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I hope somebody can help. I am organising an event where 25 people will be seated at five tables of five people.

Each person will spend five minutes talking about their subject, meaning a table session will last 25 minutes. After each session I need to rotate the individuals in 'speed dating' style, so they meet a new set of people at the next session. Throughout the day, everyone should meet everyone else but no two people should meet twice.

Therefore, six of these sessions should ensure that everyone has met, but nobody met twice.

Does anybody have a template or solution for this? Any help greatly appreciated. Thanks.

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    Key search term: social golfer problem. – 2017-02-14
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    Hi - thanks, I have read a few articles on the social golfer problem where the principle is the same as the situation I described. But I can't find a solution specific to my 5x5 problem anywhere. – 2017-02-14
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    See also http://math.stackexchange.com/questions/69325/social-golfer-problem-quintets – 2017-02-14

2 Answers 2

1

Based on Warwick Harvey's tables on the Web Archive wayback machine, 

{A, B, C, D, E}, {F, G, H, I, J}, {K, L, M, N, O}, {P, Q, R, S, T}, {U, V, W, X, Y}

{A, F, K, P, U}, {B, G, L, Q, V}, {C, H, M, R, W}, {D, I, N, S, X}, {E, J, O, T, Y}

{A, G, M, S, Y}, {B, H, N, T, U}, {C, I, O, P, V}, {D, J, K, Q, W}, {E, F, L, R, X}

{A, H, O, Q, X}, {B, I, K, R, Y}, {C, J, L, S, U}, {D, F, M, T, V}, {E, G, N, P, W}

{A, I, L, T, W}, {B, J, M, P, X}, {C, F, N, Q, Y}, {D, G, O, R, U}, {E, H, K, S, V}

{A, J, N, R, V}, {B, F, O, S, W}, {C, G, K, T, X}, {D, H, L, P, Y}, {E, I, M, Q, U}

is one possibility

0

\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline 1 & 2 & 3 & 4 & 5 & 1 & 2 & 3 & 4 & 5 \\ \hline 6 & 7 & 8 & 9 & 10 & 6 & 7 & 8 & 9 & 10 \\ \hline 11 & 12 & 13 & 14 & 15 & 11 & 12 & 13 & 14 & 15 \\ \hline 16 & 17 & 18 & 19 & 20 & 16 & 17 & 18 & 19 & 20 \\ \hline 21 & 22 & 23 & 24 & 25 & 21 & 22 & 23 & 24 & 25 \\ \hline 1 & 2 & 3 & 4 & 5 & 1 & 2 & 3 & 4 & 5 \\ \hline 6 & 7 & 8 & 9 & 10 & 6 & 7 & 8 & 9 & 10 \\ \hline 11 & 12 & 13 & 14 & 15 & 11 & 12 & 13 & 14 & 15 \\ \hline 16 & 17 & 18 & 19 & 20 & 16 & 17 & 18 & 19 & 20 \\ \hline 21 & 22 & 23 & 24 & 25 & 21 & 22 & 23 & 24 & 25 \\ \hline \end{array}

First round (right one):

$(1,2,3,4,5), (6,7,8,9,10), \ldots$

Second round (down one):

$(1,6,11,16,21), (2,7,12,17,22), \ldots$

Third round (down one plus right one):

$(1,7,13,19,25), (2,8,14,20,21), \ldots$

Fourth round (left one plus down one):

$(1,10,14,18,22), (2,6,15,19,23), \ldots$

Fifth round (right two plus down one):

$(1,8,15,17,24), (2,9,11,18,25), \ldots$

Sixth round (right one plus down two):

$(1,12,23,9,20), (2,13,24,10,16), \ldots$