I am less than 1000. The sum of my digits is 26. My ones digit is 8. What number am I?
To find the number that satisfies these conditions, we can start by narrowing down the possibilities. Since the ones digit is given as 8, it means the number must end with 8.
Next, we know that the sum of all the digits is 26. We can work backward from the ones digit to determine what the tens and hundreds digits are.
Let's list the possible tens digit options and check if they satisfy the given conditions. For the tens digit, it can be any whole number between 0 and 9 (inclusive). Let's try each possibility:
1. If the tens digit is 0, the ones digit is already 8, so the hundreds digit must be 26 - 8 = 18. However, 18 is not a valid digit, so this possibility is invalid.
2. If the tens digit is 1, the hundreds digit would then be 26 - (1 + 8) = 17. Again, 17 is not valid, so this possibility is also invalid.
3. If the tens digit is 2, the hundreds digit would be 26 - (2 + 8) = 16. Once again, 16 is not valid, so this possibility is invalid as well.
4. If the tens digit is 3, the hundreds digit would be 26 - (3 + 8) = 15. Similarly, 15 is not a valid digit, ruling out this possibility.
5. If the tens digit is 4, the hundreds digit would be 26 - (4 + 8) = 14. Once again, 14 is not valid, so this possibility is invalid.
6. If the tens digit is 5, the hundreds digit would be 26 - (5 + 8) = 13. Like before, 13 is not a valid digit, so this possibility is also ruled out.
7. If the tens digit is 6, the hundreds digit would be 26 - (6 + 8) = 12. Again, 12 is not a valid digit, so this possibility is invalid.
8. If the tens digit is 7, the hundreds digit would be 26 - (7 + 8) = 11. Just like before, 11 is not a valid digit, ruling out this possibility.
9. If the tens digit is 8, the hundreds digit would be 26 - (8 + 8) = 10. Surprisingly, 10 is a valid digit, so this possibility is valid.
Since the hundreds digit can only be 10, the number that satisfies all the given conditions is 108.