Explanation

To find the pattern, let's break down the given series:

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

Looking at the differences between consecutive numbers:

32 - 13 = 19

24 - 32 = -8

43 - 24 = 19

35 - 43 = -8

So, it seems like there's an alternating pattern of adding and subtracting 8 and 19 between the numbers.

Following this pattern:

35 + 19 = 54

54 - 8 = 46

So, the missing number is 54.

Thus, the completed series is:

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