Consider the fraction, n/d, where n and d are positive integers. If nd 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 10,000?

+-#gcd
def gcd(a,b)
  return a if b==0
  gcd(b,a%b) 
end

def p73
  count=0
  (4..10000).each do |d|
    (((d/3.0+1).floor)..((d/2.0-1).ceil)).each do |n|
      count+=1 if gcd(n,d)==1
    end
  end
  puts count
end