A Sudoku That Teaches You A Discovery

** TODAY'S PUZZLE **
A very clever sudoku today that teaches you something you probably didn't know and/or realise! The puzzle's called Downward Spiral and it's by a collection of setters calling themselves The Sudoku Skunkworks (!). We believe the 'skunkworks' is made up of Virtual, Sotek, XeonRisq, Bremster, Riffclown, and Eclectic Hoosier. Give it a try at the link below:
app.crackingth...
Rules:
Normal sudoku rules apply. Digits on a purple line must be a set of consecutive, non-repeating digits in any order. Cells separated by a black dot contain digits with a 1:2 ratio. Cells separated by a white dot must contain consecutive digits. Not all possible dots are given.
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[@virtual256]

Simon, on behalf of this chunk of the Sudoku Skunkworks, thank you for the lovely solve! The discovery you identified came out of a collaborative setting session where we had 6 setters in a voice chat and started playing with an empty grid, some renban lines some Kropki. Once we found it, we knew we had to make a puzzle worthy of the discovery! Also, hearing you utter the same words we did when we found it in the first place made my day. So glad you enjoyed the puzzle! The Skunkworks itself has many more folks than just the 6 of us, we happen to be the ones who hopped in and started exploring together. Cheers! ~Virtual

[@riffclown8909]

100% Echoing What Virtual said. The energy in the Sudoku Skunkworks is unbelievable. Loved the solve. Expect more to come. "There's nothing you can say about a 4 cell Renban.". hehehe

[@sotek2784]

I will say, though, nothing beats the dramatic irony of Simon's "There's nothing, really, we can say about a 4-cell renban" at the start of the solve. :D Such a fun discovery, and a lovely showcase of our repeatedly-refined puzzle to showcase that discovery :)

[@pouletbelette]

Very nice puzzle! Well done all of you and thank you!

[@SolverTom]

Really beautiful use of the 4 cell renban observation. Incredibly elegant throughout the puzzle. Well done to the skunkworks!

[@emilywilliams3237]

Enjoyed this puzzle very much - thank you, Skunkworks!

[@taniabn]

Two months ago I could never solve this puzzle. But I've been binge watching Simon's videos and I decided to try this one before watching Simon do it. It took me 62:45 to complete all by myself. It wasn't the quickest, but I'm pretty pleased that I manage to solve it at all.

[@EntirelyPointlessContent]

Very nice. I was also scared because of the >30 minute video length but also got it, unfortunately a bit closer to 2 hours!

[@DevonParsons697]

Simon, you've really mastered explaining the rules and providing example situations for people who are new to the channel. I think that's a big factor in how well the channel has grown. It's a very welcoming and open community with plenty of acceptance and guidance for new members.

[@samuelcardwell577]

And I'd add - it doesn't get annoying for repeat viewers. Okay, I tend to skim forward the first couple minutes to get to the action, but I never tire of hearing about "the secret" or "a complete set of the digits 1-9" because he explains it so quickly and charmingly

[@longwaytotipperary]

Well said!

[@emilywilliams3237]

I completely agree. Having been fairly new to variants when I started watching the channel last summer, I now can explain the rules to the standard ones quite well, and even can "prove" the Phistomefel theorem with exactness, having heard Simon and Mark do it so often. I will add, also, that the Discord server is also very good for people new to the channel and to variant sudoku, or for people very familiar with all of the nuances possible and desiring a greater challenge.

[@bobblebardsley]

All of the above AND I appreciate that the explanations (eg of the Phistomefel ring) get more elegant over time too as Simon becomes aware of less complicated ways to explain them. So anyone joining the channel always gets the easiest way to learn and understand every rule or technique, rather than an unnecessary "this is complicated and you won't understand it..." just for the sake of sounding clever.

[@piarittersporn]

It is so divinely wonderful when Simon expresses his explanations with his dancing arms and happy face, with full fervor and enthusiasm. I hope that my insufficient English was enough for a correct and understandable formulation.

[@emilywilliams3237]

I completely agree.

[@piarittersporn]

@@emilywilliams3237 That makes me very happy.👍🙂

[@dmdeemer]

Your "insufficient" English is more erudite than a lot of native speakers I know.

