Certainly! Based on the problem statement for Snuke and the Japanese counter words, here is a test case generator in Python:

```python
import random

def tcgen():
    """
    Test case generator for the problem of determining how to read the count of pencils in Japanese.
    """
    N = random.randint(1, 999)
    return N

# Example usage:
if __name__ == "__main__":
    for _ in range(10):  # Generate 10 test cases
        print(tcgen())
```

Explanation:
- The generator function `tcgen()` randomly selects an integer \( N \) between 1 and 999 (inclusive), as per the problem constraints.
- The function returns this randomly selected integer \( N \).
- In the example usage, we generate and print 10 test cases to demonstrate its functionality.

This generator will help create diverse test cases for evaluating the solution to the problem.