project_euler.problem_073.sol1
==============================

.. py:module:: project_euler.problem_073.sol1

.. autoapi-nested-parse::

   Project Euler Problem 73: https://projecteuler.net/problem=73

   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 there are 3 fractions between 1/3 and 1/2.

   How many fractions lie between 1/3 and 1/2 in the sorted set
   of reduced proper fractions for d ≤ 12,000?



Functions
---------

.. autoapisummary::

   project_euler.problem_073.sol1.solution


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

.. py:function:: solution(max_d: int = 12000) -> int

   Returns number of fractions lie between 1/3 and 1/2 in the sorted set
   of reduced proper fractions for d ≤ max_d

   >>> solution(4)
   0

   >>> solution(5)
   1

   >>> solution(8)
   3