[@piarittersporn]

@@dmdeemer That's very kind of you. But I must admit to use a translator sometimes, because I don't know enough vocabulary.

[@alexandraritter3542]

@@piarittersporn Composing a natural translation, even with a translator, is no small feat. Your English is excellent.

[@SMTRodent]

"We need to do sudoku!" he says as if it is a completely new idea. I am so loving this solve!

[@boristolokonnikov5172]

Simon, please, do use more of those toffish words like panache and recalcitrant - don't only exercise us in sudoku, but also in vocabulary :) P.S. "As useful as a chocolate teapot" is now one of my favourite idiom thanks to you

[@bobblebardsley]

I agree, Simon's vocabulary is quite salubrious :)

[@boristolokonnikov5172]

@@bobblebardsley as in "good for one's health (mind in this case)"?

[@bobblebardsley]

@@boristolokonnikov5172 Yes (it was the most fancy sounding word I could think of...!)

[@cloud_strife_9999]

Thank you very much for the shout-out Simon! While it is true that I try to be a good solver, I can think of a lot of people who are better solver than me. Perhaps my name is familiar to you because of the e-mails I sent to you with my entries to Sam Cappleman-Lynes's and Philip Newman's solving competitions (the latter of which just a few days ago).

[@HelloNotMe9999]

And now we have the Skunkworks Theorem.

[@Jostradomas]

Really love your work! Watching these puzzle solves has become my go to entertainment when im doing sudoku at my desk. Hearing you solve these monster puzzles helps me think of the simple sudoku's im doing in new ways and solve them faster! Thanks and keep up the awesome work!

[@HunterJE]

Interesting that Simon starts with parity to get the possible arrangements of the top left, while my immediate insight upon looking at the grid was totally different logic reaching the exact same conclusion - namely, only two of the possible black dot combos on a four cell renban work with a white dot on the other two digits. 12 are themselves adjacent and so you can get away with putting the other two "outside" as a 34, while 36 have two digits between them, so the remaining adjacent adjacent pair can fit in between as a 45; 24 and 48 break because there's either too little or too much room between to fit a white dot pair while making the renban work.

[@HunterJE]

Although I guess come to think of it this is kind of the same as the parity argument looked at another way - the black dot digits can't have an odd number of digits between them to accommodate the white dot, which is another way of saying they can't have the same parity...

[@olivier2553]

@@HunterJE The impossibility for 48 does not even need the white dot. There just cannot be any 4 and 8 on a four cells renban because four cells renban (they would need to put 5, 6 and 7 in the remaining two cells) The 36 spiral was very elegant..

[@spderweb]

Watched you figure out the beginning and then worked most of it out afterwards on my own. I'm definitely enjoying following along and trying to take over for myself. I'm used to just normal Sudoku, so these have been, as you say, quite interesting.

[@G.Aaron.Fisher]

Kudos on how many times TSS was able to fit the same trick into one grid in slightly different ways.

[@jetzeschaafsma1211]

Five hundred and twenty five days!!! That's how long ago I funded the Kickstarter. And finally, yesterday, I was able to pick up the book! And it's fantastic! Beautiful effort, Mark&Simon&team!!!

[@MattYDdraig]

14:16 Insane how cleanly that unwinds once you spot the break-in! Magnificent.

[@B1GB1RDB4G3L]

Your enthusiasm and appreciation for good suduko setting makes me smile :)

[@alarictaqiarentza9451]

13:04 solved for me. Really happy with my time today. Very very clever puzzle!

[@julieannmyers8714]

Wow! 👏👏👏

[@L-po8rx]

13 minutes is crazy. It took me 81 minutes to solve. Well done!

[@alarictaqiarentza9451]

@@L-po8rx Thanks. I've been following the channel and solving sudoku for almost 2 years now. So it definitely helps a lot and probably also happen to get lucky to spot the break-in right at the start. :)

[@bobblebardsley]

Out of interest do you know where exactly you started? Curious if on a solve that fast, you started on that bottom black dot or not? Nice work either way!

