Four bowling teams (named A, B, C, and D) will be participating in a round robin (every team plays every other team once, no team is eliminated) playoff. A playoff is called a roll-off in bowling. Each team will play three games. For each game, two teams will bowl each other on lanes 3 and 4, while the other two teams bowl each other on lanes 5 and 6. One of the organizers draws up a complete schedule, showing which teams play which teams, and who bowls on which alley:
The coach of one team then complains that one of the teams (team A) will get to bowl on the same pair of lanes all three games. In general, repeatedly bowling on the same pair of lanes should be an advantage. Using only the two pairs of lanes mentioned, can you suggest a schedule which will have no team bowling on the same pair of lanes for all three games?
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