Question 891360
Ideally, we want as many 9's in front. There are only three 9's (9, 19, 29) and 99930 doesn't work. Next try 998abc. We cannot use the 9 in 29, so we are forced to use the 8 in 28, so abc can be anything in 2930. The best solution is 998930, and the sum of the digits is 9+9+8+9+3+0 = 38.