[@alarictaqiarentza9451]

@@bobblebardsley Hope this answer your question :) SPOILERS: Started with black dots in B1. 12 / 36 is the only valid option since it must have 1 odd & 1 even forcing R1C1 & R2C1 must have 4. This forced black dots in B7 to be 12 / 36, same logic forcing R8C2 & R8C3 must have 4 and forcing black dots in B8 to be 12 / 36. 12 option for B7 black dots break black dots option for B8. This fix all previous candidates for black dots & renban in B1 B7 B8. A few moments later I realize a 4 cell renban must have at least 1 of 36 and immediately place 36 in R2C9 and I manage to placed all 36 in renban after that. Unlike Simon, I prefer to do a lot of pencil marking since it have a very limited option and that helps me to spot the restriction better.

[@ritchards]

Since Simon is always reluctant do to Sudoku in a Sudoku puzzle, his greatest nemesis is then... A Classic Sudoku! ;) ;) ;)

[@markp7262]

Nah, because in a classic, there nothing else to do. Give him one rule that's only used once at the end, and he'll be flummoxed.

[@purpleli4760]

@@markp7262 I would love to see that.

[@dmdeemer]

At 28:48, you can remove the 2 from r9c7, then the 4-5 pair chain in r3c7,r9c7,r7c9,r7c6 means that r3c6 cannot be 4 or 5, and must be 7. Saw something similar on 1s and 2s earlier, but it didn't seem to be as helpful. As for me, I couldn't spot the break-in, so I "solved" on one screen while playing Simon's solve on the other. That's a really fun way to play along, and if you don't allow yourself to pause it, it limits the amount of your day that you've lost to sudoku.

[@ZeroCiaran]

I can barely solve a normal Sudoku but watching you power through these, discovering each cell is always super enjoyable. I love the content here on the channel, keep it up!

[@bensballsofyarn]

I've been watching Simon's videos for about a month now and decided to try and actually do one of these sudokus myself. I tried this one and it took me 5 attempts and over 9 hours but I did it!!! 😁😂😭

[@_-_-Sipita-_-_]

36:52 for me. while the first 20 minutes i was sleepy and clueless of what to do, i found that really specific trick, the first 2 numbers of my time says it all.

[@bobblebardsley]

I choose to believe it took you 36:52.5 just to maintain the 1:2 ratio on both minutes and seconds :D

[@alainculos9294]

A fabulous puzzle for sure and just as good a solve. What never ceases to amaze me, other than the setting and solving genius at play here, is that when one can and does solve the puzzle before watching the video, it almost invariably seems unbearably slow - despite having solved it in at least double the time and much less elegantly - and not spending any time carefully wording great explanations! Yet on those frequent enough occasions when I do not find my way through the puzzle, the video seems unbearably fast, even a long video!

[@bobblebardsley]

Every time I hear 'setter' I think of the dog breed so "this is by a team of setters" is extremely enjoyable to imagine.

[@emilywilliams3237]

haha I can conjure up this image very well!

[@xeonrisq2919]

If they could also be playing poker... that would just put the icing on the cake!!

[@therocknrollmillennial535]

25:49 for me today. I was a little slow working out the Kropki but I will blame my stepdad for blasting his music and distracting me--unintentionally--with my favorite song (All My Love, Led Zeppelin). Thank you to Skunkworks for the lovely puzzle! And thank you, Simon, for the wonderful guidance through these puzzles!

[@adrianhead6272]

Giving clues in the sudoku name make them far much easier - the "spiral" is clearly significant. Completed in 18m32s.

[@ericpraline1302]

Very nice puzzle, thanks. Interesting how the renbans resolved themselves.

[@MegaGamer21]

simple and yet beautiful. this is the type of sudoku i enjoy the most

[@bristolrovers27]

Excellent puzzle Skunkworks produce great puzzles from approachable to omg

[@inspiringsand123]

