Locust [Kropki Killer Sudoku]
(Published on 12. December 2020, 13:00 by Panthera)
-~-~-~-~-~-~
First, some background: these past few months, I have watched far too many videos from the lovely folks at Cracking The Cryptic, and through some sort of weird sudoku osmosis, I have somehow started to have my own ideas for puzzles. This is incredibly dangerous for someone whose usual wheelhouse is cryptic crosswords, but still. One of the videos in the past fortnight or so (I forget exactly which) prompted me to ask the question: "what would happen if you enforced Kropki constraints on the values of killer cages?" Answer: you'd get something like this Willy Wonka puzzle from back in September. It's a really good puzzle that was an absolute joy to solve, but it didn't quite require the sort of deductions that I'd expected from the constraint. This may be because my first instinct when considering the ruleset was "gee, this could be a fun way of testing people's basic algebra", a fact which tells you a lot about who I am as a person. The sort who'd let the word "fun" get within striking distance of the word "algebra", apparently...But I digress: I left a comment on Willy Wonka's puzzle, and got a very nice one back that motivated me to keep picking away at the concept. I drew a fair bit of inspiration from what I'd seen too, especially in regards to the potential actions of the negative constraint, and after a week or so of poking about I've finally wound up with a grid that I'm... proud of? There are some deductions in here that I'm pleased I was able to make work, and it even looks pretty neat too! The confinement of cages to their boxes and the symmetric placement of dots were self-imposed constraints that stemmed from my initial doodling, though I was perhaps a bit too much of a slave to symmetry - I didn't get to play with any particularly large cages like I'd wanted to as a result. Guess I'll just have to churn out a sequel at some point! Oh, and I'm absolutely prepared to explain the intended logical solve path on request... it definitely has one. Honest!
So yeah - big thanks to Willy Wonka for motivation, inspiration, and a convenient formulation of the rules that I still rewrote in my voice because, well, of course I did. Please do leave your feedback - as you may have been able to deduce, this is the first sudoku I've ever released, so I'd love to hear from anyone who dares tackle it. I hope you find it enjoyable, and good luck with your solving!
(p.s. - I named the puzzle Locust because it's a Kropki/Killer hybrid... so it's a KropKiller... sorry not sorry)
-~-~-~-~-~-~
RulesNormal sudoku rules apply.
The sum of digits within each cage, described by dotted lines, is its "cage total".
Where a white dot exists between adjacent cages, their cage totals differ by one; likewise, black dots appear between adjacent cages where one cage total is double the other. The negative constraint also applies - that is, all such dots have been given.
You can solve it on f-puzzles here; if you do, I recommend switching into "Setting" mode so that you can redraw the cages with their totals once you've deduced them. Alternatively, SudokuExplorer has very kindly set the puzzle out in Penpa, in case you find that easier.
Solution code: Row 8 and Column 8
Comments
on 15. January 2021, 01:07 by DiMono
This is a beast of a puzzle. Took me about 3 hours without random guessing, but I did eventually find I believe the intended logical path. The logic is there, but it's very well concealed in some places.
on 30. December 2020, 12:10 by nordloc
Algebra IS fun!
on 29. December 2020, 17:37 by RockyRoer
Whew! A beast! I resolved to solve it without hints -- though I may watch the video now to see some logic i missed :-) Loved Willy Wonka's first, and this is a worthy sequel!
After watching the video, it’s very beautiful!
on 27. December 2020, 16:36 by ICHTUES
A great puzzle. I solved it with my brother without the video in 4h.
on 15. December 2020, 09:39 by PrimeWeasel
Ok. I take everything back. Forgive me for thinking that you hadn't realized what you had created. This is much more sophisticated than I had anticipated. I just wasn't expecting such a clever construction when I started a 3 star puzzle from a newcomer. Thanks for the video. Looking forward to your next puzzle
on 15. December 2020, 08:32 by stephane.bura
Thanks for the video, Panthera :)
It's official, you're much better at this than I am ;)
on 15. December 2020, 01:38 by Panthera
Welp, folks, if you want to listen to me mumble my way through the mid-puzzle logic, starting at box 6 and moving on to the intended corner break-in, recorded for posterity in a single take of gloriously unedited video using my built-in mic that randomly drops out every so often... then please, fill your boots: https://youtu.be/Qty8LUlyABc
on 14. December 2020, 17:57 by medvitz
That was multiple days, and I kept thinking that I has in a deadly pair situation. Got there a few times, until I realized that I was overlooking that final constraint. Excellent Fun!
