The Zotmeister

solving the puzzle of life one entry at a time

Jan. 7th, 2011

03:13 am - Puzzle 52: Heartbreaker


"I couldn't follow suit," Tom said brokenheartedly.


- Adam R. Wood, original Tom Swifty

I love playing cards. I love collecting them; I love handling them; I love playing games with them; I love giving (and receiving) decks as gifts. I had to make Puzzle 52 based on playing cards. The problem was that there weren't any appropriate types of playing-card-based puzzles that I was aware of and liked... so I invented my own. Took awhile, but I'm quite happy with what resulted. Inspired by various card games and based on a fairly awful pun, I submit for your entertainment Heartbreaker:



To the left is an unsolved sample puzzle; to the right is the same puzzle with all the fun pre-removed. In addition to the solution (in blue), I also highlighted (in green) the heartbreaker in order to make explaining the rules (and the sample solution) that much easier.

The concise instructions: ...actually, I'm not going to bother this time - this is one of those puzzles, the kind that are relatively simple in execution but for which a rigorous explanation of the rules is, well, a real heartbreaker. Hopefully this will do:

  1. Each cell of the grid is to hold a playing card; the deck in use will be defined in the text accompanying the puzzle. Each card of the deck is to be placed in exactly one cell; the object of the puzzle is to determine the position for every card in the deck.

  2. Some cells may have a rank, or suit, or both depicted in it; the card placed in such a cell must match what's already there.

  3. Loops (in the style of Perfect Fit) may appear around some cells. I call these 'cardtouches', as Egyptologists could use a clever pun after all the obvious 'mummy' jokes and I'm going for broke on pun overload already anyhow. The cards to be placed into the cells inside a cardtouche must make a valid Rummy meld - that is to say, they must either be (a) [a 'set'] all of matching rank, but each a unique suit; or (b) [a 'run'] all of matching suit, but in sequential ranks (although the physical positioning of the cards doesn't have to match that sequence). Remember that aces are only sequential to deuces for this purpose - aces are always LOW in Rummy!

  4. Some rows and/or columns may have "signs" (a labeled arrow) pointing at them. The labels are all Poker hand ranks; the labels for the standard ranks, from weakest to strongest, are: N, 1P, 2P, 3K, S, F, FH, 4K, SF. [I'm not beyond using freak hands if they will make for an interesting puzzle; I will define any label other than these in the text accompanying a puzzle that uses one.] The strongest Poker hand that could be made with any combination of up to five cards from the row/column a sign points to must match that sign's label.

  5. Every Hearts penalty card - cards of the heart suit and Queens of Spades - must be part of a snake. That's a technical term puzzle veterans will recognize: the cells of a snake must form a chain, each orthogonally adjacent to the next. Snakes cannot touch themselves - that is to say, cells in the snake can only be orthogonally adjacent if they are consecutive in the chain, and can only be diagonally adjacent if they are two links in the chain apart. [Alternatively, they cannot comprise any two-by-two blocks of cells, nor can they enclose an area on all sides (that is, not using a grid edge to do so) leaving that area orthogonally disconnected from the rest of the grid.] If multiple snakes are to appear (as would be the case if a double deck were prescribed), they can't touch each other, either - cells belonging to different snakes cannot be adjacent, not even diagonally.

  6. Each snake must have exactly one of every rank of heart, which must all be physically in order in the snake, from ace down to whatever the lowest-ranked heart in the deck is. Remember - Ace is always HIGH in Hearts!

  7. Each snake must also have exactly one Queen of Spades as well. However, it can appear ANYWHERE in the chain - before the ace, after the lowest card, or anywhere in between, interrupting the otherwise perfect sequence of hearts. You guessed it - just as some play the card game, the Queen of Spades breaks hearts. I told you it was awful.


The deck for the sample puzzle is a mere twenty cards, just Ace through Ten in each of the four standard suits. This means it must have exactly one snake of exactly six cards, basically a heart royal flush in order with a Queen of Spades tagging along or butting in. Look at those six cards in the solution above and you'll find they're wrapped around the top of the central gap; the Spade Queen is between the Heart Jack and Ten, but the hearts are otherwise in order - Ace, King, Queen, Jack, Ten. This is what needs to happen.

That '3F' is for "three-card flush" - that is, the three cards in that column need to be the same suit. (Technically, they can't be sequential ranks either, as then it would be a three-card straight flush, but that isn't important for this puzzle.) It's actually a fairly illuminating sample puzzle - one of my better ones in my opinion - and should prove an interesting solve if you want to tackle it yourself. Of course, if you would just like a walkthrough - and after that rules definition, I wouldn't blame you - that can be arranged:

How to solve the sample puzzle )

This first full-size Heartbreaker uses a standard 52-card poker deck. In some ways it's actually easier than the sample - I tried to keep it cute as opposed to educational - but I did manage to highlight a few curiosities. Certain possibilities came to mind as I composed it, so I'll have some tricks up my sleeve - uh, no pun intended that time - for the next one. Actually, maybe the one after next, since I'm probably using a Pinochle deck next time... - ZM


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Current Music: various songs titled "Heartbreaker" (see inline comments)
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