Rules: 03:48 Let's Get Cracking: 06:16 Simon's time: 27m34s Puzzle Solved: 33:50 What about this video's Top Tier Simarkisms?! Maverick: 2x (00:27, 08:29) Phistomefel: 1x (06:20) And how about this video's Simarkisms?! Ah: 18x (08:50, 10:58, 12:31, 12:33, 13:58, 15:54, 18:00, 18:17, 23:15, 24:36, 25:13, 25:52, 26:37, 27:51, 28:18, 28:55, 30:09, 33:05) Beautiful: 9x (00:18, 02:07, 13:24, 13:38, 14:12, 15:36, 16:57, 34:14, 34:33) In Fact: 4x (09:32, 10:55, 16:25, 18:42) Lovely: 3x (14:17, 14:17, 34:38) By Sudoku: 3x (22:18, 25:39, 32:53) The Answer is: 2x (16:09, 26:44) Extraordinary: 2x (01:30, 01:32) Panache: 2x (14:52, 14:54) Nature: 2x (19:17, 21:41) Good Grief: 1x (32:14) Sorry: 1x (00:21) Out of Nowhere: 1x (32:31) Clever: 1x (32:22) I Have no Clue: 1x (05:55) Stuck: 1x (24:05) Deadly Pattern: 1x (19:35) Gorgeous: 1x (34:57) Approachable: 1x (01:26) Hang On: 1x (24:21) Magnificent: 1x (01:45) Surely: 1x (12:54) Obviously: 1x (33:15) Intriguing: 1x (03:16) Progress: 1x (11:20) Wow: 1x (21:23) That's Huge: 1x (32:39) Most popular number(>9), digit and colour this video: Ten (3 mentions) Three (96 mentions) Black (18 mentions) Antithesis Battles: Odd (9) - Even (6) Black (18) - White (6) FAQ: Q1: You missed something! A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn! Q2: Can you do this for another channel? A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!

[@tessabrisac7423]

Wow, almost no “sorry” today, that is telling much about the puzzle and the solve!

[@DaedalusYoung]

@@tessabrisac7423 And the one that _is_ in there wasn't even from the solve.

[@Timlagor]

Thanks for posting this

[@Ulija100]

The discovery was very nice, though took me a bit longer than Simon, but it was a delight to find. And then of course the fun of watching the video to see when and how Simon finds it, and his reaction!

[@boman987]

As an Indiana native, I am goin to pronounce Hoosier this way now.

[@jakobr_]

37:14! It was fun to realize that all of these renban lines had to have either a 3 or a 6 on them if not both

[@facilvenir]

Loved the puzzle. I don't know what the discovery is, so I'll have to watch to the video (as if I need an excuse), but I still enjoyed solving it.

[@Aliessil]

36:43 loved that one, and really pleased with my time!

[@bentomkins9905]

Simon, thank you for taking time out of your day to send your birthday wishes; I do hope my wife wasn't too pushy in asking you! Today's puzzle was particularly fun so thank you for introducing us to it.

[@kathyjohnson2043]

Bird songs are a bonus!

[@kathyjohnson2043]

Hello from "Hoosier" country: Indiana USA. (Hue-zer or hoo-zer)!

[@emilywilliams3237]

I did have to do a double-take to be sure of what word he was pronouncing in that lovely French way. And then chuckled, but only a little bit because overall I love the unique English pronunciations of so many words that Simon and Mark have.

[@Phoenixcaptain46]

I picked up that as well! haha

[@eclectichoosier5474]

Hello!

[@andrewpalmer5189]

I think I have a peculiar knack of finding the hard way to solve these, rather than the easy way. This took me a good couple of hours. I didn't catch on to the break in and only realised it when I watched the video after I'd solved the puzzle. I need to improve my logical thinking!

[@stevesebzda570]

Lol [@11:32] Oh, Simon. You LUV busting on Mark. Lol : )) 😂

[@th.nd.r]

Incredible setting, great solving, a few really nice steps, awesome aesthetics, and THE DISCOVERY WOW. Very cool!

[@ocaly]

52:08 for me but i took a break in the middle so probably around 40 minutes. it was indeed nice to discover that either 3 or 6 has to go on the 4 renbens and the 57 pairs it created

[@WyanetJ]

"By the power of sudoku." 👌🏻👏🏻😁

[@JalebJay]

17:55 Very nice break in, a lot of coloring was used, and probably wasn't needed.

[@PathOfShrines]

Neat idea! I got caught up for entirely too long after forgetting about the white dot in box 7. 37:01

[@markp7262]

23:06 finish. Very fun, and interesting path around the downward spiral (enter gratuitous Nine Inch Nails reference here)!

