------
## 最终结论
```python
def max_difference(tuple_list):
    max_diff = 0
    for pair in tuple_list:
        diff = abs(pair[0] - pair[1])
        if diff > max_diff:
            max_diff = diff
    return max_diff

# Test cases
assert max_difference([(3, 5), (1, 7), (10, 3), (1, 2)]) == 7
assert max_difference([(4, 6), (2, 17), (9, 13), (11, 12)]) == 15
assert max_difference([(12, 35), (21, 27), (13, 23), (41, 22)]) == 23
```