------
## 最终结论
```python
def find_max(tuples):
    max_value = float('-inf')  # Initialize max_value to the smallest possible number
    for tup in tuples:  # Iterate through each tuple in the list
        current_max = max(tup)  # Find the maximum value in the current tuple
        if current_max > max_value:  # Compare with the global maximum
            max_value = current_max  # Update global maximum if current is larger
    return max_value  # Return the found maximum value

# Test cases
assert find_max([(2, 4), (6, 7), (5, 1), (6, 10), (8, 7)]) == 10
assert find_max([(3, 5), (7, 8), (6, 2), (7, 11), (9, 8)]) == 11
assert find_max([(4, 6), (8, 9), (7, 3), (8, 12), (10, 9)]) == 12
```