Worksheet 1: Fill in the missing numbers in Pascal's Triangle using the given pattern.

I'll solve this Pascal's triangle worksheet step by step.

Understanding Pascal's Triangle:
In Pascal's triangle, each number is the sum of the two numbers directly above it. Let me work through each section.

Section A:
The pattern shows:
```
15
/ \
35 35
\ /
86
```

Working from top to bottom:
- The two 35s below 15 should add up: 35 + 35 = 70 (not 86)
- This means there are missing numbers between 15 and the 35s

Let me work backwards. If we have 35 and 35 in a row, what's above them?
- Two numbers that add to give 35 on each side
- Working with the standard Pascal's triangle pattern...

Actually, let me reconsider. Looking at the hexagon structure, each hexagon connects to others. Let me identify the actual rows:

Row with 15 at top, then next row has two numbers (let's call them x and y), then 35 and 35, then 86.

If 35 + 35 = 70, but we see 86, there must be intermediate values.

Let me try: if the row above 35, 35 contains numbers that sum to 35 each:
- Left: a + b = 35
- Right: b + c = 35
- And a + c = 15 (from the top)

From a + c = 15 and a + b = 35: b - c = 20
From b + c = 35: adding these gives 2b = 55, so b = 27.5 (not an integer)

This approach isn't working. Let me look at the complete triangle structure more carefully.

Looking at the full Pascal's triangle shown:
```
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
```

Each entry = sum of two entries above it.

For Section A:
Given the structure with 15 at top, I need to find what fits the Pascal's triangle pattern.

Let me check if 15 appears in standard Pascal's triangle:
- Row 6: 1, 6, 15, 20, 15, 6, 1 ✓

So 15 is C(6,2) or C(6,4).

Below 15 in row 6 would be entries from row 7:
- Row 7: 1, 7, 21, 35, 35, 21, 7, 1

So below 15 (which is at position 2 or 4 in row 6) would be 35 and 35! ✓

And below those in row 8:
- Row 8: 1, 8, 28, 56, 70, 56, 28, 8, 1

35 + 35 = 70, not 86. So the bottom number should be 70, not 86.

Wait, let me re-examine. Maybe 86 is given and I need to verify or there's an error in my understanding.

Actually, looking more carefully at the hexagonal arrangement - maybe the connections are different. Let me check if 86 could be correct with different intermediate values.

Hmm, let me try a different approach for each section:

Section B: 91, 14, 1
- These don't follow Pascal's triangle (91 ≠ 14 + 1)
- In Pascal's triangle: Row 13 has 1, 13, 78, 286...
- Actually 91 = C(13,2) = 13×12/2 = 78... no that's wrong
- 91 = C(13,2)? Let me calculate: 13×12/2 = 78. No.
- 91 = C(?,?): 91 = 13 × 7, so maybe C(13, something)
- C(13,1) = 13, C(13,2) = 78, C(13,3) = 286
- Hmm, 91 doesn't fit easily

Let me reconsider. Maybe these are portions where some numbers are missing and need to be filled in based on the Pascal's triangle rule.

For B with 91, 14, 1: if they're in a triangular arrangement where each bottom number equals sum of two above...
- If 14 and 1 are above, their sum would be 15, not 91
- If 91 is at top, and splits into two numbers below that sum to 91...

Actually, I think I need to see these as small excerpts where we fill in missing values. Let me assume standard Pascal's triangle relationships.

Let me search for information about this specific worksheet to understand the exact format better.