Between 100 and 200, how many numbers are there in which one digit is the average of the other two?  Choose the correct choice from the following answers.
A) 11 B) 12 C) 10 D) 8 E) 9
Answer is 11 :A   Let's list the numbers between 100 and 200 that have digits in which one of them is average of the other 2.   (One rule before listing, it should always start with 1XX)   {102, 111, 123, 135, 147, 159 } in these five, except 111, the others has 2 ways of rearranging, i.e., 123 can also be written as 132, and so is for 135 as 153.   Therefore  1 + 2 * 5= 
<gadget id="calculator"> 1 + 2 * 5</gadget>
<output>11</output>
11
<result>A</result>
Between 100 and 200, how many numbers are there in which one digit is the average of the other two?