Question

Find the number which will replace the question mark. 

Hint:

In grid-based number puzzles, always start by checking for simple row-wise or column-wise arithmetic relationships (addition, subtraction, multiplication, division). If that fails, look for more complex patterns like squares, cubes, or alternating operations.

Answer 1

Step 1: Understanding the Concept: 
This question requires identifying the logical pattern or rule that governs the numbers in each row of the given grid. Once the pattern is found, it can be applied to the last row to find the missing number. 

Step 2: Key Formula or Approach: 
Let the numbers in each row be represented by C1, C2, and C3 (for Column 1, Column 2, and Column 3). We need to find an arithmetic relationship between C1, C2, and C3 that holds true for all rows. 

Step 3: Detailed Explanation: 
Let's test simple arithmetic operations on the first few rows: 
- Row 1: 2, 4, 5. We can see that \(2 + 4 - 1 = 5\), or \(C1 + C2 - C3 = 1\). 
- Row 2: 1, 3, 3. Let's check if the same rule applies: \(1 + 3 - 3 = 1\). The rule holds. 
- Row 3: 5, 4, 8. Checking the rule: \(5 + 4 - 8 = 1\). The rule holds. 
- Row 4: 1, 1, 1. Checking the rule: \(1 + 1 - 1 = 1\). The rule holds. 
- Row 5: 3, 4, 6. Checking the rule: \(3 + 4 - 6 = 1\). The rule holds. 
- Row 6: 2, 3, 4. Checking the rule: \(2 + 3 - 4 = 1\). The rule holds. 
- Row 7: 5, 3, 7. Checking the rule: \(5 + 3 - 7 = 1\). The rule holds. 
The consistent pattern across all rows is: Column 1 + Column 2 - Column 3 = 1. Step 4: Final Answer: 
Now, we apply this rule to the last row (4, 4, ?). 
\[ C1 + C2 - C3 = 1 \] \[ 4 + 4 - ? = 1 \] \[ 8 - ? = 1 \] \[ ? = 8 - 1 \] \[ ? = 7 \] The number that replaces the question mark is 7.