Last Week in Training (I'm a Cycleball player) a logial problem/puzzle tricked us. And I'm wondering if there exists a logical solution for the next time.
Cycleball is played in pairs (2 Players vs. 2 Players) and last week we were 5 People who joined the training - let's call us Player A,B,C,D,E.
Our Goal was to play a bunch of matches with the condition that every player had played in a team with each other. So we started and thought that we don't need to plan that. But we run into a conflict because in the last game (each player must play 4 matches) A and B would have to play with E at the same time.
I started by listing the possible Teams (AB,AC,AD,AE,BC,BD,BE,CD,CE,DE) , arranged them in a circle and connect the possible meetings. Each Team in the Circle is connected to 3 others. But here starts the puzzle for me. What's the solution? and are there general view on that problem?
Sorry for my bad english - corrections are always welcome!!!