Sure, I can help you write a test case generator for the "Elevator Hall Number" problem. Below is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate a random number of elevators N (2 ≤ N ≤ 6)
    N = random.randint(2, 6)
    
    # Generate random low and high floor ranges for each elevator
    ranges = []
    for _ in range(N):
        low = random.randint(1, 99)
        high = random.randint(low, 99)
        ranges.append((low, high))
    
    return N, ranges

def generate_multiple_test_cases(num_cases):
    test_cases = []
    for _ in range(num_cases):
        N, ranges = tcgen()
        test_case = f"{N}\n"
        for low, high in ranges:
            test_case += f"{low} {high}\n"
        test_cases.append(test_case.strip())
    return test_cases

def main():
    num_cases = 5  # You can specify the number of test cases you want to generate
    test_cases = generate_multiple_test_cases(num_cases)
    for test_case in test_cases:
        print(test_case)
        print()  # Print a blank line between test cases

if __name__ == "__main__":
    main()
```

Explanation:
1. **`tcgen` Function**: This function generates a single test case.
    - It randomly selects the number of elevators \(N\) within the range [2, 6].
    - For each elevator, it generates a random floor range with `low` and `high` values such that \(1 \leq \text{low} \leq \text{high} \leq 99\).

2. **`generate_multiple_test_cases` Function**: This function generates multiple test cases.
    - It calls `tcgen` multiple times to create the specified number of test cases.
    - It formats each test case as a string and stores them in a list.

3. **`main` Function**: This function controls the overall execution.
    - It sets the number of test cases to generate.
    - It prints each test case, followed by a blank line for separation.

To use the generator, simply run the `main` function. You can adjust the `num_cases` variable to generate the desired number of test cases.