Problem Analysis:
The image shows a triangular pattern of numbers arranged in a hexagonal grid. The task is to determine the missing number in the pattern. Let's analyze the structure and identify the underlying rule.
#### Observations:
1. The numbers are arranged in rows, starting from the top.
2. The topmost row has a single number:
1.
3. Each subsequent row appears to be built based on the numbers in the row above it.
4. The numbers seem to follow a specific pattern, likely involving addition or some other mathematical operation.
#### Pattern Identification:
Let’s examine the rows step by step:
-
Row 1:
```
1
```
- This is the base case.
-
Row 2:
```
1 1
```
- Each number in this row is
1.
-
Row 3:
```
1 2 1
```
- The middle number (2) is the sum of the two numbers directly above it in Row 2: \(1 + 1 = 2\).
-
Row 4:
```
1 3 3 1
```
- The middle numbers (3, 3) are sums of the numbers directly above them:
- \(1 + 2 = 3\)
- \(2 + 1 = 3\)
-
Row 5:
```
1 4 6 4 1
```
- The middle numbers (4, 6, 4) are sums of the numbers directly above them:
- \(1 + 3 = 4\)
- \(3 + 3 = 6\)
- \(3 + 1 = 4\)
-
Row 6:
```
1 5 10 ? 5 1
```
- The missing number (?) should follow the same rule: it is the sum of the two numbers directly above it in Row 5:
- The numbers above the missing number are
6 and
4.
#### Calculation:
The missing number is:
\[
6 + 4 = 10
\]
Final Answer:
\[
\boxed{10}
\]
Parent Tip: Review the logic above to help your child master the concept of mind teasers worksheet.
