From the Foxger’s Den #9: Slitherlink (Domino)
or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between edgex mode where left click+drag draws lines and right click marks X’s and a line drawing mode to mark the dominoes.)
This is a “Twisted Tuesday” puzzle variation.
Theme: Double Domino – both domino-based clue groupings, and a domino-based loop.
Rules: Standard Slitherlink rules; also, the interior of the loop must be divisible into dominoes (1×2 rectangles) in at least one way without any overlaps.
Answer String: Enter the length in cells of each of the internal loop segments from left to right for the marked rows, starting at the top. Separate each row’s entry with a comma.
Time Standards (highlight to view): Grandmaster = 4:30, Master = 7:00, Expert = 14:00
Editorial Note: This puzzle is a fair bit more difficult than our usual Tuesday puzzles, but this may be a side effect of the new Twisted Tuesday format.
Solution: PDF
Will that domino thing influence the solve because only after drawing the loop , it is possible to divide the region?!I cant see how i can use that domino while solving. Ok after trying let me see!
By the way i thought the fox’ den was raided last week and there would be no more puzzles.Good to see that it is open again and more puzzle are being hacked out 🙂
You’ll need to consider the domino factor to get very far in the puzzle. When you start to draw enough of the loop, you can often determine, when one cell is part of a domino, which other cell must be too. The loop has to also contain this second cell which can affect the border. Also, certain kinds of loops will add just +1 cell versus +2 cells and may not allow any new domino to be placed. The thinking is very unusual, which is why this puzzle takes a longer time to solve as it is not just Slitherlink patterns.
Grant – nice puzzle. In addition to needing to think carefully about where dominoes might go, there were some nice slitherlink-clue-only situations that I hadn’t seen before.
motris – this doesn’t convince me that you’re right about the uniqueness discussion.
I didn’t think it would. I only said last week that I knew an upcoming puzzle would revive the discussion.
This is another one I’ll fit into “part” < "whole", so non-unique clue assignment does not diminish the puzzle itself. I'll note that one tester requested I make the "there can be more than one tiling" fact clear up-front as it led to a potentially faulty deduction. Saying only unique domino tilings are allowed is a much smaller puzzle space, adds an ability to use "uniqueness" now to avoid internal 2x2 open squares not yet tiled, and yet doesn't feel natural.
>> Saying only unique domino tilings are allowed is a much smaller puzzle space
This might be the essential disagreement that we have. I think the uniqueness requirement creates a different, possibly interesting, but not necessarily smaller, puzzle space. For example, the universal requirement that the solution be unique as a whole (with or without sub-uniqueness of parts) puts constraints on what constitutes a valid puzzle – ie where, what and how many clues are needed to uniquely encode the solution. Change the rules to require sub-uniqueness, and yes, it would seem that you are making things more restrictive (and therefore reducing the size of the puzzle space), but you are also opening up new puzzles (ie combinations of clues) that wouldn’t have been valid in the previous variant without the sub-uniqueness constraint. Different, not smaller.
Further, I would suggest that adding sub-uniqueness constraints may be a good idea in that, potentially, it leads to using logical reasoning in a way that most logic puzzles exclude. Using uniqueness to solve a puzzle is generally considered a cheat since the puzzle writer can’t rely on it to create the puzzle. However, if sub-uniqueness is coded into the rules, then both the solver and the creator are free to use it. Super-uniqueness (ie uniqueness of the full solution under the given rules and clues) would still be unusable by the creator and therefore discouraged by the solver.
>> adds an ability to use “uniqueness” now to avoid internal 2×2 open squares not yet tiled, and yet doesn’t feel natural.
Well, a couple of thoughts on this:
1. Sub-uniqueness may not be a good fit for this particular variant.
2. Your “ick” reaction may be due to your (and mine and the community as a whole’s) distaste for super-uniqueness deductions. Incorporating sub-uniqueness rules allows for the same sort of uniqueness deductions that you use when creating a puzzle to avoid problematic regions of clue space, but in a way that is consistent for solver and creator.
The sense of smaller I am always using is counting up the # of solutions. It is very difficult to count the # of possible puzzles, and even harder if not impossible to count the # of interesting puzzles. But these numbers will correlate at least loosely to the # of solutions for almost all puzzle types. Any other implications I make that “unique tiling” or “unique path” are less interesting come from my instincts as a puzzle designer with thousands of puzzles under my belt. And I have literally written a book on writing these kinds of puzzles.
