To solve the problem:

Step 1: Analyze the requirements

1. Two 4-digit numbers are being added to produce another 4-digit number.
2. The digits of the first number must sum to 22.
3. The digits of the second number must sum to 3.

Step 2: Create possible numbers

First number (sum of digits = 22):

Examples:

• 7999: $7 + 9 + 9 + 9 = 22$
• 8897: $8 + 8 + 9 + 7 = 22$

Second number (sum of digits = 3):

Examples:

• 3000: $3 + 0 + 0 + 0 = 3$
• 2010: $2 + 0 + 1 + 0 = 3$

Step 3: Test combinations

To keep the sum as a 4-digit number, pick combinations like:

• $7999 + 3000 = 10999$ (Invalid; exceeds 4 digits)
• $8897 + 2010 = 10907$ (Invalid; exceeds 4 digits)

Adjust to ensure the sum stays within range:

• Example: $7990 + 2000 = 9990$, which works as a valid 4-digit sum.

Would you like me to explore more possibilities or explain this further?

Here are some follow-up questions:

1. What other combinations could yield valid solutions?
2. How can we systematically generate numbers with specific digit sums?
3. What constraints ensure the sum remains a 4-digit number?
4. How do carryovers affect the digit sums when adding the numbers?
5. Can we programmatically generate all possibilities?

Tip: When solving problems with constraints like these, it’s useful to write down smaller test cases to find patterns.