Brain Teaser #2: Find the missing number in the number pattern diagram.

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 recheck the diagram carefully. The bottom row is:

```
1 5 10 10 5 1
```

And above that, the row before it is:

```
1 4 ? 4 1
```

But wait — the diagram shows that the row above the bottom one has five numbers:
`1 4 ? 4 1` — but there are only four positions between the two rows?

Let’s count the rows properly.

Here’s the full pyramid as shown:

```
1
1 1
1 2 1
1 3 3 1
1 4 ? 4 1
1 5 10 10 5 1
```

So we have 6 rows, from top to bottom.

Now, notice that each number in the pyramid seems to be formed based on the numbers above it — just like Pascal's Triangle!

In Pascal’s Triangle:
- Each number is the sum of the two numbers directly above it.
- The edges are always 1.

Let’s test this idea.

Step-by-step verification:

Row 1:
`1`

Row 2:
`1 1`

Row 3:
`1 2 1` → 1+1 = 2

Row 4:
`1 3 3 1` → 1+2=3, 2+1=3

Row 5:
`1 4 ? 4 1`

Let’s compute the missing number using the rule.

The third number in Row 5 should be the sum of the two numbers above it in Row 4.

Looking at Row 4: `1 3 3 1`

So the two numbers above the missing spot are:
- The second number in Row 4: 3
- The third number in Row 4: 3

So:
`3 + 3 = 6`

Therefore, the missing number should be 6.

Let’s verify the rest of the pattern.

Row 5: `1 4 6 4 1` — yes, this matches the pattern of Pascal’s Triangle.

Now check Row 6: `1 5 10 10 5 1`

Does this match?

- First number: 1 (edge)
- Second: 1+4 = 5 ✔
- Third: 4+6 = 10 ✔
- Fourth: 6+4 = 10 ✔
- Fifth: 4+1 = 5 ✔
- Sixth: 1 ✔

Perfect! So everything checks out.

---

✔ Final Answer: 6

The missing number is 6.

This is Pascal’s Triangle, where each number is the sum of the two numbers directly above it.

Answer: 6 ✔