Write a Python function `max_difference` that takes a list of tuples as input. Each tuple contains two integers. The function should calculate the absolute difference between the two integers in each tuple and return the maximum difference found among all the tuples.
#### Example Usage
```python [main.nopy]
print(max_difference([(3, 5), (1, 7), (10, 3), (1, 2)])) # Output: 7
print(max_difference([(4, 6), (2, 17), (9, 13), (11, 12)])) # Output: 15
print(max_difference([(12, 35), (21, 27), (13, 23), (41, 22)])) # Output: 23
```
#### Constraints
- The input list will contain at least one tuple.
- Each tuple will contain exactly two integers.
- The integers can be positive, negative, or zero.