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 Question from Dee: I have 5 players who are playing in a 4-player partnership game & want to rotate the 5th person in in such a way that each person is each other person's partner for a game. How can such a rotation be done?

Hi Dee,

I have names your players 1, 2, 3, 4 and 5 and placed them at the vertices of a regular pentagon. A line joining two vertices of the pentagon represents an instance when the two players at these vertices form a team.

For the first round of play have person 1 sit out, 2 and 3 form a team and 4 and 5 form a team.

For the next round of play rotate the pentagon one fifth of a revolution counterclockwise, leaving the players unmoved. For this round player 2 sits out and players 3 and 4 form a team and players 5 and 1 form teams.

For the third round of play rotate the pentagon again one fifth of a revolution counterclockwise, leaving the players unmoved. For this round player 3 sits out and players 2 and 5 form a team and players 1 and 2 form teams.

Repeat this process until it is time for player 1 to sit out again. This time, round 6, have players 3 and 4 and players 5 and 2 form teams.

Rotate again to have player 2 sit out and players 4 and 5 and players 1 and 3 form teams. Continue rotating until player 1 is to sit out again. This will be round 11 and in this case have player 1 sit out and players 2 and 4 and players 5 and 3 form teams.

Continue to rotate the pentagon until you have completed 15 rounds of play. In these 15 rounds each player has sat out 3 times and each pair of players has formed a team 3 times.

Penny

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