Sure! Let's create a test case generator for the given problem statement. Here is the code:

```python
import random

def tcgen():
    N = random.randint(1, 100)
    i = random.randint(1, N)
    return N, i

# Example of generating a test case
if __name__ == "__main__":
    N, i = tcgen()
    print(f"{N} {i}")
```

This generator will create a random test case with values for \(N\) and \(i\) within the specified constraints.

To understand how the test case is generated:

1. **N** is generated randomly between 1 and 100.
2. **i** is generated randomly between 1 and \(N\).

These values are then printed out in the format expected by the problem statement. To test the generator, you can run the script, and it will output a random test case each time.

Let's walk through a few generated examples to ensure clarity:

1. If the generator outputs `4 2`, this means:
   - \(N = 4\), which indicates there are 4 cars in the train.
   - \(i = 2\), which means we need to find the position of the 2nd car from the front when counting from the back.

   The solution can be calculated as \(j = N - i + 1\). In this case, \(j = 4 - 2 + 1 = 3\).

2. If the generator outputs `15 11`, this means:
   - \(N = 15\), which indicates there are 15 cars in the train.
   - \(i = 11\), which means we need to find the position of the 11th car from the front when counting from the back.

   The solution can be calculated as \(j = N - i + 1\). In this case, \(j = 15 - 11 + 1 = 5\).

This generator provides a valid and random set of inputs each time it is called, ensuring thorough testing coverage for the problem.