Which Sudoku Theorem Shall We Use?!

[@longwaytotipperary]

Thank you for your kind and sensitive comments about Omar. You and Mark regularly give me something to look forward to, and help to raise my spirit. Leaving positive comments in response to your videos help the other readers who get a boost as well. Sometimes even little things can be very helpful to someone who is having a difficult time. Thank you!

[@joelstevens5670]

Well said. Simon and Mark really do make a world of difference, even from their little corner of the internet. I get a lot from the sudoku videos that helps me feel better if I’ve had a bad day and provides great entertainment, both as a watcher and a solver. The comments are also great, full of interesting thoughts or things to make you smile/laugh. It’s a brilliant community. Thanks from a semi-regular commenter to yourself and the other commenters.

[@davidrattner9]

Exceptionally said my wonderful friend!!! Thrive off your positivity and I know what this channel, community, Simon, Mark and all encouraging comments from me, Emily and numerous others mean to you!! ❤❤

[@longwaytotipperary]

@@joelstevens5670 thank you Joel. Many of us that comment on this channel support and encourage each other - Simon and Mark attract supportive and encouraging people, as they are themselves.

[@longwaytotipperary]

@@davidrattner9 yes, you are absolutely right, my friend! You are someone whose comments I always look for, as I know you are wonderfully supportive of Simon, Mark, the setters, and other commenters! It is so refreshing to know there is somewhere you can “hang out” on KZbin where the atmosphere is regularly positive! Much ❤️to you, my dear friend!

[@michaellautermilch9185]

I tried the puzzle for myself first, then watched the video. Amazing how much faster you are at seeing the same next steps.

[@Jodawo]

It's funny how many times I watch Simon miss the low-hanging fruit but usually can work around and get it the hard way. Still he is able to do it faster than I could ever dream to be able to do it. For example, in Box 4 he had a 5 pencil marked and column 3 and an x-wing of 4's in Box 1 and 7. The 4 could not go on the three celled Renbans in Box 4 but 5 and 1 would have to be on them. That would give an easy 123 and 567 on the two small Renbans. Leaving a 489 triple in the other cells in Box 4. Simon missed simple metaphorical addition and went straight to calculus. He found basically the same thing in a more complicated way. He did it though faster than I did the easy way. I think that is what's fascinating is watching how someone else's mind works. I think it attributes to how Simon can find some of the hardest break-ins in some of the most brutal puzzles we have seen on this channel.

[@ianward71]

Agree completely. I struggle to keep up with his mind sometimes. Ok many times ;).

[@studgerbil9081]

that's the appeal of his videos to me ... Simon reminds me of Rube Goldberg, finding the most ridiculously creative and complex ways possible of getting a task done. Some of us think outside the box once in awhile. Simon has to be forced into the box out of necessity.

[@MyriamTT]

That is Simon's special talent...

[@longwaytotipperary]

@@ianward71 ditto!

[@kobe11111]

1:04:23 Simon: "I feel like i've put a lot of 5's in the grid." while there's an extra 5 in column 6 lol

[@brianshilling]

I was pleased with myself that the first thing I noticed was the 159 restriction before Simon. I was less pleased when I sat in complete silence for about an hour trying to figure out any of the next 30 steps, requiring Simon for some hints of next steps. Amazing solve as always.

[@Cymindis]

Me too!

[@Myclutchisgone]

Same! Then at some point I realized many digits were symmetrical compared to other digits (3-4 and 1-5 for instance) and it got simpler 😬

[@davidrattner9]

Wonderful, heartfelt words about Omar and what this channel means to mental health Simon!! Constanty praise you and Mark for reaching out to those in need, not feeling great, and spreading out the word about how serious this silent deadly disease is in this world. This channel is very special to me and I count my blessings everyday that I am just a small part of it.

[@longwaytotipperary]

@davidrattner9 very well said! And a very heartfelt ditto! ❤️

[@davidrattner9]

For 2 amazing videos today, with such an important message, along with EVERYTHING you 2 do on a daily basis for a plethora of people in the world. There aren't enough words to describe what this channel and community means to me and others.

[@CrackingTheCryptic]

Thank you very much David! And thanks also for the positivity you bring to the comments every day.

[@longwaytotipperary]

@@CrackingTheCryptic@davidrattner9 ditto!

