First we want to have as small of a hundreds digit as possible,
since hundreds count more than tens or ones. So we choose the
hundreds digit to be 1.
First we want to have as small of a tens digit as possible,
since tens count the more than ones. To be sure we have
the smallest tens digit possible, we make the ones digit
as LARGE as possible, so that the tens digit will be as
small as possible. So we choose the ones digit as 9, and
that leasves 7 for the tens digit, so that the sum of
digits is 17.
Answer: 179 is the smallest.
Edwin
PS: [If you had been asked for the largest, the answer would have been 980]
