Problem of combinatorics

Hello everybody!

I am wracking my brains about a problem of combinatorics, but I haven't
found a solution yet. The problem is the following:

There is a sports team of 21 people. Each day, these 21 people are competing
against each other in 7 groups, with 3 people in each group. For example,
the first day looks like this:

1/2/3 - 4/5/6 - 7/8/9 - 10/11/12 - 13/14/15 - 16/17/18 - 19/20/21

The second day might look like this:

1/2/15 - 3/4/20 - 5/6/19 - 7/8/18 - 9/10/17 - 11/12/16 - 13/14/21

Now there is a condition that each person may be in a group with any other
person no more than twice. In the examples above, person 1 and 2 have
already been in a group together, so they may not appear in the same group
again.

I am trying to figure out all possible combinations, so that I got a list
that shows the group combinations for each day. Who knows the solution?

--
Matthias Hofmann
Anvil-Soft, CEO
http://www.anvil-soft.com - The Creators of Toilet Tycoon
http://www.anvil-soft.de - Die Macher des Klomanagers


.

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