In general, while uniqueness can be about the solution or about a particular part, as any form of rule it is very inelegant. I will never release a puzzle like this “Unique Slitherlink”. Does it have one answer? Yes, if you trust me. You can use uniqueness to find it, which limits the freedom of these basic clues like a corner 2 from two possibilities down to one. This is not a step forward for puzzle design on the grand scale.
What I find elegant about a puzzle is that the single rule in slitherlink that the loop uses N edges around each clue of value N lets a particular pattern have a single answer. I want to minimize extra rules, and particularly rules that explicitly limit possibilities. Which any uniqueness rule — meta to the solution or a component of the solution — is really doing to the solution space as a whole. The solver wants the freedom to go left or to go down but your rule says “no, you must go down”.
My instincts as a puzzle designer say, with “novelties” like this “Unique Slitherlink” or saying “it is not allowed for the path of a word to have multiple choices” as last week, you are really not doing much to move puzzles forward into interesting and not just esoteric places.
I can’t post this as a reply to Snyder’s comment because it’s too many layers deep but regarding “Unique Slitherlink”, the big issue with uniqueness logic is that one can take any solution and argue, “This is a valid solution. If the solution is unique, it must be this one!”
No Grant. In “Unique Slitherlinks”, a 2 in an otherwise unclued corner must have all 4 dots as part of the loop. I can prove it easily. Anything else would have more solutions and I said there was just one.
So all the answers you found are really just not smart enough to match wits with my incredible puzzlemaking.
Don’t you mean a 2 that doesn’t share an edge with another number?
Yes, while I was working to both shorten the indenting on my css style sheet, I was also editing my comment to say “2 in an otherwise unclued corner”. I need to stop engaging in sarcasm wars while updating the site to fix bugs.
Really? You just now figured out that there are times when sarcasm is unmerited? You meathead!
On a more serious note, it’s amazing how much discussion this puzzle has, and most of it isn’t about this puzzle specifically. Rex Parker said you’ll never see a Sudoku blog, but the discussion on this blog proves otherwise.
It’s also ironic that one of the most famous crosswords (and Will Shortz’s favorite) has two answers. Or at least did when it was accepted until history defined one.
>> In general, while uniqueness can be about the solution or about a particular part, as any form of rule it is very inelegant. I will never release a puzzle like this “Unique Slitherlink”. Does it have one answer? Yes, if you trust me. You can use uniqueness to find it, which limits the freedom of these basic clues like a corner 2 from two possibilities down to one.
But there’s a fundamental difference between using the super-uniqueness to solve the puzzle (inelegant solve) vs using the sub-uniqueness to solve a puzzle that has that explicitly as part of both the solving and the construction rules. You can’t construct “Uniqueness Slitherlinks” by using the uniqueness rule while you construct. That’s fundamentally different from what I’m suggesting.
What I find inelegant (no offense to Grant) is that in this puzzle, while the loop that I’m finding is unique, the other part – the positioning of the dominoes – isn’t. I have to come up with a solution that has a possible placement of dominoes rather than placing dominoes. This seems to violate at least the spirit of unique solutions that all other logic puzzles (implicitly or explicitly) have to abide by.
>> The sense of smaller I am always using is counting up the # of solutions. It is very difficult to count the # of possible puzzles, and even harder if not impossible to count the # of interesting puzzles. But these numbers will correlate at least loosely to the # of solutions for almost all puzzle types.
I’m not sure I buy this argument. The number of solutions may be less, but I don’t think that’s the right metric to measure the puzzle space. At any rate, you wouldn’t reject, say, Nurikabe if I could demonstrate that there were less possible Nurikabe solutions for 10×10 grids than there were Slitherlink solutions for 10×10 grids. Why? Because the logic in Nurikabe puzzles is different than the logic in Slitherlink puzzles.
I’m comparing close variants, not apples and oranges. So let’s take Nurikabe and Nurikabe that cannot have square islands. I’d prefer Nurikabe every day of the week. Nurikabe without square islands will have a smaller solution space than Nurikabe without a compelling reason to be constrained in this way. Unnecessary and inelegant constraints are the enemy. I don’t consider either of your argued for uniqueness constraints to be additions for the puzzles they appeared on. And most uniqueness rules, like the one I can apply to make my small example above work, are nasty things that contort logic instead of helping it to shine by standing in the background.
