MathDB

a) A game master divides a group of

40

players into four teams of ten. 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

7

teammates and

2

opposing players on each card (possibly in a mixed up order). Now he wants to write the names in such a way that the players together cannot determine the four 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 four teams, if now each card contains the names of

6

teammates and

2

opposing players (possibly in a mixed up order)?

Problem Statement