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Exactly 2: 243 of them.
there are 899 whole numbers that have three digits.
There are no 3-digit whole numbers whose digits sum to 3. The smallest 3-digit number is 100, and the largest is 999, but in neither case is the sum of the digits equal to 3.
There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.