404 ERROR: sudoku not found
- Normal sudoku rules apply.
- Dynamic fog: The grid is partially covered with fog. Correctly placed digits may clear the fog somewhere in the grid. Guessing is not required.
- Killer cages: Digits in cages must sum to the number in the top-left corner. Digits may repeat in a cage if allowed by other rules.
- Slow Thermometers: Along thermometers, the digits must increase or stay the same starting from the bulb. All thermometers in this puzzle have a unique colour.
- Arrows: Digits along an arrow sum to the digit in the connected circled cell. Digits may repeat on an arrow if allowed by other rules. There is one arrow in the puzzle.
- Odd/Even: Cells with a grey square contain an even digit. Cells with a grey circle contain an odd digit. NB: there is a grey square in R9C9 (it's a little hard to see).
- Renban: Digits along a pink line contain a set of consecutive digits in any order with no repeats.
- Digits separated by V sum to 5.
Solve it on CTC .
Old link with 5-sum cage instead of V-sum:CTC
Please feel free to ask any question regarding the puzzle in the comments and I’ll do my best to respond ASAP :)
Happy solving!
Lösungscode: Column 8, top to bottom. Answer should be 9 characters, no spaces.
am 17. März 2025, 05:18 Uhr von TheNineElements
@mnhuik
No worries! I definitely can understand why the "trick" could be missed entirely or misunderstood, especially if you haven't seen it in other puzzles before.
I am quite familiar with killer/FoW puzzles, and have seen this sort of trickery used in several puzzles before. I've noticed that this idea is becoming more popular in recent puzzles, but it does rely on a fairly concrete understanding of how killer cages are displayed & constructed.
I tried to respond to your comment *very thoroughly* in order to clarify how this works in general, since I suspect several other solvers will also reach the same point in the solve and then effectively guess the final digits. Since this trick is really a "meta" trick, it can be really difficult to figure out unless you've already seen it before or had it directly explained - so I hope my (slightly excruciatingly) detailed response will serve to inform you, and anyone else who gets stuck there, how to proceed.
I hope the very long explanation wasn't too intimidating, but I really wanted to ensure that the explanation could be applied generslly to other puzzles that use the same trick - which ended up being quite long.
Best of luck solving!
am 17. März 2025, 04:01 Uhr von mnhuik
@TheNineElements
Thank you for your patience,you truely helped me to find out that I erroneously ragarded the 1 cell as a cage.I shouldn't have arbitrarily labeled others' comments as fake,I apologize.
am 16. März 2025, 12:55 Uhr von Snookerfan
Nice puzzle! I had to get used to the different use of dynamic fog: usually a correctly entered digit at least clears the fog of that cell. It made me think I did something wrong constantly, but that's ok. The cage inside another cage was unusual, but I see you have changed that during my solve. Thank you
am 16. März 2025, 12:42 Uhr von graggle
Correcting a typo with the previous edit.
am 16. März 2025, 12:34 Uhr von graggle
Changed a 5-sum cage to a V-sum. This is purely a cosmetic change for the sake of clarity and does not affect the solve.
am 16. März 2025, 07:32 Uhr von TheNineElements
@mnhuik
I'm not the constructor of this puzzle, but any version of SudokuPad (whether on PC, mobile browser, or the standalone app) renders killer cages that intersect fog the same way. AFAIK the mobile app doesn't support dFoW, but the way killer cages are displayed around either type of fog is the SAME, regardless of the platform.
To answer your question: No, it is not different. And no, the comment is not "fake".
When you reach the point in the puzzle where you have a deadly pattern of three 1/2 pairs (with all other cells filled), you should see a 3×3 region of fog centered on R5C4. At this stage, you will NOT see any cage borders around cells that border the foggy region.
The way killer cages interact with fog is as follows:
- A cage border will only appear at the outermost cell of a cage IF AND ONLY IF that cell touches a non-caged cell.
- If a cell is inside a cage and does NOT display a cage border, then ALL of its orthogonal neighbors must also be in the same cage.
- If a cell does show a cage border on any of its edges, you can conclude that the adjacent cell (on that side) is not in the same cage. (Note that this does NOT apply to ANY cells on their edges that border a foggy cell)
Since the entire grid is enclosed within a large killer cage that sums to 404 - one less than the full grid sum of 405 - we know exactly one cell must be outside the large cage.
Now, if you look at the nonfoggy cells that share a border with the fog, you’ll notice that NONE of them display a cage border on their side that touches the fog. If ANY of the eight outermost foggy cells were outside the large cage, a border would be visible in the adjacent nonfoggy cells. This confirms that ALL of the foggy cells surrounding the center must be part of the SAME large cage. The ONLY foggy cell that could possibly be outside the cage is the one at the center of the 3×3 foggy region.
