I'm running a volleyball club at school and we currently have 5 active members. Is there a way of having everybody play in a duo with everybody else and have one person sit out each game practising? I posted this here because this is more a maths problem than a volleyball one.

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    $\begingroup$ Welcome to Puzzling.SE, @JamesMann ! Any relation to Leslie? ;) $\endgroup$ – Chowzen Sep 22 '18 at 13:13

The answer is:

Sure, of course.

Have a look at the following diagram:


If you:

Let each dot be a player. Then rotate that diagram 5 times: the lone circled person will be each person exactly once, each pair of adjacent people will be the green (upper) pair exactly once, and each pair of non-adjacent people will be the red (lower) pair exactly once.

Here is one possible roster:

2-5 vs 3-4 (1 alone)
3-1 vs 4-5 (2 alone)
4-2 vs 5-1 (3 alone)
5-3 vs 1-2 (4 alone)
1-4 vs 2-3 (5 alone)


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