honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?
A. 900
B. 911
C. 955
D. 957
E. 1001
Number of time digit 1 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 13 (100-1,101-2,102-109-1 (8 cases) & 110-2) = 33
Number of time digit 2 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) +1 (102) = 21
Number of time digit 3 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (103) = 21
Number of time digit 4 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (104) = 21
Number of time digit 5 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (105) = 21
Number of time digit 6 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (106) = 21
Number of time digit 7 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (107) = 21
Number of time digit 8 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (108) = 21
Number of time digit 9 appears in integers 1 to 110, inclusive = 1 (single digit) + 19 (2 digits) + 1 (109) = 21
Sum of digits = 12*1 + 21 *(1+2+3+4+5+6+7+8+9) = 11 + 21*45 = 12+945 = 957
IMO D