A circle is divided into $ n $ equal parts. Marceline sets out to assign whole numbers from $ 1 $ to $ n $ to each of these pieces so that the distance between two consecutive numbers is always the same. The numbers $ 887 $, $ 217 $ and $ 1556 $ occupy consecutive positions. How many parts was the circumference divided into?
Problem
Source: OIFMAT II 2012 day 1 p1 - Chilean Math Forum FMAT Olympiad https://artofproblemsolving.com/community/c2484778_oifmat
Tags: combinatorics