rounds are possible.

I would like to figure out a way to do this without resorting to VBA if possible.

Advice is greatly appreciated!

Because my objective is to generate a listing of all possible rounds given a number of players, I expect to see pairings duplicated as a particular pairing could appear in more than one possible round.

Since there are only 3 possible combinations of matches with only 4 players, pairings don't have to repeat to get to all the possible rounds. This isn't true with 6 players.

Once I have a complete listing of all possible rounds, I intend to use another criteria to determine what rounds will actually be played. However, that process is outside of the scope of what I am asking here.

Not sure if you are still monitoring this, but one way of scheduling games (and avoiding duplicates) is to use a 2-d table. Suppose your teams are a b c d e and f, then list these on the top row (starting in the second column) and in the first column (starting in the second row). Now, you can imagine the teams in the first column have to play the teams in the top row, so the intersection of these rows and columns can be used to store the date of the game, or the resulting score etc. Obviously, team a cannot play themselves, so the leading diagonal is redundant. If your teams are not playing home and away, then one of the triangles is also redundant. Here is a possible schedule for the games, where the numbers represent the rounds:


a b c d e f
a * 1 2 3 4 5
b * 4 5 3 2
c * 1 5 3
d * 2 4
e * 1
f *

(hope the multiple spaces are retained - some forums remove them) and this translates into:

Round 1: ab cd ef
Round 2: ac de bf
Round 3: ad de cf
Round 4: ae bc df
Round 5: af bd ce

There are other solutions - if you swap the positions of all three of one round number with another you will get another schedule, although that is just like swapping the Round 3 matches above with those in Round 5 (for example).

Hope this helps.

Pete

EDIT: no, the multiple spaces were removed. Imagine the top row a b c d e f etc is moved across, and then each of the rows below is moved across so that the asterisk is located progressively underneath each of the teams. I tried to add a picture but wasn't allowed to.

Pete

Thanks for the response. I have played around with this method a bit, but I am not sure it gets me what I need. I really need to figure out how to systematically generate all possible rounds. perhaps I could cycle though the process you describe above?

I am a little confused about how you decided what numbers went on the third line of the diagram how did you pick 4,5,3,2? Was this random?

I know from manually writing them all out, that there are exactly 15 possible rounds with 6 players (see my example spreadsheet I attached above). Meaning that there are no other rounds possible. Every possible combination of match-ups can be found in these 15 rounds. No others are possible.

The problem is, I haven't been able to figure out any way to generate a listing of all possible rounds given an arbitrary even number. Heck, I haven't even been able to figure out a formula to figure out how many possible rounds there are given such a number. The only reason that I know 6 players result in only 15 possible rounds is that I wrote them all out.

Hi

Unless you absolutely need to to do this in Excel try http://www.fixturelist.com which is designed to do exactly what you are looking for. Alternatively try this Wikipedia link http://en.wikipedia.org/wiki/Round-r...nt#cite_note-1 which explains in detail how you can create your matchups.

regards

Jeff

How about just the rounds of a round-robin tournament?

http://www.box.com/s/z41sn0yrp5lo1cuozke3