What is the pattern used to solve these number relationship problems and what is the missing number in Problem 27?

Here's a step-by-step solution for each problem:

The pattern for these problems involves two relationships:

1. The middle number is the sum of the products of the numbers on the left side and the numbers on the right side. That is, (Top-left $\times$ Bottom-left) + (Top-right $\times$ Bottom-right) = Middle number.
2. The bottom-right number is one more than the top-right number. That is, Bottom-right = Top-right + 1.

Let's verify these patterns with the given examples.

:
Given numbers: Top-left = 6, Top-right = 8, Middle = 18, Bottom-left =