Found this on another message board... stumped me but good.
Thought I would post it and let everyone else pull some hair out :grin:

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Hi all,

I've also got a combinatory riddle. :-) It is related to Germany's
"national card game".

There is a skat competition, with 3 or 4 players sitting at each table.
After each round, the players have to change their places in a way, so
that any player sits at a table together only with people, with whom
s/he had not previously played.
(I hope this is understandable.)

Following these rules, what are the maximum numbers of rounds, that say
12,13,14,15 or 16 players can play, and in what combinations do they
have to sit at the tables in all those rounds,
a) when there are as many tables as possible with 3 players ?
b) when there are as many tables as possible with 4 players ?

Example: 12 players
-------------------
a) t1 t2 t3 t4
round #1: {"ABC","DEF","GHI","JKL"}
round #2: {"ADG","BEJ","CHK","FIL"}
round #3: {"AEH","BDL","CIJ","FGK"}
round #4: Not possible. Is this true?

b) t1 t2 t3
round #1: {"ABCD", "EFGH", "IJKL"}
No more rounds possible!

Does anyone know a general algorithm to solve this puzzle?
Posted on 2004-06-21 22:48:03 by Graebel