071.py

"""
Project Euler 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.
"""
from sympy import Rational
from math import floor, ceil

fraction = 3 / 7
num = 0

diff = float("inf")

for i in range(3, 1000001):
    curr_num = floor(i * fraction)
    # print(curr_num / i)
    if 0 < (fraction - curr_num / i) < diff:
        diff = fraction - curr_num / i
        # print(fraction, curr_num, i, diff)
        num = curr_num

print(num)