[@andremouss2536]

Instead of painstakingly excluding 9 and 8 from box 4, it would have been much simpler to realise that there must be a 5 in it !😂

[@snjyjn]

I had a similar thought - if you try to create 2 renbans out of a 1..9 set, you can only leave out a 1,5 or 9. With the configuration here - the phistomefel ring, and the 4 corner renbans - the 2 inner cells must be from 1,5,9. After this, one can get the 489 in col3 of box 4, which gives us the 123 / 567 renbans in box 4 - and of course, at this point, I slowed down...

[@dannstarrjp]

Wrote almost the same comment before spotting this one. Classic Simon 😂

[@janaendemann2154]

And then again later in box 6...😅

[@Gusquoise]

I was screaming it at the screen, but still I love it, Simon being Simon and working out the weirdest way

[@flobiish]

@43:50 That would have been easier if you noticed from column 3 that there's a 5 on one of the length 3 lines in box 4.

[@eclectichoosier5474]

It's been such a joy watching the evolution of Simon's explanation of the Phistomefel ring. At first, the explanation was accurate, but a bit long and convoluted. Then he'd find a slightly better way, and then another, and now he's got it down to something that is elegant and easy to understand. I love this channel.

[@Paolo_De_Leva]

True, but not so linear. This proof was used a long time ago already by Simon, then abandoned, and now ridiscovered. Indeed, in my opinion this is the most elegant proof, because it dodges the annoying problem of "double-counted" cells (i.e. cells where two columns or rows with the same colour intersect), which increases proof complexity and requires additional explanations.

[@CptRyaffio]

Oh, "sasher cake" is Sachertorte! A chocolate cake with a layer of apricot preserve and chocolate glazing. It is named after its claimed inventor, a Viennese baker named Franz Sacher. The name is German and pronounced with an unvoiced velar fricative /x/ sound for the ; like the in Scots and Scottish English "loch." Also, the at the end isn't silent, though unstressed. Torte is just one of the German words for cake. Some cakes are "Kuchen" (generally ones without glazing, often with thinner dough bottoms and fruit on top) and others are "Torte" (generally taller ones with glazing and layers).

[@martysears]

This puzzle contains some of the best use of renbans I have seen. And also one of the slickest uses of the Phistomefel ring. What a fantastic debut, hope Twan2797 makes more

[@Twan2797]

Awesome to see my puzzle on this channel! Thanks for featuring it!!

[@馬善萄]

I think another way to prove the yellow digit and orange digit have to be 159, is to think about we can only put at most four 1,5,9 on the 4 4-cell renban lines in the corners. That means we can only put at most four 1,5,9 on the Phistomefel ring. However, there must be six 1,5,9 on the 2 9-cell renbans in total, therefore the yellow digit and orange digit must be 159.

[@joelstevens5670]

That’s brilliant! 😄 Well done for spotting it.

[@RichSmith77]

That's very neat. I think we can go slightly further, and say there will be *exactly* four of (1,5,9) on the four 4-cell renbans, as each has to have precisely one of those digits. It doesn't change the overall conclusion any though.

[@joelstevens5670]

@@RichSmith77 Yep, I had the exact same realisation. It’s because of the property of the digits being 4 apart of course, meaning there has to be overlap with one of those digits, or else there would only be a maximum sequence length of 3 (for the digits in between them).

[@leestoddart7014]

My logic was that the green ring contains two sets of 1 to 9, each of which is missing a digit AND the blue corners need four sequences of 4. So each half or the green ring has to contribute two sequences of four... therefore the only digits that can be missing are 1,5 or 9. It always amazes me when I can see something which I think is immediately obvious that Simon takes a long and complex other route to find. But those instances are few and far between as Simon spots so many things I am completely blind to.

[@RichSmith77]

@@leestoddart7014 "So each half of the green ring has to contribute two sequences of four." Maybe that's intuitive, but I'm not quite seeing why this has to be the case? Why couldn't, say, a pair of corner sequences be split across the two green halves?

[@drhackchess]

Having watched your videos for years now, this is actually my favorite puzzle of all time. The logic was possible to follow using all of the tricks you've taught us over the years. Congratulations to Twan!

[@chocolateboy300]

I finished in 74 minutes. This was such a good puzzle. The break-in using the Phistomefel Ring was fantastic and quite surprising that a single X and V clue can disambiguate it. The middle of the puzzle really tested my scanning ability. I really liked this one. Great Puzzle!

