You should be following the 1 white path before the n black paths, not afterwards. In particular, following "3 blacks then 1 white" in the last step, when the final digit is three, is an error; it will produce the wrong modulus for any number that is not divisible by 7.
(1) 1 white then 1 black, ending up in state 1
(6) 1 white then 6 blacks, ending up in state 2
(0) 1 white then 0 blacks, ending up in state 6
(3) 1 white then 3 blacks, ending up in state 0
The graph keeps track of ((the number so far) mod 7); following a white arrow multiplies your total by 10, and following a black arrow increases your total by 1.
psyklic|10 years ago
(1) 1 black then 1 white.
(6) 6 blacks then 1 white.
(0) 1 white.
(3) 3 blacks then 1 white.
And you end up at the bottom node, indicating it is divisible by 7.
thaumasiotes|10 years ago