What is the smallest five-digit number with non-zero digits such that the digits add up to 20?
To find the smallest five-digit number, I want to minimize the leftmost digit and maximize the rightmost digit, because the leftmost digit contributes more to the value of the number than the rightmost digit. So I will start by assigning the leftmost digit as 1, and the rightmost digit as 9. Then I have 1 _ _ _ 9, and the remaining digits must add up to 20 - 1 - 9 = 10. To minimize the second digit, I will assign it as 1 as well. Then I have 1 1 _ _ 9, and the remaining digits must add up to 10 - 1 = 9. To minimize the third digit, I will assign it as 1 too. Then I have 1 1 1 _ 9, and the remaining digit must be 9 - 1 = 8. So the smallest five-digit number with non-zero digits such that the digits add up to 20 is 11189. 