[@bobh6728]

“I feel like I’ve put a lot of 5’s in the grid” 9 to be exact, but none in column 5. 😂

[@janaendemann2154]

Almost like he did it on purpose 😂

[@Raven-Creations]

@ 38:47 - "What on earth is going on?" - It's all about 1s and 5s. In box 4, one line is 123, the other includes 5 but not 4, so it's 567 and 489 go in C3. 89 must go in R3C1/2. This puts a 567 triple at the top of C3. There's now only one place for 9 on the upper 9-line. 8 has two places on the upper line, which rules 8 out of R4C5, so 8 in box 5 is in R6C5/6. This resolves the 48 pair in box 4. In box 6, you have the 1 and 5 in the opposite rows to box 4, so the 2-cell line is either 12 or 5 with a 4 or 6. Some sudoku gets you to where you can tell which way the 1s and 5s go. Other than that, this wasn't the easiest puzzle to spot all of the steps. There were very subtle interactions between the elements, so spotting the effect of any deduction needed alertness. Sadly, I was really too tired to do it justice. There may well have been things I was missing due to my tiredness, but you didn't spot anything I hadn't, so perhaps not. I really enjoyed this. It looked like it would be quite simple once the Phistomefel ring and corners were determined, but it was surprisingly resilient.

[@inspiringsand123]

Rules: 07:15 Let's Get Cracking: 08:43 Simon's time: 57m25s Puzzle Solved: 1:06:08 What about this video's Top Tier Simarkisms?! Phistomefel: 7x (08:51, 09:34, 12:54, 13:46, 15:15, 16:00, 24:01) Bobbins: 3x (37:16, 49:41, 1:04:33) Three In the Corner: 2x (57:45, 59:12) Maverick: 2x (33:38, 33:45) Knowledge Bomb: 1x (08:38) ​Scooby-Doo: 1x (12:41) Nori Nori: 1x (1:05:15) And how about this video's Simarkisms?! Sorry: 12x (04:36, 06:24, 13:27, 22:18, 29:36, 37:20, 37:20, 39:07, 39:07, 40:36, 52:23, 54:34) Beautiful: 9x (12:33, 12:36, 23:09, 23:33, 23:42, 31:43, 31:43, 31:46, 1:06:29) Hang On: 9x (20:47, 25:30, 25:30, 28:01, 32:23, 43:21, 50:28, 50:28, 1:04:37) Ah: 8x (25:26, 30:30, 31:43, 43:51, 57:20, 57:34, 1:00:06, 1:03:02) In Fact: 5x (08:59, 21:02, 23:01, 27:43, 43:54) Cake!: 5x (05:35, 05:41, 05:41, 06:36, 06:39) Bother: 4x (54:26, 55:06, 58:45, 1:03:37) Pencil Mark/mark: 4x (33:03, 38:23, 45:38, 53:45) Clever: 3x (49:41, 49:45, 1:07:23) Gorgeous: 3x (23:22, 47:18, 47:21) Wow: 3x (42:08, 56:08, 1:06:09) Symmetry: 3x (41:16, 41:18, 41:24) Good Grief: 2x (50:21) What on Earth: 2x (17:46, 38:42) What a Puzzle: 2x (1:06:05, 1:06:05) The Answer is: 2x (18:05, 42:24) Out of Nowhere: 2x (43:17, 59:05) Lovely: 2x (23:30, 45:45) Fascinating: 2x (24:12, 24:22) By Sudoku: 2x (23:56, 43:56) I've Got It!: 2x (28:19) Obviously: 2x (29:24, 1:06:14) Marries Up: 2x (39:52, 43:43) What Does This Mean?: 2x (12:36, 32:23) Apologies: 1x (01:15) Naked Single: 1x (1:04:59) Naughty: 1x (1:01:25) In the Spotlight: 1x (59:15) Stuck: 1x (32:23) Brilliant: 1x (00:52) Incredible: 1x (00:47) Discombobulating: 1x (07:07) Shouting: 1x (08:49) Alacrity: 1x (45:49) Surely: 1x (1:02:48) Proof: 1x (09:38) Pregnant pause: 1x (29:36) Plonk: 1x (57:11) Scrabble Tiles: 1x (11:24) Nature: 1x (30:12) Most popular number(>9), digit and colour this video: Sixteen (6 mentions) Two (142 mentions) Green (21 mentions) Antithesis Battles: High (4) - Low (3) Even (4) - Odd (1) Column (19) - Row (18) 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!

[@SasankMukkamala]

19:52 How did Simon eliminate the possibility of 6789 renbans in opposite corners?

[@AvatarBowler]

I wish I knew this too. He just kinda glossed over it. If I had to guess, it’s probably because the ring and renban logic in this puzzle mattered more than the locations of 2 identical renban sequences, so it’d be a waste of time to talk about it.

