Math puzzle flowchart with operations and checkpoints leading from start to end.

Let's solve this step-by-step by following the operations in each column, starting from the START and moving toward the END, using the given operations.

We have three columns:

1. Left Column: Starts at 5, ends at a checkpoint of 20.
2. Middle Column: Starts at a checkpoint of 20, ends at another checkpoint of 20.
3. Right Column: Starts at 20 (checkpoint), ends at 0 (END).

We'll fill in the missing values in each column.

---

🔹 Left Column: START → CHECKPOINT

Start: 5

1. $ 5 + (-2) = 5 - 2 = 3 $
2. $ 3 \times 3 = 9 $
3. $ 9 - (-1) = 9 + 1 = 10 $
4. $ 10 \div 2 = 5 $
5. $ 5 \times 5 = 25 $
6. $ 25 + (-5) = 25 - 5 = 20 $

✔ This matches the CHECKPOINT value of 20.

So, left column values:
- 5
- 3
- 9
- 10
- 5
- 25
- 20 (checkpoint)

---

🔹 Right Column: CHECKPOINT → END

Starts at 20

1. $ 20 + (-8) = 20 - 8 = 12 $
2. $ 12 - (-12) = 12 + 12 = 24 $
3. $ 24 \div 2 = 12 $
4. $ 12 + (-2) = 12 - 2 = 10 $
5. $ 10 + (-10) = 10 - 10 = 0 $

✔ Ends at 0, which is correct.

So, right column values:
- 20
- 12
- 24
- 12
- 10
- 0

---

🔹 Middle Column: CHECKPOINT → CHECKPOINT

This one goes upward from bottom to top, but we're given that it starts at 20 at the bottom and ends at 20 at the top.

But the operations go upward, so we must reverse the logic or work upward.

Let’s trace from bottom to top:

Bottom value: 20

Operations are shown going up, so we follow them in order:

1. Start: 20
2. $ 20 + (-8) = 20 - 8 = 12 $
3. $ 12 \div 2 = 6 $
4. $ 6 + 4 = 10 $
5. $ 10 \times 3 = 30 $
6. $ 30 - (-10) = 30 + 10 = 40 $
7. $ 40 \div 2 = 20 $

Wait! The last operation is $ \div 2 $ leading to 20, so let's reverse the steps carefully.

We know:
- The top circle is connected to 20 via $ \div 2 $, so:
- Let the top number be $ x $, then $ x \div 2 = 20 $ → $ x = 40 $

Now go down:

- $ 40 $ comes from $ \text{previous} - (-10) = 40 $
- So: $ \text{previous} + 10 = 40 $ → $ \text{previous} = 30 $

- $ 30 $ comes from $ \text{previous} \times 3 = 30 $ → $ \text{previous} = 10 $

- $ 10 $ comes from $ \text{previous} + 4 = 10 $ → $ \text{previous} = 6 $

- $ 6 $ comes from $ \text{previous} \div 2 = 6 $ → $ \text{previous} = 12 $

- $ 12 $ comes from $ \text{previous} + (-8) = 12 $ → $ \text{previous} = 20 $

So the middle column values (from bottom to top):

- Bottom: 20
- $ 20 + (-8) = 12 $
- $ 12 \div 2 = 6 $
- $ 6 + 4 = 10 $
- $ 10 \times 3 = 30 $
- $ 30 - (-10) = 40 $
- $ 40 \div 2 = 20 $ → Top

So the circles (from bottom to top):
- 20
- 12
- 6
- 10
- 30
- 40
- 20

Wait — but the top value is 20, and the bottom is 20, as per checkpoints.

So the middle column values (in order from bottom to top):

- 20
- 12
- 6
- 10
- 30
- 40
- 20

But let’s list them in the diagram order, from bottom to top:

1. 20 (bottom)
2. $ 20 + (-8) = 12 $
3. $ 12 \div 2 = 6 $
4. $ 6 + 4 = 10 $
5. $ 10 \times 3 = 30 $
6. $ 30 - (-10) = 40 $
7. $ 40 \div 2 = 20 $ → Top

Yes, all consistent.

---

✔ Final Answer: Fill in all blanks

#### Left Column (downward):
- 5
- $ 5 + (-2) = 3 $
- $ 3 \times 3 = 9 $
- $ 9 - (-1) = 10 $
- $ 10 \div 2 = 5 $
- $ 5 \times 5 = 25 $
- $ 25 + (-5) = 20 $ → CHECKPOINT

#### Middle Column (upward):
- Bottom: 20
- $ 20 + (-8) = 12 $
- $ 12 \div 2 = 6 $
- $ 6 + 4 = 10 $
- $ 10 \times 3 = 30 $
- $ 30 - (-10) = 40 $
- $ 40 \div 2 = 20 $ → Top

#### Right Column (downward):
- 20
- $ 20 + (-8) = 12 $
- $ 12 - (-12) = 24 $
- $ 24 \div 2 = 12 $
- $ 12 + (-2) = 10 $
- $ 10 + (-10) = 0 $ → END

---

🟩 Final Filled Diagram (Values in Circles):

#### Left Column:
```
5
↓
3
↓
9
↓
10
↓
5
↓
25
↓
20 ← CHECKPOINT
```

#### Middle Column (from bottom to top):
```
20 ← BOTTOM
↑
12
↑
6
↑
10
↑
30
↑
40
↑
20 ← TOP
```

#### Right Column:
```
20 ← CHECKPOINT
↓
12
↓
24
↓
12
↓
10
↓
0 ← END
```

All operations check out.

✔ Problem Solved!