Let's analyze the pattern in the sequence:
- The numbers are alternating between increases and decreases.
- From 32 to 40, the difference is +8.
- From 40 to 24, the difference is -16.
- From 24 to 16, the difference is -8.
- From 16 to 24, the difference is +8.
It follows a pattern of alternating between +8 and -8, with -16 as the only exception.
So, following this pattern, the next difference should be -8:
\[
24 - 8 = 16
\]
Thus, the missing number is \( \boxed{8} \).
Therefore, the correct answer is \( \boxed{3} \).