But if you do want to talk about rating different styles of puzzles, I do actually rate each puzzle style mentally with a number N of what I consider to be the necessary number of puzzles of that style before all the relevant space is well-mined. The world probably needs 1000 sudoku, no more, once you have the perfect set. Slitherlink may have a larger N than Nurikabe; it may have less. In my mind it is clear that Slitherlink deserves more puzzles than a one-off style like Domino Slitherlink. By many fold. And (Unique) Domino Slitherlink deserves even less.
But the WPC and other groups that explore such esoteric minor variants may view and rate puzzles differently from me. I’m not saying all variants are bad. I’m saying you must properly judge the benefits of any change and then make the appropriate exploration of the space. There is a functionally infinite supply of any puzzle type, but only a finite number of new and interesting experiences with each one.
Or the TL;DR form of this whole thread. If you asked me if this puzzle is better if I said “also, maximize the number of horizontal dominoes”, I would say no. Any such rule, however stated, is more than is necessary because the puzzle is a slitherlink and you have just one loop. On that we can agree.
I managed to botch the solve again. Would have easily made Master time otherwise. As for uniqueness, I personally think that a puzzle needs to have a unique solution, but that uniqueness should not be needed to make deductions, be it a “uniqueness requirement” or abusing the fact that a puzzle has a unique solution to rule out certain placements. Though, if I see the chance in a competition (or working with a number link puzzle), I will use such logic.
It’s a delicate balance. I state upfront that a “Grandmaster XXXXX will have a unique solution that can be reached by logic alone.” In other places where my puzzles get published no such claim is made and I sometimes get feedback like “I wish you said the puzzles had a single answer” which I guess means there is a lot of crap out there or that basic logic puzzle design rule is not well known.
But knowing there is a unique solution and using that fact to “solve it” are different things. My puzzle editor hat is quite different from my competition hat, and I do have to shut off many of my speed tricks nowadays. I’ve always said solving for fun is not the same as solving for speed. Uniqueness is not a fun argument to use, ever, in my opinion so it only matters for speed.
I find it rather surprising, since most of the puzzle books I have done assumes that the answers are unique. Maybe those solvers are coming in from something like brain teasers (ex. fox-chicken-grain and related puzzles) where uniqueness is usually not enforced.
The fox-chicken-grain puzzle has no solution, because as a fox, I can testify that we eat grain, too.
Maybe these solvers who don’t expect unique solutions are coming from that one Mystery Hunt puzzle where you have to count the solutions to the puzzles.
I’m with Thomas on this. The solution to this puzzle is purely the Slitherlink loop. I feel this is similar to the Inside Path Slitherlink by Palmer. I don’t remember if this discussion even came up there. For the domino tiling, uniqueness is such a strong constraint. And from a constructor’s point of view, it’s really hard to have to avoid the 2×2 area. So maybe as a fellow constructor I feel the same on whether this should be a problem or not.
What loop? The answer is xxx,xxxx,xxx,xxxxxx.
Sarcasm aside, now that you mention it, a good deal of what constitute as a “unique” solution depends on a lot on both the writer’s and the solver’s interpretation of a solution. For example, while the fox-chicken-grain’s solution is far from unique, the minimum number of crossings is.
I guess what I really want to say is this. If there is a solution manual at the back of the book, and I wrote my solution in the same style of the solution manual, then in no case should there be a difference if we have both done it correctly. Like in this case I am not bothered by the 2×2 square, as the answer string does imply the solution to be the slitherlink itself, but if the solution manual has a loop and dominos drawn, I would be rather bothered.
Really loved this variation. Once I started to figure out how the domino rule affected the solve, it sped up the process. I also finally started applying some of the other slitherlink techniques I’ve read about, but never really used. Really fun solve!
Very nice puzzle. The southwest corner gave me some trouble.
I wonder, though, if a puzzle could be made that uses the full set of dominos (00 – 33) as clues. Hmmm…
In my mind, there’s an unwritten rule that you can’t have two given 0’s sharing a corner or an edge in a Slitherlink. An exception is in MellowMelon’s Domino Slitherlinks, where some spaces are shaded and must be fillable with a full set of dominoes. Since the 0’s aren’t outright given, though, I don’t see it as a violation. (When I submitted this, I called it Interior Domino to distinguish it from MellowMelon’s variation.)
In any event, one of these puzzles with 28% fewer givens? That would impress me.
>> unwritten rule
Rules, especially unwritten ones about style, are meant to be broken, especially when theme outweighs other considerations.
