13, 32, 24, 43, 35, ?, 46, 65, 57, 76

45
52
54
55

The answer is $\boxed{\text{54}}$.

The sequence is a simple alternating addition and subtraction of 9. Starting with 13, we add 9 to get 22, then subtract 9 to get 13. We continue this pattern, adding 9 and then subtracting 9, to get the following sequence:

13, 32, 24, 43, 35, 54, 46, 65, 57, 76

Therefore, the missing number is $\boxed{54}$.