Comment by ryao

  a = [int(x) for x in str(n)][::-1]
  assert n == sum(d*(10**i) for i, d in enumerate(a))

Now when you're operating mod 9, 10 == 1 % 9, thus

  10**i == 1 % 9

Comes from the fact that

  (a*b) % 9 == (a % 9) * (b % 9)

Now using

  (a+b) % 9 == (a % 9) + (b % 9)

We get that that sum(a) and n are same mod 9.