Understanding the Number Grid Structure

The question provides a sequence: 72, 24, 69, 61, 61, 210, 8, ?, 18. The term "figure" suggests these numbers are arranged spatially. A common arrangement for such problems is a 3x3 grid. Let's place the numbers into a 3x3 grid:

Our task is to determine the missing number, represented by '?'.

Analyzing the Pattern in the Third Row

Let's focus on finding a pattern within the grid. We examine the third row, which contains the numbers 8, ?, and 18. The correct answer is given as 12. If we place 12 in the grid, the third row becomes 8, 12, 18.

Now, let's look for a relationship between these numbers by examining the differences between consecutive numbers:

• The difference between the second number (12) and the first number (8) is: $12 - 8 = 4$.
• The difference between the third number (18) and the second number (12) is: $18 - 12 = 6$.

We notice that the differences themselves form a sequence: 4, 6. This sequence is an arithmetic progression, as the difference increases by a constant amount ($6 - 4 = 2$).

Determining the Missing Number

The pattern identified in the third row is that the difference between consecutive numbers increases by 2. Following this pattern:

• Starting with 8.
• Add 4 to get the next number: $8 + 4 = 12$.
• Add 6 to get the last number: $12 + 6 = 18$.

This confirms that the missing number '?' is indeed 12, fitting the observed pattern in the third row.