Fill in the blanks so the sum of the three boxes on each side matches the indicated number.

To solve the problem, we need to fill in the blank spaces in each diagram such that the sum of the three boxes on each side matches the number indicated at the top. Let's solve each part step by step.

---

Part (a):

The top number is 50, and the bottom numbers are 13, 14, 28, 37, 52. The middle box is already filled with 20.

#### Step 1: Analyze the structure
- There are three sides to the triangle.
- Each side must sum to 50.
- The middle box (20) is shared by two sides.

#### Step 2: Assign variables
Let the boxes be labeled as follows:
```
50
/ | \
A B C
/ | \
13 20 37
```
Here:
- Side 1: \(13 + A + 20 = 50\)
- Side 2: \(A + 20 + C = 50\)
- Side 3: \(C + 20 + 37 = 50\)

#### Step 3: Solve for each variable
1. Side 1: \(13 + A + 20 = 50\)
\[
33 + A = 50 \implies A = 50 - 33 = 17
\]

2. Side 3: \(C + 20 + 37 = 50\)
\[
C + 57 = 50 \implies C = 50 - 57 = -7
\]

3. Side 2: \(A + 20 + C = 50\)
\[
17 + 20 + (-7) = 30 \neq 50
\]
This indicates an error in the problem setup or constraints. However, if we assume the problem is solvable with the given numbers, we might need to recheck the provided numbers or constraints.

Given the discrepancy, let's assume the problem is correctly stated and proceed with the next parts.

---

Part (b):

The top number is 100, and the bottom numbers are 7, 9, 44, 46, 49. The middle box is empty.

#### Step 1: Analyze the structure
- There are three sides to the triangle.
- Each side must sum to 100.
- The middle box is shared by two sides.

#### Step 2: Assign variables
Let the boxes be labeled as follows:
```
100
/ | \
A B C
/ | \
7 44 49
```
Here:
- Side 1: \(7 + A + B = 100\)
- Side 2: \(B + C + 44 = 100\)
- Side 3: \(C + 49 + 7 = 100\)

#### Step 3: Solve for each variable
1. Side 3: \(C + 49 + 7 = 100\)
\[
C + 56 = 100 \implies C = 100 - 56 = 44
\]

2. Side 2: \(B + C + 44 = 100\)
\[
B + 44 + 44 = 100 \implies B + 88 = 100 \implies B = 100 - 88 = 12
\]

3. Side 1: \(7 + A + B = 100\)
\[
7 + A + 12 = 100 \implies A + 19 = 100 \implies A = 100 - 19 = 81
\]

#### Final Answer for Part (b):
\[
\boxed{81, 12, 44}
\]

---

Part (c):

The top number is 52, and the bottom numbers are 6, 7, 10, 42, 48. The middle box is empty.

#### Step 1: Analyze the structure
- There are three sides to the triangle.
- Each side must sum to 52.
- The middle box is shared by two sides.

#### Step 2: Assign variables
Let the boxes be labeled as follows:
```
52
/ | \
A B C
/ | \
6 11 42
```
Here:
- Side 1: \(6 + A + B = 52\)
- Side 2: \(B + C + 11 = 52\)
- Side 3: \(C + 42 + 6 = 52\)

#### Step 3: Solve for each variable
1. Side 3: \(C + 42 + 6 = 52\)
\[
C + 48 = 52 \implies C = 52 - 48 = 4
\]

2. Side 2: \(B + C + 11 = 52\)
\[
B + 4 + 11 = 52 \implies B + 15 = 52 \implies B = 52 - 15 = 37
\]

3. Side 1: \(6 + A + B = 52\)
\[
6 + A + 37 = 52 \implies A + 43 = 52 \implies A = 52 - 43 = 9
\]

#### Final Answer for Part (c):
\[
\boxed{9, 37, 4}
\]

---

Summary of Answers:

1. Part (a): Not solvable with the given numbers due to inconsistency.
2. Part (b): \(\boxed{81, 12, 44}\)
3. Part (c): \(\boxed{9, 37, 4}\)