4. Alana, Beatrix, Celine, and Deanna played 6 games of tennis together. In each game, the four of them split into two teams of two and one of the teams won the game. If Alana was on the winning team for 5 games, Beatrix for 2 games, and Celine for 1 game, for how many games was Deanna on the winning team?
Solution: Each game has two winners, to there will be a total of $6 \times 2=12$ winners.
Let $A, B, C, D$ be the number of wins for Anna, Beatrixm Celine, and Deanna respectively. Then the total number of wins can also be expressed as $A+B+C+D$. These two quantities are equal, so $A+B+C+D=12$.
With $A=5, B=2, C=1$ we have $D=12-5-2-1=4$.