To generate test cases for the problem "How old are you," we need to create various combinations of the magician's queries and the values involved in those queries. Below is a test case generator in Python for this problem:

```python
import random

def tcgen():
    # Number of queries - N
    N = random.randint(1, 15)
    
    # List to store queries
    queries = []
    
    for _ in range(N):
        # Randomly choose a query type (1, 2, or 3)
        q = random.randint(1, 3)
        # Randomly choose a value for x (1 to 10)
        x = random.randint(1, 10)
        # Append the query in the form of (q, x)
        queries.append((q, x))
    
    # Return N and the list of queries
    return N, queries

# Example usage:
N, queries = tcgen()
print(N)
for query in queries:
    print(query[0], query[1])
```

This test case generator creates:
1. A random number of queries \( N \) between 1 and 15.
2. Each query is randomly chosen from the set {1, 2, 3} (representing multiplication, addition, and subtraction operations respectively).
3. Each query value \( x \) is randomly chosen between 1 and 10.

Here is an example of how the output might look when you run the generator:

```plaintext
7
3 6
2 7
2 4
3 9
1 2
1 5
2 4
```

This represents 7 queries where:
- The first query is "subtract 6".
- The second query is "add 7".
- The third query is "add 4".
- The fourth query is "subtract 9".
- The fifth query is "multiply by 2".
- The sixth query is "multiply by 5".
- The seventh query is "add 4".

You can run the test case generator multiple times to get different sets of test cases for comprehensive testing.