Minimum number of states

Question

What is the No of states in Min.DFA  on $ E={0,1,2} $which accepts the ternary no whose equivalent is divisible by $9?$

Answer 1

For a number to be divisible by $9$ in Base-3 representation last 2 bits should be $0$.

So, DFA will comprise of $3$ states and will look like $\Rightarrow$

$9 = (100)_3$,  $18 = (200)_3$, $27 = (1000)_3$ and $36 = (1100)_3$ and Above DFA accepts all these strings.