jowair already said this [1], but here's a less concise explanation: The black arrows implement the operation of adding one mod 7, the white arrows implement t

jowair already said this [1], but here's a less concise explanation: The black arrows implement the operation of adding one mod 7, the white arrows implement the operation of multiplying by ten mod 7. The decimal expansion of a number tells you how to build it out of the operations of adding 1 and multiplying by 10, for example, to get 321, start at 0 and then do the operations +1, +1, +1, x10, +1, +1, x10, +1. Of course, if you do the operations mod 7, by following the arrows in the graph, instead of getting your number you get its residue mod 7. [1]: http://news.ycombinator.com/item?id=3909866 http://news.ycombinator.com/item?id=3909866