Discussion
What is the smallest number with distinct digits whose digits add up to 45?
Answer: C
The smallest such number is 123456789.
The digits 0 to 9 add up to 45, so distinct digits summing to 45 must be all ten digits or all of 1 to 9 (leaving out 0, which adds nothing). A nine-digit number is smaller than any ten-digit one, and arranging 1 to 9 in increasing order gives the smallest: 123456789.
123555789 repeats the digit 5, and 99999 repeats 9, so neither has distinct digits. 123457869 uses the right digits but is larger than 123456789, because its sixth digit is 7 instead of 6.
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