The maximum sum of digits of a three-digit number is obviously
the sum of the digits of 999 which is 9+9+9 or 27, a two-digit
number, the sum of whose digits is 9. All two-digit numbers
between 20 and 26 have sum of digits less than 9. So we look
at the two-digit numbers less than 20 and see if any have sum
of digits greater than 9. We quickly find that 19 has the
maximum sum of digits (1+9=10) of all integers less than 27.
So the three digit numbers with maximum sum of digits of sums
of digits are those whose digits have sum 19. There are many
three-digit numbers with sum of digits 19, such as 199,
595, 649, 991, 829, 577, etc. etc.
So the answer is 10, choice B.
Edwin
