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###
# 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?
###
# HCF means Higest Common Factor (aka Greatest Common Divisor)
# HCF(n, d) is to ensure that the fraction is reduced.
# Eddie Woo GCD: https://www.youtube.com/watch?v=ui5yjN1riQA
const TOP = 12_000
# ~15s
result = length(
Set([
n // d
for d in 1:TOP
for n in 1:d
if 1 // 3 < n // d < 1 // 2
])
)
println(result)
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