on 14. December 2020, 12:24 by Panthera
Very quick drop-in to say that, yes, I did know that box 6 had two options when I was setting the puzzle, and that bigger's latest observation is the one intended to set you on a course towards resolving that. I will see if I can't provide some sort of logic explainer later today, but for now I can only offer my apologies to those put off / frustrated by my deficiency in difficulty judgement, especially in regards to how tractable the corners are...
on 14. December 2020, 10:38 by bigger
I think I have to clearify one thing. Although the corner box are really annoying, box 4 can be logic out. box 6 not only made a 1 in row 5, but also make sure one of 89 is in row 5 of box 4, and that is definitely interesting
on 14. December 2020, 07:19 by bigger
agreed, box 2 and 4 is fine by me, but the corner box is just brutal. I tried all combination in box 7 and all have to go though all other corner box to find error. I really want to know if there is an actual logic way to crack the corner. it's so frustrating.
BTW since you think it a 3 star, I really want to see a 5 star (how hard can it be)
on 14. December 2020, 05:01 by stephane.bura
Sure :)
My troubles started when I noticed that there were two valid arrangements for box 6 (XYX and YXY) and four for box 4 and no obvious way to pick a combination among the eight ones they created. Since they affect the corner boxes differently, it takes a while to test hypotheses and, because of my luck, I had to go through all eight before finding the one that works.
The same thing occurred then with r4c3 and box 7 and 9.
Great first trial, though :)
A good puzzle can be hard, but it keeps you believing that there is a logical next step, even if you can't see it at the moment.
After a while with this puzzle, I felt I was stumbling in the dark. So, you can be more generous with clues ;)
Looking forward to your next puzzles.
on 14. December 2020, 00:47 by Panthera
Bumped up the difficulty rating based on feedback, and added SudokuExplorer's link to the puzzle in Penpa.
@PrimeWeasel - many thanks for giving me a chance, even if it didn't quite pan out properly! Turns out these corner boxes are giving folks more grief than I expected... and that I'm a terrible judge of difficulty!
@SudokuExplorer - oh, you're an absolute star! As far as I'm concerned, Penpa is some kind of dark sorcery... I've popped that link into the main puzzle text for anyone else who'd find it easier to handle.
@stephane.bura - well, consider me completely flattered! The logic of box 2 was the impetus behind the entire puzzle, so I'm left basking in the warm glow of your praise for it!
Did you note when it was in your solve that you had to resort to brute force? Based on my own assessment of the trickier bits and the comments received thus far, I'm beginning to develop a hunch. To avoid spoilers, here's an observation in rot13 that may also serve as a hint to those who are stuck:
Nsgre gur prageny guerr ebjf naq pbyhzaf, zl vagrag jnf sbe obk guerr naq pbyhza rvtug gb or gnpxyrq arkg; fcrpvsvpnyyl, gur gjb yvaxrq pntrf va obk avar nssrpg obk guerr'f fvatyr pryy pntr. Gb frr ubj, lbh zvtug jnag gb fgneg guvaxvat nobhg cnevgl.
on 13. December 2020, 21:00 by stephane.bura
After about the middle of the solve, I had to brute force the puzzle, so maybe I missed something. But I continued because the logic behind box 2 is just amazing!
5-star difficulty for me.
on 13. December 2020, 16:49 by SudokuExplorer
Here's a Penpa+ link: https://git.io/JINS7
(I usually find it easier to keep track of cases on Penpa+ for these kinds of puzzles)
on 13. December 2020, 13:01 by PrimeWeasel
I've spent a considerable amount of time on your puzzle, and it feels as though it is a great puzzle. However, I had almost completely filled it in, when I found out I had broken it somehow, and the problem is somewhere in the top right box I guess. I will get back to it later. Try this one people, so far the reasoning has been great. This deserves solves. It's definitely not 3 stars by the way.