Using the sum of the large cage, along with the known location of the only cell that can exist outside of it, you can deduce its digit - which will resolve the deadly pattern.
As you mentioned, you didn't find or see any cage borders. This is intended behavior, and this is precisely why you can solve the final puzzle without guessing. Since you can see that the outer eight foggy cells are caged, you are left with only one possible cell that may or may not be in the same cage. But since you know that the large killer cage must have all of the sudoku grid contained, except for one cell, you need to ask where that cell belongs.
If you exmaine the the starting/initial grid before clearing any fog or placing any digits, you can see some of the cage cells already visible, and can see that the cage border is always displayed within a caged cell that is on the edge of the caged region. This might be how you could logically infer this behavior based on your given information.
Apologies if this was too detailed, but it was difficult to describe this behavior both accurately and comprehensively.
am 16. März 2025, 06:26 Uhr von TheNineElements
Solve Time: 36:28
I rated this 3/5 difficulty.
Nice dFoW puzzle that is definitely unique and had some nice early logic surrounding the slow thermos. The puzzle felt between a harder 2* and easier 3*, with the break-in difficulty leaning it towards 3/5.
I thought that break in (the early slow thermo and arrow logic) was neat. It had several clever ideas, and was probably my favorite aspect of the solve. The break-in was quite approachable, although the logic for the blue thermo (and how it interacted with the other clues) was a bit trickier than the rest, but still definitely within the 3* difficulty range for me.
The midgame was also generally approachable, although I did get stuck for a few minutes (about 2/3 through my solve) until I realized I overlooked a sudoku hidden pair. Also, the logic for the renbans was interesting, and they led to some other nice classic Sudoku tricks that resolved most of the puzzle for me.
The final disambiguaton was a bit goofy, but a fun idea for dFoW puzzles. As soon as I started the puzzle, I was fairly certain that the massive cage would be the "final" dFoW trick. Ever since I solved @gdc and @ChinStrap's "Cagey Architects", I've been on the lookout for those sorts of tricks - and I finally encountered one "in the wild". Even though I saw it coming, I did find it a bit confusing due to the embedded 5-sum cage in the much larger cage. I thought that, somehow, the 5-cage wasn't part of the 404 sum. Even though that is mathematically impossible, I did spend a few minutes reworking the math to confirm I wasn't crazy. Once I realized that the embedded cage contributed to the larger cage, it was obvious what it meant. I think this unusual cage embedding, plus the prerequisite knowledge of how killer cages render around fog, is what confused me.
Since a killer cage being embedded within another killer cage is very abnormal (along with the unusual use of dFoW relying on the cage), it may be worth noting how that is supposed to work in the description. I think using a 'V' clue to replace the 5-sum killer cage would have been more straightforward, but of course you would need to recreate the puzzle AND add an additional rule to the description, which some constructors and solvers may prefer to avoid. Not sure if you would want to make either of those changes retroactively, but it may prevent some confusion/ambiguity. Either way, this is fairly minor issue.
I think the rating % being so low is unfortunate, as it is overall a nice puzzle with several neat uses of dFoW. Ive noticed that dFoW puzzles (especially slightly harder ones) get generally lower rating %s by default. Perhaps the unusual killer logic led to a few solvers rating the puzzle lower - which would be really unfortunate because the rest of the puzzle was very nice & definitely worth giving it a go. Even with the abnormal killer cages being considered a "con"/issue, the 75% rating still seems unfairly underrated.
Overall I enjoyed the puzzle & it was definitely unique & interesting! Other than the minor hiccup at the end, I found the solve path to be smooth, approachable, and overall nice. Thanks for sharing!
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Graggle: Thanks for such a thorough comment! Whilst I usually might have been a little disappointed with such a low % rating, honestly I don’t really mind with this one – I half expected it. It is, as you say, a little gimmicky and goofy, hehe. Glad that you enjoyed it though!
Also, I agree with the comments about the embedded cage. I think I’ll change that.
am 16. März 2025, 05:15 Uhr von mnhuik
I finally got three pairs of 12 while the cell out of the killer cage was hiden in the fog,and then I have to guess. Comment told that the cell can be found by noticing the cage border of the fogged cells, I tried and I have to say that comment should be fake because I found no border can be shown in the fog.Is it different when playing moblie version or something?
am 15. März 2025, 18:43 Uhr von askaksaksask
Cool puzzle, a very fun way to clue something...i particularly enjoyed the thermo logic, but there were plenty of fun nuggets to enjoy throughout. Thank you!