MathDB

a) A game master divides a group of

12

players into two teams of six. The players do not know what the teams are, however the master gives each player a card containing the names of two other players: one of them is a teammate and the other is not, but the master does not tell the player which is which. Can the master write the names on the cards in such a way that the players can determine the teams? (All of the players can work together to do so.)
b) On the next occasion, the game master writes the names of

3

teammates and

1

opposing player on each card (possibly in a mixed up order). Now he wants to write the names in such away that the players together cannot determine the two teams. Is it possible for him to achieve this?
c) Can he write the names in such a way that the players together cannot determine the two teams, if now each card contains the names of

4

teammates and

1

opposing player (possibly in a mixed up order)?

Problem Statement