Whenever he says, "Ah. Ahh, wow. Okay," you know something amazing is about to happen.

It's amazing how much easier this puzzle is in hindsight, with the knowledge of Phistomophel's Theorem in mind...

You almost discovered Phistomefel's Theorem.

Glad you enjoyed it :)

Brutal indeed, jellyfish into y-wing into skyscraper? *Oof*, I wasn't even aware of 2 of these patterns, and can't recognize the other on my own yet!

It’s crazy how he saw this grand pattern hidden in plain sight but didn’t notice a simple 8 in column 9

I was inspired by watching these for several months to finally try my hand at the puzzle before watching. It’s my first time ever trying a puzzle of anywhere near this difficulty. It took me over an hour, but I was able to solve it! Every time I spotted a trick, I could hear Simon’s voice in my head describing how it worked. 😅

He solved in 20 minutes. I took 90, using Phistomophel's Ring... I still have soooo much to learn and practice 😅

The intro music was... Entertaining.

Seeing the ring pattern appear at the 6:00 mark is even more significant now that a later video published in mid April revealed that these exact same digits most also appear in the four 2x2 corner boxes.

This was a great one! I got the jellyfish and an empty rectangle on 6s that did the same thing as the skyscraper, but while I found the Y-wing I didn't realize the full implications of it so I had to eventually find a logic chain that proved that at least one of r3c2 and r9c7 was a 5, which eliminated the 5 from the center of the Y-wing and got me the rest of the way there.

And while I'm thinking about it - thank you for creating this channel, Mark and Simon.

That central square outline highlights a recently found method as well, where the numbers in that outline must be the same numbers that appear in the 2x2 squares at the corners of the puzzle. There is no 3 in the central square outline, therefor there cannot be a 3 in row 9 column 2. So you can duck the jellyfish by applying an even more obscure property of the puzzle.

Great solve. Much appreciated.

Its so much easier to identify the x wing, y wing, and skyscraper on your puzzles! I still have trouble seeing it when I do my own. Thanks for another great example!

27:09 for me. Solved it very similar to you, getting the 6 in row 3 out of the skyscraper logic and unwinding the rest of the puzzle from there.

astonishing. Even if I'd seen the bent triple, I'd have never seen the jellyfish or skyscraper. I'd be struggling with endless chains. Genius to solve, genius to compile

The 3 can also be placed using Phistomefel's theorem. We can also place the 6 in a similar way (ie, instead of the skyscraper we use Phistomefel's theorem)

BTW: I've always wondered what a skyscraper pattern told me. Now I know. Thanks :D

Given the name of the puzzle, I was looking for jellyfishes, and found the one you discovered, as well as one in the columns (3,4,6 and 7, although ultimately they gave the same information). I didn't spot the skyscraper, but I was able to use an empty rectangle in the top-right box and eventually solve the puzzle in 21:08; which I am very proud of. I am getting better every day thanks to this channel!

The new intro music caught me by surprise! Why did you change it? :D

After a few months of watching I’ve finally done one of these hard classics in a half hour finally

At 6:00 "It feels like there should be something I should be appr3ciating about this". We all know now that's Phistomofel!!

I've been watching for a while, but this was the first I've tried to solve before watching the video. I got stuck at the point of the Skyscraper. I hadn't seen that technique before. I really enjoy these videos and it has given me a hobby. This channel is a delight.

LOVE the new intro music lol

I'm watching this a year later and I think, this would've been a much easier solve using Phistomefel's theorem/ring, because Simon got the middle square filled in quite early, so it shouldn't be an issue to fill in the corners which he didn't get resolved until the very end. But this video was recorded four months before Phistomephel's discovery, I think :)

The 5-6 pair on the left was a great setup for an empty rectangle in box 3 to eliminate a 6 in box 9. I didn't expect the skyscraper after how you've gone on about how much you love empty rectangles :)

I once got stung by a jellyfish when I was careless in placing a number 1

oh wow, i had no chance to spot that Jellyfish! i got upto there no problem, but then had to turn to the video. very good solve Simon!

14:59 by myself and I LOVED the reference to The Sting. My favorite Paul Newman movie.

Yes. that is my difficulty level - diabolic. thanks for the tips i.e. considering the numbers by column on its entirety...and process of elimination by column. I will apply that tip and trick!

The *sting* of a jellyfish is only *entertaining* when it happens to someone else. This puzzle teaches you to be careful where you *place* your *3's.*

Very happy to see a brilliant, challenging classic Sudoku on this channel. (not that I don't like the variants!) Managed to solve in 11:59, but I have to admit I probably wouldn't have noticed the jellyfish without the thumbnail hint and the 'stinger' reference... personally was a bit of a spoiler, but nevertheless really enjoyed solving this puzzle. Thank you once more!

