A 4-digit number consists of four digits, each ranging from 0 to 9, with the first digit being non-zero. To find all possible 4-digit numbers whose digits add up to 18, we can represent the digits as A, B, C, and D, where A + B + C + D = 18 and A cannot be 0 (since it’s a 4-digit number).
The sum of the digits must equal 18, and since A must be at least 1, we can begin by allocating 1 to A and then finding combinations for B, C, and D such that together with A they total 18. This gives us the equation: 1 + B + C + D = 18; simplifying this, we find B + C + D = 17.
Next, we can generate the combinations of B, C, and D that add up to 17 without exceeding 9 for any single digit. For instance, if we set B = 9, then C + D must equal 8. We can permute the digits and also consider values for A, B, C, and D in a similar way.
Putting these pieces together leads us to valid combinations. Here are a few examples of 4-digit numbers where the digits sum to 18:
- 8991
- 9810
- 9720
- 9009
Each of these combinations meets the criteria. Finding all possible combinations can be systematic, often requiring a little bit of calculating or programming to ensure all valid numbers are identified.