How many integers between 1 and 10^16 are such that the sum of their digits is 2? Choose the correct option
A) 106
B) 116
C) 126
D) 136
E) 146
The integers with a sum of 2 are:   2, 20, 200,...,2*10^15 and there are 16 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 + ... + 15   Thus, the total number of integers is 1 + 2 + ... + 15 + 16 = 16*17/2= 
<gadget id="calculator">16*17/2</gadget>
<output>136</output>
136   The answer is 136.
<result>D</result>
How many integers between 1 and 10^16 are such that the sum of their digits is 2?