# Problem 358: Cyclic numbers
A cyclic number with n digits has a very interesting property: When it
is multiplied by 1, 2, 3, 4, ... n, all the products have exactly the
same digits, in the same order, but rotated in a circular fashion! The
smallest cyclic number is the 6-digit number 142857 : 142857 × 1 =
142857 142857 × 2 = 285714 142857 × 3 = 428571 142857 × 4 = 571428
142857 × 5 = 714285 142857 × 6 = 857142 The next cyclic number is
0588235294117647 with 16 digits : 0588235294117647 × 1 =
0588235294117647 0588235294117647 × 2 = 1176470588235294
0588235294117647 × 3 = 1764705882352941 ... 0588235294117647 × 16 =
9411764705882352 Note that for cyclic numbers, leading zeros are
important. There is only one cyclic number for which, the eleven
leftmost digits are 00000000137 and the five rightmost digits are 56789
(i.e., it has the form 00000000137...56789 with an unknown number of
digits in the middle). Find the sum of all its digits.