[sean2]

I can see how you'd like to hold the order of operations correct for readability purposes (especially if the states were labeled with digits), but I don't see where psyklic's method could produce an error for the divisibility test.

Your initial white doesn't change anything, since it brings you back to the starting node. Any whites after the the final digit either keep you on the starting node or keep you in the graph where.

[thaumasiotes]

The graph isn't just a divisibility test, it reports the remainder after division by seven. I specifically acknowledged that this error won't mutate a "divisible by 7" result into "not divisible by 7" (because any number that is divisible by seven will still be divisible by seven after multiplying it by ten), but in every other case it will give you the wrong answer. (e.g. "remainder 2" will mutate into "remainder 6".)