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### #1 bmx

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Posted 30 June 2012 - 05:25 PM

9 ping pong players will participate in a tournament. There are only 3 tables where 3 games can be played simultaneously. Two players will be playing in each game, while a third will be acting as the arbitrator. For example, the first round would be 12 3 45 6 78 9 with 3, 6 and 9 being the arbitrators and 12 45 78 playing against each other.
There are two rules for the tournament:
1. It must be completed in 12 rounds of 3 simultaneous games, where each player will play against each of the other 8 only once, and will be arbitrating exactly 4 games.
2. After each player arbitrates one game, he must play at least 2 times against another athlete before being allowed to arbitrate again.
You will realize that it is impossible to have all two conditions met together. Can you write a schedule that would meet the first condition and would break the second condition for a minimum number of times? The answer must be 12 rows of 9 digits each, where the 3rd, 6th and 9th digit of each row will be the arbitrator, while all the others will be the players playing against each other, e.g. 12 3 45 6 78 9 for the first round (1 is playing against 2 and 3 arbitrates, 4 against 5 etc).

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### #2 MikeD

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Posted 30 June 2012 - 08:42 PM

Spoiler for a first try

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### #3 bonanova

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Posted 01 July 2012 - 02:58 AM

Spoiler for a first try

I'm thinking it would be hard to improve on that. Nice.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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