I've never heard of this Jellyfish Pattern before. However, I've eliminated the 3 from cell r9c2 early on, by using the Phistomefel ring thingy. Once I got all the numbers in the ring, I noticed it didn't include any 3s. 1Subsequently, the outer boxes couldn't include any rings either, hence, no 3 in the cell. Of course, I got stuck later because I hadn't been able to figure the either/or elimination thing you've conjured up...

I used phistomefel ring (probably wasn't a thing when the video was uploaded) to solve it but I didn't see the bent triple so I spent a little too much time (65 mins) but I'm proud of myself! I'm new to this hard sudokus. :)

Clever find on the 2's. I would not have noticed that. Then again I'm a beginner!

managed to do it as per the creator's solve path, but paid the price, just over 90 mins!, had some naked singles missing then found the skyscraper, but then took me so long to find the jellyfish, and then the bent triple, but still very pleased i got the intended solve

This was really fun. The jellyfish and bent triple were the only exotic patterns I needed, once I saw that r3 had only one place for its 7. The rest of the puzzle just fell out for me. That jellyfish is really cool. I didn't know it had a name -- I think of it as the "N-Equations-in-N-Unknowns" rule -- 1 digit, in one of four places in a row and four places in intersecting columns. When its 2x2, we call it "X-wing". 3x3, we call it "Swordfish". Here, it's 4x4 (jellyfish). Of course, it leads me to ask if a 5x5 ever comes up and what its name is if so.

Oh wow, i didn't know about this jellyfish thing, thanks for giving me this new technique ! After having this one the rest isn't too bad

chasing that 56 around the board was intense. very proud of myself for solving this one.

I solved it much like Simon did, but I don't recognize jellyfish or skyscrapers. I can see "bent triples" sometimes but I think of them as "oh, one of those". I did not notice the unusual box in the center either. My big clue was that there were a lot of places that could only be a 3, 4, or 5, so I followed that lead using Ariadne's thread and was able to eliminate possible digits and solve the thing. I thank Mr. Neal for a great puzzle!

I'm watching this after you've shown the property for which the amount of each digit in the four 2x2 blocks in the corners must be the same than the amount of each digit in the square making the jellyfish, which helped me solve this puzzle since it made it easier to rule out the 3 at J2 without resourcing on the bent triplet because there was no 3 in the jellyfish square (leaving only the 45 pair) and helping spot the 6's positions without needing to resource in the sky crapper technique: having two 6 in the jellyfish square means there could be only two 6 from the four candidates in the corners' 2x2 blocks, so should the 6 were the one from the 1-6 candidates pair at the lower right corner, it'd be ruling out the other 6 in the same corner, the 6 in the upper right corner from being in the same column and the 6 from the lower left corner, leaving only one 6 among the four corners, that wouldn't match the number of 6 in the jellyfish block, hence the 1 must be in that cell instead, leaving one 6 in the same lower right corner (at J8) and the other from the 1-6 pair at the upper right corner, while ruling out the 6 from the lower left corner from being in the same row, leading to the right amount of 6 matching the amount of 6 in the jellyfish block. Hence it seems to me the property telling the amount of each digits in the jellyfish block must be the same than the amount of each digit in the four 2x2 corners seems to override the jellyfish technique altogether while helping cut corners.

Not that it made any difference in the path to finding a solution, but the threes formed a second jellyfish in columns 3,4,6 and 7. Very beautiful puzzle.

Woof, what a puzzle! Took me 56:38, and I had to get some video help to get past my first ever jellyfish and to point out the skyscraper, but after that was smooth sailing.

that was stunning

Yeah, I gave this a try. Ended up taking 3 tries with a total of 4.5 hours to solve. Didn't use any of those diabolical techniques. I have a lot to learn.

Interesting that for once I could do this reasonably quickly, once you mentioned the square. I used Phistomafel's square and corners to place the outer corner digits, and it all went swingingly after that!

02:56:11 - Yes, another one took me nearly 3 hours. But, no help, no hints. When I got to the point where so many 8's are pencil marked, I knew some were bogus, but didn't know the right logic to eliminate the bad ones. I noticed that regardless of which pencil marked 8 i pick in the West Box, the same 8 gets eliminated from the East Box. It pointed out a problem, so I tried it thinking that cell can never be an eight, but the puzzle broke trying that. So I went back and to where I tried it just using logic only, and eventually the other 8 in the East Box was forced by normal Sudoku, I kept making mistakes at the end unwinding the pencil marks, and had to go back to resolving the 1, 5 and 6 in the Southwest Box several times, before noticing one of the pencil marked 6's can't be a six and apply all logic as it arose. Finally, that worked out. Somewhere along the line after that I recognized a deadly pattern and used uniqueness to know which way to go,

I did try this alas to no avail! But I love the way you solve difficult puzzles.

