5. Each game of bridge involves two teams of two partners each. In a bridge club, a game can not be played if any two of the four people have previously been partners. At the start of the evening at this bridge club, there are 14 members present who play games until each has played exactly four times. After this, they are able to play six more games (total 12 more partnerships). Just as they are ready to wrap-up for the night, a 15th member arrives. Prove that the arrival of this new member allows at least one more game to be played.

Fig: 1