How many positive integers between 10 and 2016 are divisible by 3 and have all of their digits the same?
(A) 9
(B) 12
(C) 6
(D) 18
(E) 3
The positive integers between 10 and 2016 which have all of their digits the same are: $11,22,33,44,55,66,77,88,99,111,222,333,444,555,666,777,888,999$, and 1111.

To be divisible by 3 , the sum of the digits of the positive integer must equal a multiple of 3 .

From the list above, the only 2-digit numbers whose digit sum is a multiple of 3 are 33, 66 and 99 (with digit sums of 6,12 and 18 , respectively).

(We may verify that each of the other digit sums, $2,4,8,10,14$, and 16 are not multiples of 3 .) A 3-digit positive integer with all digits equal to $d$ has digit sum $d+d+d=3 d$ (which is a multiple of 3 ).

Thus, all 3-digit positive integers with equal digits are divisible by 3 .

That is, all 9 of the 3 -digit integers listed above are divisible by 3 .

Finally, the number 1111 has digit sum 4 and thus is not divisible by 3 .

There are $3+9=12$ positive integers between 10 and 2016, having all of their digits the same, that are divisible by 3 .

ANSWER: (B)