To generate test cases for the given problem, we need to achieve the following:

1. Randomly generate \(N\) (number of papers) within the given constraints.
2. Randomly generate a list of integers \(T_i\) representing the time it takes to scan each piece of paper, also within the given constraints.

Here's the test case generator for the given problem:

```python
import random

def tcgen():
    # Constraint for N
    N = random.randint(1, 50)
    
    # Constraint for T_i
    T = [random.randint(1, 50) for _ in range(N)]
    
    return N, T

# Example usage
if __name__ == "__main__":
    N, T = tcgen()
    print(N)
    for t in T:
        print(t)
```

### Explanation:

1. **Generating \(N\)**:
   - `N = random.randint(1, 50)` generates a random integer between 1 and 50 inclusive.

2. **Generating the list \(T\)**:
   - `[random.randint(1, 50) for _ in range(N)]` generates a list of \(N\) integers, where each integer is between 1 and 50 inclusive.

### Example Output:

Running the `tcgen` function might produce an output like:

```
10
3
45
21
30
3
8
25
10
47
29
```

This output corresponds to:
- \(N = 10\)
- \(T = [3, 45, 21, 30, 3, 8, 25, 10, 47, 29]\)

You can run this script multiple times to generate different test cases, which can be useful for testing the robustness and correctness of your solution to the problem.