Let's solve this
Brain Teaser #2: Number Patterns step by step.
We are given a pyramid made of hexagons with numbers, and we need to find the missing number in the red-outlined hexagon (which is currently blank). The structure looks like this:
```
1
1 1
1 2 1
1 3 3 1
1 4 ? 4 1
1 5 10 10 5 1
```
Wait — actually, let’s re-express it clearly based on the image layout. It appears to be a
hexagonal pyramid, but the numbers follow a familiar pattern.
Looking closely at the numbers:
```
1
1 1
1 2 1
1 3 3 1
1 4 ? 4 1
1 5 10 10 5 1
```
This looks
very similar to Pascal's Triangle!
What is Pascal's Triangle?
In Pascal's Triangle:
- Each number is the sum of the two numbers directly above it.
- The edges are always 1.
- Row n has n+1 elements (starting from row 0).
Let’s verify:
- Row 0: 1 → correct
- Row 1: 1 1 → correct
- Row 2: 1 2 1 → yes, 1+1=2
- Row 3: 1 3 3 1 → 1+2=3, 2+1=3 → correct
- Row 4: 1 4 ? 4 1 → should be 1 4 6 4 1
- Row 5: 1 5 10 10 5 1 → correct
So, in
Row 4, the middle number (the third element) should be
6, because:
- 4 + 2 = 6? Wait — no.
Wait! Let’s look again.
Actually, in Pascal’s triangle, each number is the sum of the two numbers
above it, diagonally.
Let’s label the rows:
- Row 0: 1
- Row 1: 1 1
- Row 2: 1 2 1
- Row 3: 1 3 3 1
- Row 4: 1 4 ? 4 1
- Row 5: 1 5 10 10 5 1
Now, let’s reconstruct Row 4.
The
third number in Row 4 (index 2) should be the sum of the two numbers above it in Row 3:
- From Row 3: positions 1 and 2 → 3 and 3
- So: 3 + 3 = 6
Therefore, the missing number is
6.
Let’s check if that makes sense with Row 5:
- Row 5: 1 5 10 10 5 1
- Check the 3rd number (index 2): should be sum of Row 4's index 1 and 2 → 4 and 6 → 4+6=10
✔
- Then next: 6 + 4 = 10
✔
Perfect!
So the missing number is
6.
---
Final Answer: 6
✔ The missing number in the diagram is
6, following the pattern of
Pascal's Triangle, where each number is the sum of the two numbers directly above it.
Parent Tip: Review the logic above to help your child master the concept of math puzzles brain teasers.
