What seemed like a simple setup for a team picnic has turned into a nightmare logic puzzle.
There are 8 teams and 8 events/locations. Each event requires two teams who play against each other.
There will be 8 total timeslots, broken into morning and afternoon sessions. Four of the events will be available in the morning and the remaining four will be available in the afternoon.
With the exception of the 8th timeslot (where overlap is unavoidable) each team should face each other team only once AND each team must participate in each event.
What would the schedule look like where the above stipulations are met? Here's my best attempt so far:
Event 1 Event 2 Event 3 Event 4 Time 1 1v5 2v6 3v7 4v8 Time 2 2v7 1v8 4v5 3v6 Time 3 4v6 3v5 2v8 1v7 Time 4 3v8 4v7 1v6 2v5 Event 5 Event 6 Event 7 Event 8 Time 5 3v4 7v8 1v2 5v6 Time 6 5v7 1v3 6v8 2v4 Time 7 #v# #v# #v# #v# Time 8 #v# #v# #v# #v#
Which leaves the following requirements without a good way to meet them:
Team 1 needs to face Team 4 Team 2 needs to face Team 3 Team 5 needs to face Team 8 Team 6 needs to face Team 7 Team 1 needs to play Events 5 and 8 Team 2 needs to play Events 5 and 6 Team 3 needs to play Events 7 and 8 Team 4 needs to play Events 6 and 7 Team 5 needs to play Events 6 and 7 Team 6 needs to play Events 5 and 6 Team 7 needs to play Events 7 and 8 Team 8 needs to play Events 5 and 8
I've can't seem to figure this out and am beginning to think that one of the requirements makes it impossible!