I always solve the puzzle before watching the video, it took me 30 mins and 48 seconds, I only knew a few techniques like x-wing, y-wing and rectangle elemination, and i use rectangle elemination a lot in this puzzle. A lot of comments mentioned Phistomophel's theorem, I don't know what that is but I guess it's a pretty useful technique, so after this video I'm gonna search it up.

You missed a hidden pencil marked 3s in column 7. After you knew the 3 in row 7, the jellyfish removed the 3 from all other squares in box 9 except the 2 in column 7, which reduced the 3 in box 3 to row 3 a little earlier. But I don't know how much that would or wouldn't have helped you, though. You still did it better than I probably could have. Good job on the solve!

Great puzzle!

Simon, could you solve this puzzle again using the phistomofel ring?

First time actually trying the puzzle before watching the video. Got it done in about 28 minutes! ^^ (albeit, I messed up 4 squares at about 25 minutes, but was able to fix them)

just wondering, if I buy the app on steam, can I then download it for android aswell, or would I have to buy it twice? I mostly play on my laptop, but would be nice if I could play on my phone aswell, and save my progress.

1:08, I had to watch your video to see the relevant cells highlighted for spotting both the jellyfish and the skyscraper.

I was able to spot the A3 6 you spotted at the 21m mark, at your ~10m position, and that broke the whole puzzle open, and I'd finished it a minute later with just basic Sudoku pretty much. Except I used the positions of the 6's in rows 2 & 8 instead.

Anyone else looking at the phistomofel ring at around 13 and thinking okay what digits are in the corners. No threes. I actually used it to infer the 7 in R3C3, because Simon had one and I didn't. But I knew I needed one from the corner!

Great solving - unfortunately I did not spot jelly fish and XY Wing pattern! I would have had to go with the pairs ( 56 or the 37 ) and see how far it takes me using ARIADNES THREAD. Does anybody know about this ‘technique’?!

Missed the jellyfish, so didn't manage to solve without help.

...... although I have to admit that spotting the jellyfish and sky scraper is more elegant .....

At 11:12, went back to my puzzle and gave it a thought, and realized both of the columns and rows making up that square were missing 3, and the corners were at corner blocks. This means each corner has to have a 3 on either a row or column making up the square, and that's how I eliminated the 3 from r9c2

10/10!

This would have taken me 2 years, 6 months, 12 days, 4 hours, 12 minutes and 49 seconds to solve.

Pre-Phistomefel sudoku is so primitive, lol

Watching this after the whole Phistomofel's ring discovery is quite fun.

very proud i could find the jellyfish on my own. i had to sleep on the puzzle though haha, and I used the other 4 columns for the jellyfish instead of the 4 rows you used edit: i also used a skyscraper on fives in columns 2 and 8 instead of yours on sixes

what a good sudoku

After filling in the 1 and 9 in box 1, an empty recangle consideration for sixes gives the 6 in r9c8, which might be a bit easier than the skyscraper.

Amazing puzzle! Got around the Jellyfish and all by the pattern you discussed in a previous video. where the 16 cells around box 5 and the 4 2x2 squares in the edges have to match. i was able to elimante a lot of marks by this. well done Derek Neal! edit: found it: /watch?v=ZLcey7qiXv8

So clever, I’d never have seen that.

Quick question! @8:06 can't you deduce that a 2 can not go into row 6 column 9 because of the unique rectangle rule? Thus putting a 2 in row 7 column 9?

Beautiful... Are there also other pattern after Xwing Swordfish Jellyfish? Something with 5 rows and 5 columns?

It's incredible how easy they look when he starts to solve eveything, it's like "oh, yes, of course, that makes sense". The thing is, how to spot the patterns

I don't think the Phistomefel theorem was a thing at this time but going back and watching this you can actually deduce at 4:40 that the empty cells in the Phistomefel ring must both be 7s.

beautiful how the 3s unwind using geometry

I tried this app for the first time. I love how the pencil marks work. 21:40.

Is there a Xwing in this on 6s too? R2C3/9 & R8C3/9

It's actually not the center 3 but just the 16 cells around the middle box5 that rule out 3 from the 16 corner cells of the grid. So this must have been pre Mephistomefels rule being known to you, Simon. Once you have established all 16 numbers in the ring you unfortunately can't just sort them to corner cells, that varies, but there's no 3 in them, therefore no three in the corners.

