Some 4 digit numbers have 4 digits that have a sum of 23. what is the smallest such number that is a multiple of 4?
To find the smallest 4-digit number that has digits summing up to 23 and is also a multiple of 4, follow these steps:
1. We know that a multiple of 4 must be divisible by 4, meaning that the last two digits of the number must be divisible by 4.
2. The sum of the four digits is 23. Since we want the smallest number possible, we need to minimize the first two digits.
3. Start by considering the largest possible digit for the first digit. The largest digit is 9, but if we include 9 as the first digit, then we would need the sum of the remaining three digits to be 23 - 9 = 14. Since 14 is not divisible by 3, it is not possible to find a combination of three digits that add up to 14.
4. Continue considering smaller digits as the first digit until you find a valid combination. The combination that satisfies the conditions is as follows:
- Let the first digit be 8. This leaves us with a sum of 23 - 8 = 15 for the remaining three digits.
- We need to distribute the remaining sum of 15 among three digits. To minimize the number, we start with 1 as the second digit. This leaves us with a sum of 14 for the last two digits.
- For the last two digits, we can choose 5 and 9 as the remaining digits, which sum up to 14.
5. Now we have our desired number: 8159.
- This number is a multiple of 4 because the last two digits, 59, are divisible by 4.
- It has four digits that sum up to 23.
Therefore, the smallest 4-digit number that is a multiple of 4 and has digits summing up to 23 is 8159.