Use the six digits given in each case to complete the additions.

Thank you for the clarification! The task is to complete the additions by arranging the provided digits in each puzzle's boxes. The goal is to use all the given digits in a way that the addition in each puzzle works correctly.

Let's break it down step by step for each case:

### Case I: 
Given digits: **1, 4, 6, 7, 8, 9**
- There are two addition squares with blank boxes. You need to arrange the digits so that the sum is correct.

### Case II:
Given digits: **0, 1, 2, 5, 8, 9**
- Same task as above: use these digits to complete the addition correctly.

### Case III:
Given digits: **3, 4, 5, 6, 7, 8**
- Arrange the digits in the boxes to make the addition correct.

### Case IV:
Given digits: **1, 3, 5, 8, 9**
- Use these digits to complete the sum.

### Case V:
Given digits: **1, 3, 5, 6, 7, 8**
- Complete the addition using the given digits.

### Case VI:
Given digits: **1, 3, 5, 7, 9**
- Arrange these digits to make the addition valid.

I will now start solving each of these cases.

#### Let me begin solving Case I.# Defining the given digits for Case I
case_I_digits = [1, 4, 6, 7, 8, 9]

# We need to find two numbers using these digits that when added together produce a valid sum.
# We will try all possible combinations and find those that result in a valid addition.

from itertools import permutations

# Generate all possible ways to split the digits into two sets of three
possible_combinations = list(permutations(case_I_digits, 6))

valid_solutions = []

# Check each combination
for comb in possible_combinations:
    # Split the first three digits and the last three digits
    num1 = int("".join(map(str, comb[:3])))
    num2 = int("".join(map(str, comb[3:])))
    
    # Calculate their sum
    if num1 + num2 < 1000:  # Ensuring the result is a three-digit number
        valid_solutions.append((num1, num2, num1 + num2))

valid_solutions[:10]  # Show first 10 valid solutions for brevityFor **Case I**, using the digits **1, 4, 6, 7, 8, 9**, here are some possible valid solutions:

1. **146 + 789 = 935**
2. **146 + 798 = 944**
3. **147 + 689 = 836**
4. **147 + 698 = 845**
5. **148 + 769 = 917**

These are combinations that produce valid sums while using all six digits. You can choose one of these pairs to complete the puzzle.

Would you like to continue solving the other cases, or do you have any specific questions? Let me know if you'd like details on another case.

### Related Questions:
1. How do you ensure that no digits are repeated in the solutions?
2. Could there be multiple correct answers for one case?
3. What happens if you include a zero in the digits, like in Case II?
4. Can all six digits always be used to form valid additions?
5. What should you do if you can't find a valid addition with the given digits?

### Tip:
To solve these puzzles efficiently, focus on testing smaller sums first and then increase the numbers gradually to find a match.

Learn how to solve the addition puzzle using the digits 1, 4, 6, 7, 8, 9. Explore different combinations to complete the addition correctly with a step-by-step guide. Suitable for students in Grades 7-9.

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