NataliasPhoneNumberSolver.rb

class NataliasPhoneNumberSolver

  attr_reader :init_number
  attr_accessor :unique_dials, :current_unique_dial

  # 1,2,3
  # 4,5,6
  # 7,8,9
  #   0

  LOOKUP = {
    '1' => ['6', '8'],
    '2' => ['7', '9'],
    '3' => ['4','8'],
    '4' => ['3', '9', '0'],
    '5' => [],
    '6' => ['1', '7', '0'],
    '7' => ['2', '6'],
    '8' => ['1', '3'],
    '9' => ['2', '4'],
    '0' => ['4','6']
  }

  def initialize(init_number)
    @init_number = init_number
    @current_unique_dial = ''
    @unique_dials = []
  end

  def find_unique_dials!
    dial(init_number)
  end

  private

  def dial(number, depth = 0)
    @current_unique_dial += number
    LOOKUP[number].each do |next_number|
      next if current_unique_dial[0..depth].include?(next_number)
      dial(next_number, depth + 1)
    end
    @unique_dials << current_unique_dial[0..depth]
  end
end

solver = NataliasPhoneNumberSolver.new('1')
solver.find_unique_dials!
solver.unique_dials