[@dearmash]

The birds at 15:50 reminded me of the witness streams.

[@PapaDrom]

No no, Thank you!!! :D You guys rock! (Simon, Mark, the setters, the solvers, the watchers)

[@Gonzalo_Garcia_]

17:15 for me. Very nice puzzle, I loved it when I realized I had indeed found ‘the discovery’!

[@Swisswavey]

Lovely puzzle, thank you. I'll check the video to see what I should have learned...

[@e7diablo]

Can we agree that explicitly stating the negative constraint does NOT apply isn't necessary? He doesn't feel the need to mention that a random unmarked set of 4 adjacent squares could also be a renban set even though it doesn't have a purple line in it. My brain's default setting assumes any rule applies where it's mark is and doesn't think anything about unmarked areas, unless you specifically say otherwise (e.g., explicitly saying "ALL black dots are given" when the negative constraint is in play).

[@RichSmith77]

You can certainly have my agreement. Although usually the wording of the white/black dot constraint makes it unnecessary to even say "all dots are given" for the negative constraint. "All pairs of consecutive digits are marked by a white dot" implies negative constraint, "all white dots mark a pair of consecutive digits" does not.

[@Kinada]

Something about this puzzle was really hard for me and it took me much longer than I thought it would. Had to take some breaks but got through it eventually.

[@annawilson6779]

Loved this one!

[@longwaytotipperary]

Very nice puzzle!!! It's a beautiful day here as well!!

[@Sam_on_YouTube]

Solved in 43 minutes. Pretty happy with that time.

[@Coyotek4]

23:11 ... an interesting combination of two rulesets. Nice puzzle!

[@JASPACB750RR]

Simon, Can you do a live stream where you talk through the logic, but only input cells into the grid that are agreed upon and voted in by the chat? So we get to hear your voice, watch your beautiful mind work, and have your wisdom there to help “coach” us less experienced solvers complete a hard puzzle. Granted, there are probably not very many novice solvers in this community of collective genius, but I myself am not a good solver, but with the aid of the community and your logic, I could go farther than possible in my own. You could make that a series, the live interactive community solve. And if that happens, could I be a moderator? I feel that a “Groupthink” would bring a whole new level of harmony and connectivity between the channel’s community to each other, the community to the channel, and everyone as a whole to the love of these puzzles. Please reach out and let me know if this idea comes to fruition, or on your thoughts in general. I have been a follower/subscriber of this channel since the beginning. I have watched the numbers grow, watched the channel grow, and have been thinking of ways to help it grow even more. And this just came to me. Especially when you say, “I know you all are probably shouting at your screen right now that I’m missing something obvious, if you shout loud enough I may hear you.” This idea would join us together in those moments, making the solving and logical path we journey down during the solve, that much more enjoyable. Community, Can I get some likes if you all would love to see this happen? For us to share in the experiences that these puzzles share with us.

[@stevesebzda570]

That worked out really cool [With Simon's insights at the beginning -- nicely excited, also] After a bit, I looked at that renban over on the right [in boxes 6 & 9]. There was an 89 in the complementary cells in row8 r8c9. That kept that renban with the "6" NOT be a 6,7,8,9 , for it would cancel out that "89." I kept that in mind while doing others. Cool how it spiralled around though. Nice puzzle ; )

[@modestclick]

68:38, a delightful puzzle, thank you!

[@guidocalderini2381]

First time finishing a puzzle that is not a GAS. Took me 60 minutes!

[@SCOMBAG]

As enjoyable as it is to watch you solve a puzzle, Simon, I hate when I see the answer to a square before you do. I'm literally screaming at the monitor "that square's a four, it's right there by the rules of Sudoku!" and you're trying to calculate probabilities in an opposite corner. Still good entertainment, though. Keep up the good work.

[@Aliessil]

Haha, I do that all the time! It always fascinates me to solve a puzzle and then watch Simon do it COMPLETELY differently!

