problem198.rb

# A best approximation to a real number x for the denominator bound d is a rational number r/s (in reduced form) with s  d, so that any rational number p/q which is closer to x than r/s has q  d.
# 
# Usually the best approximation to a real number is uniquely determined for all denominator bounds. However, there are some exceptions, e.g. 9/40 has the two best approximations 1/4 and 1/5 for the denominator bound 6. We shall call a real number x ambiguous, if there is at least one denominator bound for which x possesses two best approximations. Clearly, an ambiguous number is necessarily rational.
# 
# How many ambiguous numbers x = p/q, 0 x 1/100, are there whose denominator q does not exceed 108?

require 'frac'
class Integer
	def closest_multiple(mul)
		rem = self % mul
		return ((rem < mul - rem)?(self - rem):(self + (mul-rem)))
	end
end

class Frac
	def best_approx(d)
		#finds t/d such that t/d is closest to self
		common_denominator_multiplier = lcm(d,denominator) / denominator
	end
end

x=Frac.new(1,4)
a=Frac.new(2,5)
b=Frac.new(1,5)

puts b-x
puts x-a

# puts 20.closest_multiple(8)