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45 if you don't count numbers that start with a zero, such as 000 or 011. If you do count them it would be 55.

You have 9 that start with 1 as their first digit since the lowest possible sum is 1 (101) and the highest possible sum which can fit in one digit is 9 (189). You have 8 that start with "2" since the lowest possible sum is 2 (202) and the highest possible sum will always be 9 (279). You have 7 that start with 3 since the lowest possible sum is 3 (303) and the highest possible sum is 9 (369) and so on until you get to numbers that start with 9 of which there is only one, 909.

So, you have 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45. If you count zero as a possible first digit then you can add ten because there's ten that start with zero.

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