The problem appears to be a sequence of numbers: 65536, 256, 16, and a question mark, and you are asked to find the next number in the sequence.

To solve this, let's identify the pattern in the sequence:

1. $65536$ to $256$:
   $65536 = 256^2 = 2^{16} \implies \sqrt{65536} = 256$

2. $256$ to $16$:
   $256 = 16^2 = 2^8 \implies \sqrt{256} = 16$

From these observations, it appears each number in the sequence is the square root of the previous number.

Following this pattern:

3. $16$ to the next number: $\sqrt{16} = 4$

Therefore, the missing number in the sequence is $4$.

The correct answer is option c. 4.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What would be the next number in the sequence after 4?
2. If the pattern was to cube the numbers instead, what would be the second number in the sequence?
3. How can you express the sequence using powers of 2?
4. What if each term was the cube root of the previous term, starting from 65536? What would the sequence look like?
5. How do we express the numbers in the sequence using logarithms?

Tip: Understanding sequences often involves recognizing patterns in operations applied between terms, such as addition, multiplication, or finding roots.