Sure! Here is a test case generator for the problem "How old are you":

```python
import random

def tcgen():
    # Define the constraints
    N = random.randint(1, 15)  # 1 ≤ N ≤ 15

    queries = []
    for _ in range(N):
        q = random.randint(1, 3)  # 1 ≤ q ≤ 3
        x = random.randint(1, 10)  # 1 ≤ x ≤ 10
        queries.append((q, x))

    return N, queries

# Example usage:
N, queries = tcgen()
print(N)
for q, x in queries:
    print(q, x)
```

This function generates a random test case for the problem. It creates a random number of queries \(N\) between 1 and 15, and then for each query, it generates a random type \(q\) (either 1, 2, or 3) and a random integer \(x\) between 1 and 10. The output is formatted as specified in the problem statement.

You can use this generator to create multiple test cases to test your solution. Here is an example of how the output might look:

```
7
3 5
1 3
2 8
1 6
1 10
3 2
2 7
```

This represents a test case with 7 queries, where each query modifies the number you're thinking of by either multiplying, adding, or subtracting a specified value.