Find all the five-digit numbers which divisible by 3 and are formed using the digits 1, 6

Question

All I have done is that the sum of each digits of the five digit number should be divisible by 3. So $$a_1 + a_2 + a_3 + a_4 + a_5 = 3x$$

Can go as far as that

Answer 1

Hint: The correct writing is:

$$a_1+a_2+a_3+a_4+a_5=3x$$

It follows that the number can have either 0 or 3 1's.

Answer 2

If the number has $a$ 1s and $b$ 6s, then $$a+b=5 \text { and } 3 \text { divides } a+6b.$$

So either

$a=0, b=5$ and the number is 55555

or

$a=3, b=2$ and the numbers are the $\begin{pmatrix}5\\3\\\end{pmatrix}=10 $ permutations of 11166.