Missing Number In Diagram

Step 1: Understanding the Concept:
This is a matrix puzzle where the numbers in the grid follow a certain logical pattern, either row-wise, column-wise, or diagonally. We need to find this pattern to determine the missing number.
Step 2: Detailed Explanation:
Let's analyze the patterns in the matrix.
Pattern 1: Row-wise Logic

Row 1: 6, 10, 14. The difference between consecutive numbers is +4. ( , ). This is an arithmetic progression.
Row 2: 9, 15, 21. The difference between consecutive numbers is +6. ( , ). This is also an arithmetic progression.
Row 3: 12, 20, ?. The difference between the first two numbers is +8. ( ). The common differences in the rows are increasing by 2 (4, 6, 8). Following this logic, the next number in the third row should also be found by adding 8. So, .
Pattern 2: Column-wise Logic

Column 1: 6, 9, 12. The difference is +3. ( , ).
Column 2: 10, 15, 20. The difference is +5. ( , ).
Column 3: 14, 21, ?. The difference is +7. ( ). The common differences in the columns are also increasing by 2 (3, 5, 7). Following this logic, the next number in the third column should be .
Both the row-wise and column-wise patterns lead to the same result.
Step 3: Final Answer:
The missing number is 28.