IBM Ponder This #163 · November 2011

This month's puzzle spawned from a true story: Danny Arnon's solution for David Meiri's volleyball practice. Thank you both for the story.

Consider 9 teams playing volleyball on three courts simultaneously.

In each round, there are three teams on each court: two are playing against each other, while the third team is refereeing.

If the teams are numbered 1-9, you can represent the first round in the following manner:

1 2 (3)   4 5 (6)   7 8 (9)

On the first court, Team 1 plays against Team 2 while Team 3 referees; on the second court, Team 6 referees the play between Team 4 and Team 5, etc.

Here are the requirements for scheduling play:

(a) We need a 12-round schedule in which each team plays all eight other teams exactly once, and referees four times.
(b) After a team serves as referee, they should have at least two consecutive rounds of play before they have to referee again.

Can you make an ideal schedule that satisfies all our requirements?

If not, find a schedule that fulfils condition (a) and minimizes the number of times condition (b) is violated.

Please send your solutions as 12 lines of 9 digits each.

Solution

Best opened after a real attempt

To be added.