class TateYoko
  attr_reader :count

  def initialize(num = 3)
    @num = num
    @matrix = Array.new(num+1){Array.new(num+1)}
    @all_nums = (1..num).to_a
    @count = 0
  end

  def calc(depth = 0)
    line = depth / @num + 1
    column = depth % @num + 1

    return if line > @num

    used_nums = @matrix[line][0, column] + @matrix.transpose[column][0, line]
    nums = @all_nums - used_nums

    nums.each do |n|
      @matrix[line][column] = n
      calc(depth + 1)
      if depth == @num**2 - 1
        @count += 1
        show_matrix
      end
    end
  end
  
  def show_matrix
    @matrix[1..-1].each {|line| puts line[1..-1].join }
    puts
  end
end

tate_yoko = TateYoko.new(3)
tate_yoko.calc
print 'total = ', tate_yoko.count