Estimate the range of the submissions for this problem. Your answer must be between $[0, 1000]$. An estimate $E$ earns $\frac{2}{1+0.05|A-E|}$ points, where $A$ is the actual answer.

[i]2022 CCA Math Bonanza Lightning Round 5.2[/i]
1. **Understanding the Problem:**
   - We need to estimate the range of submissions for a given problem.
   - The estimate \( E \) must be between \( [0, 1000] \).
   - The scoring formula is given by:
     \[
     \text{Score} = \frac{2}{1 + 0.05|A - E|}
     \]
     where \( A \) is the actual answer.

2. **Analyzing the Scoring Formula:**
   - The formula \(\frac{2}{1 + 0.05|A - E|}\) indicates that the score decreases as the absolute difference \(|A - E|\) increases.
   - To maximize the score, we need to minimize \(|A - E|\), which means our estimate \( E \) should be as close as possible to the actual answer \( A \).

3. **Range of Submissions:**
   - Since the problem asks for an estimate of the range of submissions, we need to consider the possible values that \( A \) can take.
   - Given the constraint that \( E \) must be between \( [0, 1000] \), we infer that \( A \) must also lie within this range.

4. **Optimal Strategy:**
   - Without additional information about the distribution of \( A \), a reasonable strategy is to choose the midpoint of the range to minimize the maximum possible error.
   - The midpoint of the range \( [0, 1000] \) is:
     \[
     E = \frac{0 + 1000}{2} = 500
     \]

5. **Verification:**
   - If \( A \) is close to 500, the score will be high.
   - If \( A \) is at the extremes (0 or 1000), the score will be:
     \[
     \text{Score} = \frac{2}{1 + 0.05|1000 - 500|} = \frac{2}{1 + 0.05 \times 500} = \frac{2}{1 + 25} = \frac{2}{26} \approx 0.077
     \]
   - This is the worst-case scenario, but it ensures that the estimate is within the given range.

Conclusion:
\[
\boxed{500}
\]