data/problems/73.yml
---
:id: 73
:name: Counting fractions in a range
:url: https://projecteuler.net/problem=73
:content: |+
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?