You are given a number N with the property that every next digit of N is greater than the previous digit (so second digit from the left is greater than the first digit, and third digit is greater than the second and so on). Now multiply N by 9. What is the sum of the digits of the resulting number?
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Every time you add one to a digit (which is the same as adding 10, 100, 1000, etc) you get a number that is one more than a multiple of 9, so you have to subtract one from the number, which brings the sum of the digits back to 9.
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