I've been waiting decades for anyone to be interested in a divisible-by-7 test that works right-to-left. Only 7 states required:

  #include <stdio.h>

  int x[7][10] = {
    /* 0 */ {0, 2, 4, 6, 1, 3, 5, 0, 2, 4},
    /* 1 */ {5, 0, 2, 4, 6, 1, 3, 5, 0, 2},
    /* 2 */ {3, 5, 0, 2, 4, 6, 1, 3, 5, 0},
    /* 3 */ {1, 3, 5, 0, 2, 4, 6, 1, 3, 5},
    /* 4 */ {6, 1, 3, 5, 0, 2, 4, 6, 1, 3},
    /* 5 */ {4, 6, 1, 3, 5, 0, 2, 4, 6, 1},
    /* 6 */ {2, 4, 6, 1, 3, 5, 0, 2, 4, 6}
  };

  int divisible_by_7(char *b)
  {
    char *p = b; while (*p) p++; // skip to NUL
    int state = 0;
    while (--p >= b)
      state = x[state][*p-'0'];
    return !state;
  }

  int main(int argc, char *argv[])
  {
    int i;
    for (i = 1; i<argc; i++)
      printf("%s is%s divisible by 7\n", argv[i], divisible_by_7(argv[i]) ? "" : "n't");
    return 0;
  }