Watching this after having watched the video about the 4 corners square are the same digit as the square around the centre. Would make it a lot easier

Nice

12:48 Simple Colouring Chain is possible now (D9 is 8 as hidden single).

I had never heard of jellyfishes and skyscrapers techniques to solve sudokus but I was proud to be able to spot them. Too bad I wasn't able to spot the bent triple as it was just what was missing for me to solve the puzzle!

The sudoku application you are using seems very practical, where can i have this application?, and the name?

6:00 you now know what it is, dont you :) 1h15m37s im slow but hey its nice to be able to solve sudoku without mastering none of those techniques. This is the 3rd hard sudoku that had a "crown" pattern. It helped me solve those without more advanced techniques. Tho I had to use proof by contradicton to eliminate the 6 from 56 in r7c1.

Instead of skyscrapper we could also go with the fin x wing on row 2- 8 col3-9 and the fin on row 8 col 1 which eliminates 6 from row 9 col 3 and the 6pair on row 8 col 1-3 as a result, eliminating 6 on row8 col9, therefore giving us 6 on row 9 col 8

Ragtime intro! Very Intriguing :)

4:54 - In R5, C8 you had a 7 screaming at you for a long time, because of the 37 restriction in C1 and the 7 in R9 C9. Solving that would have given you two 1's also.

You could have used the technique that uses the 16 numbers around the center are the same 16 numbers in the 4 corners. Phistomophel's Theorem

The same jellyfish was available on columns 3,4,6,7, which would have given you the same result - getting rid of that 3 from c2,r9, among others.

at the 12min mark, he finds the jelly fish. is there a second jelly fish in the above and below the box he highlighted? Row 1,2,8,9 and Column 3,4,6,7?

At 20:30, no matter which of the 2 positions the 6 is put in C1, the 6 in C9 ends up in RC29 through that forcing test.

I managed to spot a different skyscraper on the 6s, and eliminated the 3 from c2r9 using an x-cycle. But the bent triple still eludes me. It makes sense every time it's explained, but can't figure out how to use them myself.

would like to see you redo this puzzle using Phistomefel Ring.

10:00 -- It took me forever to figure out what to do with 35 at the bottom of C7 -- Its effect on B7 and B9 (blocks). If R9C7 is a 5, C2 has a 34 pair, and C3 has a 68 pair. Otherwise, if R9C7 is a 3, It forces R7 to have a 24 pair, forcing a 3 into C2. Either case, C3 of B7 can't have a 3. B7's 3 is in C2. Once you do that, you can go around the circle ruling out 3s and finally fixing a 3. Then another application of R9C7's 35 removes a 6 from B7, and this might crack the puzzle. (End of puzzle) It does. 14:00 -- Perhaps it might have occurred to me, now that you mention something similar, to rule out 3s from the corner 4x4 blocks using whats-his-name's theorem. Then if I ever recognize the pattern (or after you mention it), I could use the "bent triple" to rule out the 3s from B9's 234 pair. 19:00 -- B9 has its 3 in C7. B3's 3 must be in R3.

On row 2 6 can be only on c3 or c9 and because on column 9 6 can only be in r2 or r8 I used empty rectangle in box 7 on sixes to get rid of the 6 on r8c9. So for me it was jellyfish, y-wing and empty rectangle. Quite a repertuare of thecniques.

I'm not very good at these (slow), but here is how I solved it: R4&R6-C1 are restricted to a 37 pair. R7C1 is restricted to a 13 pair and R7C2 is restricted to a 34 pair. Therefore, R7C1 cannot be a 3 (because either R4 or R6 in C1 must be a three) and is a 1, which makes R7C2 a 3. Now R3C8 is also a three because of the x-wing consisting of R3 columns 2 & 8, and R7 columns 2 & 8, and this cracks it open. [In fact, you don't even need to use the x-wing once you realize that column 9, rows 2 & 8 are restricted to a 16 pair--then row 3, column 8 becomes a 3.]

Should the Phistomefel ring be called the Neal ring?

At 19:01 doesn't the skyscraper itself and the constraints on 6s already in box 3 mean that the only place for a 6 in box is r2c9? Because either r1c8 is a 6 which forces a 6 into r2c9 or r1c3 is a 6 which also forces a 6 into r2c9 in box by virtue of sudoku. I guess it's kind of the corollary of him saying that r1c3 has to be the 6

41:05 - I only noticed the jellyfish as "diabolical technique" - but at one point I used trial-and-error to eliminate one possibility.