Submit a positive integer $N$ between 1 and 20, inclusive. 
    If $C$ is the total number of teams that submit $N$ for this question, your score will be $\lfloor\frac{N}{C}\rfloor$

[i]Lightning 5.4[/i]
1. **Understanding the Problem:**
   - We need to submit a positive integer \( N \) between 1 and 20, inclusive.
   - The score is calculated as \( \left\lfloor \frac{N}{C} \right\rfloor \), where \( C \) is the number of teams that submit the same integer \( N \).

2. **Handling the Case \( C = 0 \):**
   - The problem states that \( C \) is the number of teams that submit \( N \). By definition, \( C \) cannot be zero because if no team submits \( N \), then \( N \) is not considered.
   - Therefore, \( C \geq 1 \).

3. **Choosing the Optimal \( N \):**
   - To maximize the score \( \left\lfloor \frac{N}{C} \right\rfloor \), we need to consider the relationship between \( N \) and \( C \).
   - If \( N \) is large and \( C \) is small, the score will be higher. Conversely, if \( C \) is large, the score will be lower.

4. **Strategy:**
   - Ideally, we want to choose an \( N \) that is less likely to be chosen by other teams to minimize \( C \).
   - However, without knowing the choices of other teams, we can only make an educated guess.

5. **Example Calculation:**
   - Suppose we choose \( N = 20 \) and only our team submits it, then \( C = 1 \).
   - The score would be \( \left\lfloor \frac{20}{1} \right\rfloor = 20 \).

6. **General Case:**
   - If \( N = k \) and \( C = m \), the score is \( \left\lfloor \frac{k}{m} \right\rfloor \).
   - To maximize this, \( k \) should be as large as possible and \( m \) as small as possible.

The final answer is \( \boxed{ \left\lfloor \frac{N}{C} \right\rfloor } \).