project_euler.problem_071.sol1
==============================

.. py:module:: project_euler.problem_071.sol1

.. autoapi-nested-parse::

   Ordered fractions
   Problem 71
   https://projecteuler.net/problem=71

   Consider the fraction n/d, where n and d are positive
   integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.

   If we list the set of reduced proper fractions for d ≤ 8
   in ascending order of size, we get:
       1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7,
       1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

   It can be seen that 2/5 is the fraction immediately to the left of 3/7.

   By listing the set of reduced proper fractions for d ≤ 1,000,000
   in ascending order of size, find the numerator of the fraction
   immediately to the left of 3/7.



Functions
---------

.. autoapisummary::

   project_euler.problem_071.sol1.solution


Module Contents
---------------

.. py:function:: solution(numerator: int = 3, denominator: int = 7, limit: int = 1000000) -> int

   Returns the closest numerator of the fraction immediately to the
   left of given fraction (numerator/denominator) from a list of reduced
   proper fractions.
   >>> solution()
   428570
   >>> solution(3, 7, 8)
   2
   >>> solution(6, 7, 60)
   47