Identify the rule in each In/Out box to complete the addition and subtraction patterns.

To solve the problem, we need to identify the pattern or rule for each "IN/OUT" box and use it to complete the missing values. Let's analyze each box step by step.

---

Box 1:

| in | out |
|----|-----|
| 9 | 19 |
| 6 | 16 |
| 17 | |
| 20 | |
| 38 | |

#### Step 1: Identify the rule.
- From the first row: \( 9 + 10 = 19 \)
- From the second row: \( 6 + 10 = 16 \)

The rule is: Add 10.

#### Step 2: Apply the rule to fill in the missing values.
- For \( 17 \): \( 17 + 10 = 27 \)
- For \( 20 \): \( 20 + 10 = 30 \)
- For \( 38 \): \( 38 + 10 = 48 \)

#### Final Box 1:
| in | out |
|----|-----|
| 9 | 19 |
| 6 | 16 |
| 17 | 27 |
| 20 | 30 |
| 38 | 48 |

Rule: Add 10

---

Box 2:

| in | out |
|----|-----|
| 30 | 45 |
| 52 | 67 |
| | 83 |
| 29 | |
| | 86 |

#### Step 1: Identify the rule.
- From the first row: \( 30 + 15 = 45 \)
- From the second row: \( 52 + 15 = 67 \)

The rule is: Add 15.

#### Step 2: Apply the rule to fill in the missing values.
- For the input corresponding to 83: \( 83 - 15 = 68 \)
- For \( 29 \): \( 29 + 15 = 44 \)
- For the input corresponding to 86: \( 86 - 15 = 71 \)

#### Final Box 2:
| in | out |
|----|-----|
| 30 | 45 |
| 52 | 67 |
| 68 | 83 |
| 29 | 44 |
| 71 | 86 |

Rule: Add 15

---

Box 3:

| in | out |
|----|-----|
| 22 | 19 |
| 43 | 40 |
| 68 | |
| 55 | |
| 97 | |

#### Step 1: Identify the rule.
- From the first row: \( 22 - 3 = 19 \)
- From the second row: \( 43 - 3 = 40 \)

The rule is: Subtract 3.

#### Step 2: Apply the rule to fill in the missing values.
- For \( 68 \): \( 68 - 3 = 65 \)
- For \( 55 \): \( 55 - 3 = 52 \)
- For \( 97 \): \( 97 - 3 = 94 \)

#### Final Box 3:
| in | out |
|----|-----|
| 22 | 19 |
| 43 | 40 |
| 68 | 65 |
| 55 | 52 |
| 97 | 94 |

Rule: Subtract 3

---

Box 4:

| in | out |
|----|-----|
| 77 | 65 |
| 36 | 24 |
| | 52 |
| 88 | |
| | 12 |

#### Step 1: Identify the rule.
- From the first row: \( 77 - 12 = 65 \)
- From the second row: \( 36 - 12 = 24 \)

The rule is: Subtract 12.

#### Step 2: Apply the rule to fill in the missing values.
- For the input corresponding to 52: \( 52 + 12 = 64 \)
- For \( 88 \): \( 88 - 12 = 76 \)
- For the input corresponding to 12: \( 12 + 12 = 24 \)

#### Final Box 4:
| in | out |
|----|-----|
| 77 | 65 |
| 36 | 24 |
| 64 | 52 |
| 88 | 76 |
| 24 | 12 |

Rule: Subtract 12

---

Box 5:

| in | out |
|----|-----|
| 38 | |
| | 76 |
| 45 | 65 |
| | 24 |
| 40 | |

#### Step 1: Identify the rule.
- From the third row: \( 45 - 10 = 65 \)
- From the fourth row: \( 34 - 10 = 24 \) (reverse calculation)

The rule is: Subtract 10.

#### Step 2: Apply the rule to fill in the missing values.
- For \( 38 \): \( 38 - 10 = 28 \)
- For the input corresponding to 76: \( 76 + 10 = 86 \)
- For the input corresponding to 24: \( 34 \) (already calculated)
- For \( 40 \): \( 40 - 10 = 30 \)

#### Final Box 5:
| in | out |
|----|-----|
| 38 | 28 |
| 86 | 76 |
| 45 | 65 |
| 34 | 24 |
| 40 | 30 |

Rule: Subtract 10

---

Box 6:

| in | out |
|----|-----|
| 56 | |
| 78 | |
| | 42 |
| 32 | 16 |
| | 0 |

#### Step 1: Identify the rule.
- From the fourth row: \( 32 - 16 = 16 \)
- From the fifth row: \( 16 - 16 = 0 \)

The rule is: Divide by 2 (or subtract half of the input).

#### Step 2: Apply the rule to fill in the missing values.
- For \( 56 \): \( 56 / 2 = 28 \)
- For \( 78 \): \( 78 / 2 = 39 \)
- For the input corresponding to 42: \( 42 \times 2 = 84 \)
- For the input corresponding to 0: \( 0 \times 2 = 0 \) (already calculated)

#### Final Box 6:
| in | out |
|----|-----|
| 56 | 28 |
| 78 | 39 |
| 84 | 42 |
| 32 | 16 |
| 0 | 0 |

Rule: Divide by 2

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Box 1: Add 10} \\
\text{Box 2: Add 15} \\
\text{Box 3: Subtract 3} \\
\text{Box 4: Subtract 12} \\
\text{Box 5: Subtract 10} \\
\text{Box 6: Divide by 2}
\end{array}
}
\]