p073.py

# -*- coding: utf-8 -*-
"""
Created on Sun Jul 19 14:00:30 2020

@author: zhixia liu
"""

"""
Project Euler 73: Counting fractions in a range

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?
"""

#%% naive bf

from math import floor, ceil
from helper import gcd

total = 0
for d in range(4,12001):
    l = ceil(d/3)
    h = ceil(d/2)
    for n in range(l,h):
        if gcd(n,d)==1:
            total += 1
print(total)