What is the largest three-digit multiple of 9 whose digits' sum is 18?
I know that the sum of the digits of any multiple of 9 is also a multiple of 9, so 18 is a possible sum. I want to find the largest three-digit multiple of 9, so I should start from the highest possible value and work my way down. The highest possible value for a three-digit multiple of 9 is 999, but its digits' sum is 27, which is too high. The next highest possible value is 990, whose digits' sum is 18, which is exactly what I want. So 990 is the answer. 