[@FleckerMan]

Boop! Cool puzzle, lovely solve as always, thanks to all involved :)

[@inf0phreak]

1h 6m for me. My time was probably significantly hurt by not writing in the 5 in the lower left box until after solving about a quarter of the puzzle... I apparently suck at Kropke - except I got the break-in about as fast as Simon.

[@Daniel-mo2vp]

Loved this, a hidden secret key. Knowledge is power.

[@crystalgehrt8861]

Fascinating

[@y_prime]

27:44 I like the idea

[@msolec2000]

That's a very nice discovery. Reminded me of the fact that any straight in poker must have a 5 or a 10 in it. :)

[@illilillilifernhaven5277]

Yay! One that I can solve! ;-)

[@soulbound11]

*tries puzzle* ...hmm, must be one of those hard ones i cant figure out. Time to watch the video. simon: "this is approachable" ... back to the drawing board.

[@shadeblackwolf1508]

On behalf of the furry community, booping, is a gentle touch to the snoot. Furries are people who go by an anthro animal character online, think Disney's Robin Hood style.

[@AndreAy1975]

Solved it with help from the video.

[@LednacekZ]

had a great start and then i hit a dead end because i mistook a white dot for a black one

[@heywingliu9085]

26:45 for me! really approachable

[@hom-sha-bom]

the way he said "hoosier" though

[@garrettsmith9788]

Bird song! We need a sudoko to be divined wholly thru listening to bird song!

[@Xiuhtec]

Found the 3456s in box 1 and 7 in a couple of minutes. An hour more looking around I can't find anything else of much use. Hate to give up and use the video but I'm clearly not seeing the great revelation that leads to breaking into this somehow.

[@leefisher6366]

8:17 - It could never have been a 4/8 pair, because 4 and 8 aren't in a consecutive sequence of four digits. More usefully, it's not a 2/4 pair, which was a possibility. Perhaps you meant that?

[@Censeo]

I usually only watch but this one I tried to solve. Somewhere I must have used faulty logic cause I broke the puzzle after I got 8 digits

[@runninonempty820]

Quote of the day: "Not the power of Grayskull, we don't need that yet"

[@BigAsciiHappyStar]

Is this an homage to my No L Sudoku? :-)

[@smylesg]

OK, who's laying odds on whether Mark will now pencil a 3 and a 6 in the corner of every cell on a four-cell Renban?

[@wanderlustwarrior]

37:44 for my time.

[@Ray-iu7hg]

43:29 but tough start!!

[@Sir_Vulcan]

41:21 on this one!

[@i8ate8]

You need to boost your vocal levels a bit. The intro music and ads are much louder than your voice.

[@joelv4495]

I think we desperately need a Grayskull rule!

[@peterjohnclayton]

MORE CLASSICS PLEASE!!!!!!!!!

[@emilywilliams3237]

I have noticed that you have posted this request on the last several days worth of videos. I think that you would enjoy Mark's solves of the GAS puzzles, which he does every four or five days or so, which usually include at least one classic sudoku. Also, the CTC Classic Sudoku App is great - 100 or so puzzles, all classics, of varying difficulties. Finally, I have been going back through older videos, and particularly in the early 15 months or so of the channel both Simon and Mark did a fair number of classics. The description box to this video includes a link to the catalogue of videos which I believe you can search to find classics.

[@peterjohnclayton]

@@emilywilliams3237 Alas, I have done them all. Hence the light hearted requests. And knight, queen versions etc.

[@RichSmith77]

It's not as if all the variant puzzles they do don't involve a lot of classic sudoku within them too, particularly towards the end (how ever much Simon tries to avoid it 🙂). Don't the variants also satisfy the standard sudoku solving urge? I find they offer far more scope to be interesting.

[@peterjohnclayton]

@@RichSmith77 I like them too, but there are often drastically different styles every day to relearn from scratch. It's nice to master styles then move on to another. And Classics are still the favourite, the bedrock of the solver and getting less and less on the channel as other styles get more outrageous.

[@kyleborders420]

1st

[@lauraengleitner9866]

not the first :')

[@kyleborders420]

@@lauraengleitner9866 yes i was

[@lauraengleitner9866]

@@kyleborders420 i was refering to myself, sorry for the confusion

[@kyleborders420]

@@lauraengleitner9866 ok