Missing Number Puzzles Questions and Answers | Puzzles for Kids ... - Free Printable

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:

```
7
9 5
2
```

#### Observations:
- The center number is 2.
- The top number is 7.
- The left number is 9.
- The right number is 5.

#### Possible Relationships:
1. Sum of the corner numbers:
\( 7 + 9 + 5 + 2 = 23 \)
This doesn't seem to be a direct pattern.

2. Difference between the top and bottom numbers:
\( 7 - 2 = 5 \)
This might be relevant.

3. Relationship involving the sides:
Notice that:
\( 9 - 5 = 4 \)
And:
\( 7 - 2 = 5 \)
The differences might be important.

Grid 2:

```
10
13 7
3
```

#### Observations:
- The center number is 3.
- The top number is 10.
- The left number is 13.
- The right number is 7.

#### Possible Relationships:
1. Sum of the corner numbers:
\( 10 + 13 + 7 + 3 = 33 \)
Again, this doesn't seem to be a direct pattern.

2. Difference between the top and bottom numbers:
\( 10 - 3 = 7 \)
This matches the difference in the first grid.

3. Relationship involving the sides:
Notice that:
\( 13 - 7 = 6 \)
And:
\( 10 - 3 = 7 \)
The differences are consistent with the previous grid.

Grid 3:

```
6
7 5
1
```

#### Observations:
- The center number is 1.
- The top number is 6.
- The left number is 7.
- The right number is 5.

#### Possible Relationships:
1. Difference between the top and bottom numbers:
\( 6 - 1 = 5 \)
This matches the pattern seen in the previous grids.

2. Relationship involving the sides:
Notice that:
\( 7 - 5 = 2 \)
And:
\( 6 - 1 = 5 \)
The differences are consistent.

Grid 4:

```
5
9 1
?
```

#### Observations:
- The top number is 5.
- The left number is 9.
- The right number is 1.
- The center number is unknown (?).

#### Applying the Pattern:
From the previous grids, we observe that the difference between the top number and the center number is consistent with the differences seen earlier. Specifically:
- In Grid 1: \( 7 - 2 = 5 \)
- In Grid 2: \( 10 - 3 = 7 \)
- In Grid 3: \( 6 - 1 = 5 \)

For Grid 4, we apply the same logic:
- The top number is 5.
- Let the center number be \( x \).
- The difference should match the pattern. Since the differences alternate between 5 and 7, we expect the next difference to be 7 (following the sequence 5, 7, 5, 7).

Thus:
\[ 5 - x = 7 \]
\[ x = 5 - 7 \]
\[ x = -2 \]

Final Answer:

The missing number in the center of the fourth grid is:
\[
\boxed{-2}
\]