To solve this puzzle, let's look for patterns that might connect each outer number to the inner number within its segment.

Each segment has an outer number, and an inner circle contains four central numbers: 31, 81, ?, and 72. Here’s one likely approach to finding the missing number:

1. Observe Patterns in Multiplication or Division:
   • In the top left segment: $5 \times 5 + 6 = 31$
   • In the top right segment: $9 \times 9 = 81$
   • In the bottom right segment: $8 \times 9 = 72$

Following this pattern, the missing value might follow a similar formula involving multiplication.

2. Calculate for the Missing Segment:
   • For the bottom left segment, we have the number 7.
   • If we try using a multiplication, let's see if $7 \times 7 = 49$ works, because adding values (like 5) may not fit without other guidance.

Answer: The missing number in the center might be 49.

Would you like a detailed explanation or have further questions?

Related Questions

1. How would you solve similar circle-based puzzles?
2. Can other operations (like subtraction) provide solutions for different configurations?
3. How to approach if the puzzle contains negative or fractional numbers?
4. Are there common tricks for puzzles involving geometric placements?
5. How could number theory help in solving number sequence puzzles?

Tip: When solving puzzles, always try different mathematical operations like multiplication, addition, or patterns involving squares and cubes.