Well, no one said the grid would have to stay the same size.
I liked this variant, and perhaps because it required some non-slitherlink logic, I found it easier than I find most hard slitherlinks (though my solution did require some massaging when I’d miscounted the number of walls adjoining one of the 2 clues).
The uniqueness argument above seems like a willfully ornery one in this case. I don’t feel this puzzle has any uniqueness flaws; the solver is looking for the unique slitherlink solution which is not impossible to cover with domino tiles.
On a separate note, is there a way for you to add the type of puzzle and any special rules to the PDF? I print these out in the mornings and may have forgotten (or in this case missed) any special solving rules or the fact that it is a Cave and not a Nurikabe, etc.
I don’t yet have a good automated way to add titles, instructions, or author names into the pdf images without me doing that manually in every time. After I’m another version ahead with my editing tools, as my book images will do such things as credit the authors, I will probably push those improvements into the pdfs.
I don’t believe any Cave and Nurikabe can be confused for each other. The number ranges are quite different in the two types (and Cave actually does not have a thick border as I present it right now). But I get the point that particularly with variations it can be difficult to solve if you don’t have them noted or the website handy. So I’ve added a text notation on the Tuesday/Friday mutants so far that can be confused for something else and will try to do that in the future.
Very tough puzzle.
I took a loooooooong time to complete.But had no fun while solving.
Difficulty :10
Fun level :0
What didn’t you like about this puzzle? Some helpful feedback would allow me to construct more puzzles towards your tastes.
First and foremost i felt this puzzle did not have a ‘certain flow’.For example i have battled with a single puzzle for more than 2-3 hours several occasions but i was always sure that the logic was somewhere within my reach and i will find it eventually.I had
I had none of that sort in this puzzle.It was as if i had been blinded in the dark in an unknown place and was asked pray god and hope for the best in this puzzle.
* At several places i used bifurcation to complete the puzzle being unsure whether it would complete or not.The domino thing did very little to help me solve the puzzle smoothly I remember only 2 or 3 places where it influenced the solve and it was very hard to find that.
* I initially tried using the domino thing but since i could not visualise the loop correctly,I presumed a number present outside the loop to be inside and was trying to use the domino thing and draw the loop accordingly(Of course i did not know that it could be inside the loop at that point of time).I went wrong several times because of that which made me doubt whether the initial slitherlink patterns that the puzzle gave rise to were done rightly by me.
*In the lower left half of the puzzle even though only 1 & 2 only were present ,i had a hard time trying to adjust the loop accordingly and at the same make this yucky domino thing work out.I dont know how many times i erased but you can completely believe me that finally when i completed i did not get that ‘jubilant’ feeling of completion which i got in other puzzles.The puzzle was desperately short of clues i felt.
Unfamiliar territory, such as new one-off variations, can easily make one feel like. I might have to start being careful with my next venture into the unfamiliar, lest I yield something unpleasant to solve. However, in defense of this particular puzzle, the domino rule plays a huge role, and there is a pretty linear solve to it. It’s merely an unusual variation that apparently caught you highly off-guard.
*feel lost. Could the doctor please doctor my comment? 🙂
One thing that I found helpful in this variant that also crops up in a couple of other Slitherlink variants is shading. The question of which part of the puzzle is “inside” vs “outside” is important, so I lightly shade the interior of the loop. It’s pretty common in this puzzle to have a forced domino extend the interior by one more square, and this gives you a nice way to quickly note that. Also I was lightly sketching in the actual domino tiles (but not full-size so they wouldn’t look like loop segments — sort of half size). From a loop standpoint, that means you can x out any segments that are inside your shaded region. The shading thing can sometimes help with seeing big complicated loops as well, although here that’s not really the issue — “loop” means “simply connected shaded blob”.
There really is a pretty nice logical path on this one, starting at the upper left and probably finishing with that “underclued” lower left.
For the record, the other slitherlink variants where I shade the interior routinely are sheep/wolves (certain squares are marked as sheep which must be inside the loop and others as wolves that must be outside) and various inside/outside variants (like “all the clues inside the loop are normal, but the ones outside the loop are reversed, so that N means 3-N segments”).
It wasn’t until recently that I started using shading as a technique on hard slitherlinks (I was obliged to use it on Palmer’s Mystery Hunt megapuzzle, which made me realize how useful it could be), and it was definitely key to solving this. I found it a very fun solve, with a nice back-and-forth interaction from slitherlink logic to domino logic.