To solve the problem, we need to identify the pattern or rule governing the numbers in each grid. Let's analyze the given grids step by step.
Grid 1:
```
5 | 3
---------
1 | 6
```
Grid 2:
```
7 | 3
---------
1 | 4
```
Grid 3:
```
1 | 2
---------
6 | 6
```
Grid 4 (with the unknown):
```
5 | 5
---------
1 | ?
```
#### Step 1: Look for a pattern in the first three grids.
We will examine the relationship between the numbers in each grid. A common approach is to check sums, products, or other arithmetic operations.
#### Step 2: Analyze the sums of the rows and columns.
-
Grid 1:
- Row 1: \(5 + 3 = 8\)
- Row 2: \(1 + 6 = 7\)
- Column 1: \(5 + 1 = 6\)
- Column 2: \(3 + 6 = 9\)
-
Grid 2:
- Row 1: \(7 + 3 = 10\)
- Row 2: \(1 + 4 = 5\)
- Column 1: \(7 + 1 = 8\)
- Column 2: \(3 + 4 = 7\)
-
Grid 3:
- Row 1: \(1 + 2 = 3\)
- Row 2: \(6 + 6 = 12\)
- Column 1: \(1 + 6 = 7\)
- Column 2: \(2 + 6 = 8\)
#### Step 3: Identify a consistent pattern.
From the analysis, it appears that the
sum of the numbers in each row and column might be important. However, there isn't a single consistent sum across all grids. Let's explore another possibility: the
difference between the sums of the diagonals.
#### Step 4: Check the diagonal sums.
-
Grid 1:
- Diagonal 1 (top-left to bottom-right): \(5 + 6 = 11\)
- Diagonal 2 (top-right to bottom-left): \(3 + 1 = 4\)
- Difference: \(11 - 4 = 7\)
-
Grid 2:
- Diagonal 1: \(7 + 4 = 11\)
- Diagonal 2: \(3 + 1 = 4\)
- Difference: \(11 - 4 = 7\)
-
Grid 3:
- Diagonal 1: \(1 + 6 = 7\)
- Diagonal 2: \(2 + 6 = 8\)
- Difference: \(8 - 7 = 1\)
The diagonal difference pattern seems inconsistent. Let's try another approach: the
product of the numbers in each grid.
#### Step 5: Check the product of all numbers in each grid.
-
Grid 1:
- Product: \(5 \times 3 \times 1 \times 6 = 90\)
-
Grid 2:
- Product: \(7 \times 3 \times 1 \times 4 = 84\)
-
Grid 3:
- Product: \(1 \times 2 \times 6 \times 6 = 72\)
The products do not seem to follow a simple pattern either. Let's try a different approach: the
sum of all numbers in each grid.
#### Step 6: Check the sum of all numbers in each grid.
-
Grid 1:
- Sum: \(5 + 3 + 1 + 6 = 15\)
-
Grid 2:
- Sum: \(7 + 3 + 1 + 4 = 15\)
-
Grid 3:
- Sum: \(1 + 2 + 6 + 6 = 15\)
The sum of all numbers in each grid is consistently
15. This suggests that the sum of the numbers in Grid 4 should also be 15.
#### Step 7: Apply the pattern to Grid 4.
-
Grid 4:
- Known numbers: \(5, 5, 1, ?\)
- Let the unknown number be \(x\).
- Sum of all numbers: \(5 + 5 + 1 + x = 15\)
- Simplify: \(11 + x = 15\)
- Solve for \(x\): \(x = 15 - 11 = 4\)
Thus, the missing number is
4.
Final Answer:
\[
\boxed{4}
\]
Parent Tip: Review the logic above to help your child master the concept of brain puzzle worksheet with answers.
