Counting fractions in a range
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?
from tools import gcf
def run():
third = 1 / 3.0
count = 0
for x in range(5, 12001):
for y in range(x / 3, x / 2 + 1):
fraction = float(y) / x
if fraction > third and fraction < 0.5:
if gcf(y, x) == 1:
count += 1
return count