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    <p>Your overall approach is sound. I'm pretty sure the problem lies with your <code>make_canonical</code> function. You can try printing out the hands with num_cards set to 3 or 4 and look for equivalencies that you've missed.</p> <p>I found one, but there may be more:</p> <pre><code># The inputs are equivalent and should return the same value print make_canonical([8, 12 | 1]) # returns [8, 13] print make_canonical([12, 8 | 1]) # returns [12, 9] </code></pre> <p>For reference, below is my solution (developed prior to looking at your solution). I used a depth-first search instead of a breadth-first search. Also, instead of writing a function to transform a hand to canonical form, I wrote a function to check if a hand is canonical. If it's not canonical, I skip it. I defined rank = card % 13 and suit = card / 13. None of those differences are important.</p> <pre><code>import collections def canonical(cards): """ Rules for a canonical hand: 1. The cards are in sorted order 2. The i-th suit must have at least many cards as all later suits. If a suit isn't present, it counts as having 0 cards. 3. If two suits have the same number of cards, the ranks in the first suit must be lower or equal lexicographically (e.g., [1, 3] &lt;= [2, 4]). 4. Must be a valid hand (no duplicate cards) """ if sorted(cards) != cards: return False by_suits = collections.defaultdict(list) for suit in range(0, 52, 13): by_suits[suit] = [card%13 for card in cards if suit &lt;= card &lt; suit+13] if len(set(by_suits[suit])) != len(by_suits[suit]): return False for suit in range(13, 52, 13): suit1 = by_suits[suit-13] suit2 = by_suits[suit] if not suit2: continue if len(suit1) &lt; len(suit2): return False if len(suit1) == len(suit2) and suit1 &gt; suit2: return False return True def deal_cards(permutations, n, cards): if len(cards) == n: permutations.append(list(cards)) return start = 0 if cards: start = max(cards) + 1 for card in range(start, 52): cards.append(card) if canonical(cards): deal_cards(permutations, n, cards) del cards[-1] def generate_permutations(n): permutations = [] deal_cards(permutations, n, []) return permutations for cards in generate_permutations(5): print cards </code></pre> <p>It generates the correct number of permutations:</p> <pre><code>Cashew:~/$ python2.6 /tmp/cards.py | wc 134459 </code></pre>
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    1. POGenerating all 5 card poker hands
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    1. USDaniel Stutzbach
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    1. POGenerating all 5 card poker hands
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    1. COThanks! Can you provide a brief description of how the canonical test works? I think I get the basic idea, but a description would be awesome.
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      1. USNick Johnson
    2. CO@Nick: Sure, I've added a docstring to the `canonical` function in my answer.
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      1. USDaniel Stutzbach
    3. COGreat answer, thank you! Actually, there is a reason to generate the canonical hand rather than just test for it: some hands have more isomorphisms than others, and knowing how many there are is important in order to know how many 'real' hands each corresponds to.
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