base.rb

class Base
  def smallest(num)
    "base #{smallest_base(num)} => #{to_dec(num, smallest_base(num))}"
  end

  def all_bases(num)
    (smallest_base(num).to_i..16).map { |base| "base #{base} => #{to_dec(num, base)}" }.join("\n")
  end

  def to_dec(num, base)
    num.to_s.chars.reverse.map.with_index { |n, i| to_digit(n) * base**i }.reduce(:+)
  end

  private

  def smallest_base(num)
    num.to_s.chars.map { |n| to_digit(n) }.max + 1
  end

  def to_digit(letter)
    letter =~ /[[:alpha:]]/ ? letter.ord - 'a'.ord + 10 : letter.to_i
  end
end