A singles tournament had six players. Each player played every other 
player only once, with no ties. If Helen won 4 games, Ines won 3 games, 
Janet won 2 games, Kendra won 2 games and Lara won 2 games, how 
many games did Monica win?

The tournament has 6 players, and each player plays against every other player exactly once. The total number of games played in a round-robin tournament with \( n \) players is given by:

\[
\binom{n}{2} = \frac{n(n-1)}{2}
\]

For \( n = 6 \):

\[
\binom{6}{2} = \frac{6(6-1)}{2} = \frac{6 \times 5}{2} = 15 \text{ games}
\]

The number of wins listed so far is:

- Helen: 4 wins
- Ines: 3 wins
- Janet: 2 wins
- Kendra: 2 wins
- Lara: 2 wins

The sum of the wins is:

\[
4 + 3 + 2 + 2 + 2 = 13
\]

Since there are a total of 15 games and each game has exactly one winner, the total number of wins must also be 15. Thus, Monica must have won the remaining:

\[
15 - 13 = 2 \text{ games}
\]

Therefore, Monica won **2 games**.

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Would you like more details or have any questions? Here are five related questions you might find interesting:

1. How many total games would there be if there were 8 players in the tournament?
2. What is the general formula for the number of games in a round-robin tournament with \( n \) players?
3. If a player won all of their games, how many games would they have won in this 6-player tournament?
4. How would the number of games change if players played each other twice instead of once?
5. What is the difference between a round-robin tournament and a knockout tournament?

**Tip:** In a round-robin tournament, every player faces every other player, so you can use combinations to calculate the total number of games.

A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win?

In a 6-player round-robin tournament, each player played against every other player exactly once. Learn how many games Monica won, using combinatorial concepts and the formula for calculating total games. This problem is ideal for students in Grades 6-8.

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