How many integers between 1 and 10^17 are such that the sum of their digits is 2? Options
A) 133
B) 143
C) 153
D) 163
E) 173
The integers with a sum of 2 are:   2, 20, 200,...,2*10^16 and there are 17 integers in this list.   Also, these integers have a sum of 2:   11   101, 110   1001, 1010, 1100   etc...   The number of integers in this list is 1 + 2 + ... + 16   Thus, the total number of integers is 1 + 2 + ... + 16 + 17 = 17*18/2= 
<gadget id="calculator">17*18/2</gadget>
<output>153</output>
153   The answer is 153.
<result>C</result>
How many integers between 1 and 10^17 are such that the sum of their digits is 2?