How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2? Choices:	A) 6	B) 7	C) 5	D) 8	E) 18
Explanatory Answer   Find the number of such integers existing for a lower power of 10 and extrapolate the results.   Between 10 and 100, that is 101 and 102, we have 2 numbers, 11 and 20.   Similarly, between 100 and 1000, that is 102 and 103, we have 3 numbers, 101, 110 and 200.   Therefore, between 106 and 107, one will have 7 integers whose sum will be equal to 2.   Alternative approach   All numbers between 106 and 107 will be 7 digit numbers.   There are two possibilities if the sum of the digits has to be '2'.   Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.   The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.   So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.   Possibility 2: One digit is 2 and the remaining are 0s.   The only possibility is 2000000.   Total count is the sum of the counts from these two possibilities = 6 + 1= 
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
7   Choice 7 is the correct answer.
<result>B</result>
How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?