Games day at home

[Andrew Gibbs]

Hi all, I’m organising a games day at home that has five activities and five teams. The tricky thing is three of the activities are team versus team and the other two activities are individual team challenges. The team versus team activities are darts, foosball, and beer pong. The two individual activities are on my arcade machine which are Pacman and Galaga (highest team score comes first, lowest team score comes last). Each time only uses the arcade machine twice, once for each of the games.

How do I create a schedule that has each team playing every other team once in the three team versus team activities and still maximising use of the arcade machine when the spare team has a bye whenever the other four teams are playing each other in the team activities?

I want to avoid teams sitting out waiting but given there are five activities but only four different areas of play (the arcade machine has two activities) I don’t think I can avoid having teams sitting around waiting?

Any advice on creating a round robin schedule that maximises play time while minimising wait time would be fantastic.

Thanks for any guidance, Andrew.

[Ian Wakeling]

Hi Andrew,

There must be a lot of waiting around.  Each team participates in 6 rounds, 4 rounds playing each of the others teams, and 2 rounds at the arcarde machine.   However there must at least 10 rounds to allow everyone 2 chances at the arcade machine.  The best solution would be to play only one of the arcade games, then it is possible to have a solution where at least 3 teams participate in every round.

 G1    G2    G3   arcade
(B E) (---) (C D)  -
(---) (A D) (---)  B
(D E) (A B) (---)  C
(---) (B C) (A E)  D
(A C) (---) (B D)  E
(---) (C E) (---)  A

So above, A has a bye in round 1, C&E have a bye in round 2, and B&D have a bye in round 6.  If you try to do something similar with only 5 rounds of play, then it cannot be arranged so that teams play each of the 3 games at least once and at most twice. I assume you want this, so I choose 6 rounds.

Hope that helps,

Ian

[Andrew Gibbs]

I can’t thank you enough Ian. I’ll certainly give your solution serious consideration. At the very least it’s given me a starting point and some options. Thanks mate.