data/problems/358.yml
---
:id: 358
:name: Cyclic numbers
:url: https://projecteuler.net/problem=358
:content: "A **cyclic number** with <var>n</var> digits has a very interesting property:
\ \nWhen it is multiplied by 1, 2, 3, 4, ... <var>n</var>, all the products have
exactly the same digits, in the same order, but rotated in a circular fashion!\n\nThe
smallest cyclic number is the 6-digit number 142857 : \n142857 × 1 = 142857 \n142857
× 2 = 285714 \n142857 × 3 = 428571 \n142857 × 4 = 571428 \n142857 × 5 = 714285
\ \n142857 × 6 = 857142\n\nThe next cyclic number is 0588235294117647 with 16 digits
: \n0588235294117647 × 1 = 0588235294117647 \n0588235294117647 × 2 = 1176470588235294
\ \n0588235294117647 × 3 = 1764705882352941 \n... \n0588235294117647 × 16 = 9411764705882352\n\nNote
that for cyclic numbers, leading zeros are important.\n\nThere 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.\n\n"