Find all unique solutions to the 4x4 playing cards puzzle

euler_square.rb

class Array
  def no_duplicates?
    tally.values.all? {|v| v == 1 }
  end
end

class Card
  attr_reader :picture, :suit

  def initialize(picture, suit)
    @picture = picture
    @suit = suit
  end
end

class Board
  attr_reader :cards
  def initialize
    @cards = Array.new(16)
  end

  def valid?
    card_lines.all? do |card_line|
      card_line.compact.map(&:picture).no_duplicates? && card_line.compact.map(&:suit).no_duplicates?
    end
  end

  def display
    cards.each_slice(4) do |card_row|
      card_row.each do |card|
        if card
          print "#{card.picture}#{card.suit} "
        else
          print '-- '
        end
      end
      puts # new line
    end
  end

  private

  def card_lines
    [
      # rows
      [cards[0], cards[1], cards[2], cards[3]],
      [cards[4], cards[5], cards[6], cards[7]],
      [cards[8], cards[9], cards[10], cards[11]],
      [cards[12], cards[13], cards[14], cards[15]],

      # columns
      [cards[0], cards[4], cards[8], cards[12]],
      [cards[1], cards[5], cards[9], cards[13]],
      [cards[2], cards[6], cards[10], cards[14]],
      [cards[3], cards[7], cards[11], cards[15]],

      # diagonals
      [cards[0], cards[5], cards[10], cards[15]],
      [cards[3], cards[6], cards[9], cards[12]]
    ]
  end
end

@solution_count = 0
def solve(board, available_cards)
  missing_card_idx = board.cards.index(&:nil?)

  if missing_card_idx
    available_cards.each do |chosen_card|
      board.cards[missing_card_idx] = chosen_card
      solve(board, available_cards - [chosen_card]) if board.valid?
    end
    # we reached a dead end! Backtrack...
    board.cards[missing_card_idx] = nil
    return
  end

  @solution_count += 1
  puts "\n\nFound solution: #@solution_count"
  board.display
end

board = Board.new

PICTURES = %i(A K Q J)
SUITS = %i(C H S D)

available_cards = PICTURES.product(SUITS).map { |picture, suit| Card.new(picture, suit) }

board.cards[0] = available_cards.find { |c| c.picture == :A && c.suit == :C }
board.cards[1] = available_cards.find { |c| c.picture == :K && c.suit == :H }
board.cards[2] = available_cards.find { |c| c.picture == :Q && c.suit == :S }
board.cards[3] = available_cards.find { |c| c.picture == :J && c.suit == :D }

solve(board, available_cards)