The fraction ⁴⁹/₉₈ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that ⁴⁹/₉₈ = ⁴/₈, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, ³⁰/₅₀ = ³/₅, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.

If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

+-#Ratio
class Ratio
  include Comparable
  attr_reader :num, :den
  @@facts=[1]
  @@dfacts=[1,1]
  def initialize(a,b=1)
    neg=1
    neg*=-1 if a<0
    neg*=-1 if b<0
    e=Ratio.euc(a.abs,b.abs);
    @num=neg*(a.abs)/e
    @den=(b.abs)/e
  end
  def expand(digits=20)
    a=@num.abs
    b=@den
    str=""
    str="-" if @num<0
    str+=(a/b).to_s+"."
    1.upto(digits) do
      a=10*(a%b)
      str+=(a/b).to_s
    end
    str
  end
  def to_s()
    @num.to_s+"/"+@den.to_s
  end
  def neg?
    @num<0
  end
  def *(o)
    if o.class==Fixnum or o.class==Bignum
      return Ratio.new(@num*o,@den)
    end
    return Ratio.new(@num*o.num,@den*o.den)
  end
  def **(o)
    if o.class==Fixnum
      ret=Ratio.new(1)
      mult=self
      bin=o.to_s(2)
      while(bin.length>0)
        ret*=mult if bin[-1].chr=="1"
        mult*=mult
        bin.chop!
      end
      return ret
    end
  end
  def /(o)
    if o.class==Fixnum or o.class==Bignum
      return Ratio.new(@num,@den*o)
    end
    return Ratio.new(@num*o.den,@den*o.num)
  end
  def +(o)
    if o.class==Fixnum or o.class==Bignum
      return self+Ratio.new(o,1)
    end
    return Ratio.new(@num*o.den+@den*o.num,@den*o.den)
  end
  def -(o)
    return self + (o*(-1))
  end
  def ==(o)
    return (self.den==o.den and self.num==o.num)
  end
  def <=>(b)
    a=self
    return 0 if a==b
    return -1 if(a.neg? and not b.neg?)
    return 1 if(b.neg? and not a.neg?)
    return (b*(-1))<=>(a*(-1)) if(b.neg? and a.neg?)
    c=a-b
    return -1 if c.neg?
    1
  end

  def sqrt(iter)
    guess = self / 2
    iter.times do 
      guess = (guess+(self/guess))/2
    end
    guess
  end

  def Ratio.fromDecimal(str)
  #String should be of type "4783.9233r123"
    neg=Ratio.new(1)
    if(str[0].chr=="-")
      neg*=-1
      str=str[1..-1]
    end
    return neg*Ratio.new(str.to_i,1) if(str=~/^\d+$/)
    if(str=~/^(\d*)\.(\d+)$/)
      whole=$1.to_i
      part=$2
      whole=whole*(10**(part.length))+part.to_i
      return neg*Ratio.new(whole,10**(part.length))
    elsif(str=~/^(\d*)\.(\d*)r(\d+)$/)
      whole=0
      whole=$1.to_i if $1.length>0
      part=0
      part=$2.to_i if $2.length>0
      rep=$3.to_i
      den=1
      if($2.length>0)
        whole=whole*(10**$2.length)+part
        den=10**$2.length
      end
      subtract=whole
      whole=whole*(10**$3.length)+rep
      whole-=subtract
      den*=(10**$3.length)-1
      return neg*Ratio.new(whole,den)
    end
  end

  protected
  def num=(a)
    @num=a
  end
  def den=(b)
    @den=b
  end
  private
  def Ratio.euc(a,b)
    while b!=0
      a,b=b,a%b
    end
    a
  end
end

+-#dig_split
def dig_split(n)
  s=n.to_s
  s.split("").map{|i|i.to_i}
end

def p33
  frax=[]
  (11..99).each do |d|
    (10...d).each do |n|
      nn=dig_split(n)
      dd=dig_split(d)
      nn.each do |dig|
        next if dig==0
        if(dd.include? dig)
          orig=Ratio.new(n,d)
	  newer=Ratio.new(nn[(1+nn.index(dig))%2],dd[(1+dd.index(dig))%2])
	  frax.push orig if orig==newer
	end
      end
    end
  end
  puts frax.product.den
end