Certainly! Let’s break down the process step-by-step:

### 1. Understanding the Problem
You have 16 teams, and each team plays every other team twice.

### 2. Number of Unique Matchups
- **Unique Matchups**: We need to find how many unique pairs of teams there are. This can be calculated using combinations, where the order of selection doesn't matter. The formula for combinations is:
  \[
  \binom{n}{2} = \frac{n \times (n - 1)}{2}
  \]
  For 16 teams (\( n = 16 \)):
  \[
  \binom{16}{2} = \frac{16 \times 15}{2} = 120
  \]
  This means there are 120 unique pairs of teams.

### 3. Accounting for Two Matches
- **Total Matches**: Since each pair of teams plays twice, we multiply the number of unique matchups by 2:
  \[
  120 \times 2 = 240
  \]
  So, the total number of matches is 240.

### Visual Example
Imagine a simpler case with 4 teams (A, B, C, D):

- **Pairs**: List out unique pairs:
  - AB, AC, AD
  - BC, BD
  - CD
- **Count**: There are \( \binom{4}{2} = 6 \) unique pairs.

If each pair plays twice, the total matches would be \( 6 \times 2 = 12 \).

### Applying the Same Logic
For 16 teams:
- Calculate unique pairs: \( \binom{16}{2} \)
- Multiply by 2 to account for each pair playing twice.

Hence, for 16 teams, you get \( 240 \) matches.

Feel free to ask more questions or clarify any part of this! Here are some further questions for you:

1. How would you calculate the number of matches if only some teams play each other?
2. What if the number of matches each team plays is different?
3. How does this calculation change if there are draws or ties?
4. Can this method be applied to non-sports tournaments?
5. What would be the total number of matches for a round-robin tournament with a different number of teams?

**Tip**: To avoid errors in such combinatorial problems, visualize with smaller numbers to see the pattern.

Learn how to calculate unique matchups and total matches in sports tournaments. This problem involves combinatorial mathematics, specifically using binomial coefficients to determine the number of unique pairs and total matches in a round-robin tournament. Suitable for advanced high school students and enthusiasts of combinatorial mathematics.

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