[@difoolgc5211]

He didn't, but since you need to put two 5's on the ring, they both has to be on the last corner renban. The digits you got left over for the last corner renban is 3-4-5-5.

[@hanshellendoorn5737]

The 2 causes an 8 on the diagonal which would produce 5 digits from 6789 on the diagonal.

[@hanness8536]

@@hanshellendoorn5737 this only works in the example. the 1234 could also be in the top left corner

[@simonl4523]

He doesn’t eliminate the possibility of 6789 in opposite corners. In fact, the solution has that very outcome.

[@joelstevens5670]

Having solved the puzzle, I can confirm it is indeed a cracker, especially the two part break-in. Some of the sudokus featured this year have been nothing short of sensational and this one was right up there. I think my favourite part was realising where the identical renbans went but I also loved the initial thinking with the ring and box 5. Many thanks to the setter. :)

[@scollyb]

It's interesting to see how different minds work. Not only Simon taking the long way of proving there had to be a 5 on the 3 cell lines in box 4. But just that's straight where I look when i get stuck. The box full of lines.

[@spt28]

Very interesting Sudoku. It has a property that would have told you immediately how you need to disambiguate the corner quads: solutions that are isomorphic under a relabelling of digits in reverse order remain valid for every constraining rule except sum-to-5. It clearly has to be the V in the bottom left that tells you whether the quad is a low range or high range, since that is the only clue in the puzzle that allows you to disambiguate 1 from 9, 2 from 8, 3 from 7 and 4 from 6.

[@oskarpetersen5722]

I'm excited to watch the video, but I just had to stop at the scrabble bag analogy because I'm not a huge fan of it and let me explain why. When removing one element from a scrabble bag there is no way of removing the same element from the other scrabble bag, without first knowing which element you took out and second emptying the other scrabble bag to find the correct one. I think visualising the bags may lead you to the wrong train of thought. In my opinion it would be clearer to say something like: "Let's imagine we remove one of the yellow+green cells and make it white. Whichever digit will occupy this cell in the finished grid, I will have removed it from both the green set and the yellow set, so the contents of the green and the yellow set must still be the same.". Anyways, thanks for the amazing content!

[@screambmachine]

maybe see 'take it out of both bags' as if the final digit is on the (covered) backside of the tile, and on the front side are coordinates like on a chess boad (A1 - I9). so you could take out the 'same' digit.

[@screambmachine]

but i get what you mean, it's overcomplicating a rather simple concept: cells that are in both sets / groups / bags don't matter. the rest must be identical still.

[@longwaytotipperary]

Always ❤ the Phistomefel explanation!!! It’s always magical!

[@debrabowen4276]

I never tire of that explanation, and I wish he still used the scrabble bags!

[@longwaytotipperary]

@@debrabowen4276 ditto! 😄

[@brianarsuaga5008]

I enjoyed this one very much. Got stuck a few times and needed a simon hint to unstick, but that doesn't bother me so much when I'm attacking puzzles i couldn't begin to solve a few years ago. Delightful.

[@michaelpdawson]

39:30 - at this point you have proven that whichever 3-cell renban in box four is not 123 must have 5 but not 4, and therefore is 567, which narrows down all the possibilities in boxes one and four.

[@Dotesmite]

This is one of those sudokus where I wish I was experienced enough to solve the break-in on my own. There's so much logic that I love in here, but it never feels right to start off on a sudoku after the break-in has already been spoiled for me.

[@masu33]

52:40 Simon does a complicated logic, deduces a 5 and says "that's by far the most straightforward thing we could have done (I think anyway)"... while there have been a naked 8 on the diagonal... then he casually scans said diagonal for the low digits... :D Classic.

[@KyleBaran90]

Scanned through the video and glad to see I had the right idea when Simon placed the 2 around 17:00 - the digits in box 5 have to be a singleton on the corners, which means only 159 is valid, but 19 is taken by the X

[@sanabas1]

I've only skimmed the video as I did this puzzle a few days ago, and the video appears to have a bad mistake on the breakin. I don't think Simon got lucky, I suspect he saw the actual breakin but then didn't explain it because he got distracted by the mistake @19:38. He just decides it can't work because you can't have 2 of the same quartets in the corners. Which is wrong, you can (and do) have 2 quartets together if they're in opposite corners. When he says 'the count is wrong', I assume he noticed the actual reason. If you use 1 & 2, then you need 2 lots of 6789, you need 1 lot of 1234, and the other 4 digits are 3455. The more elegant way to think about it is to just think about 159. They can't appear together on a 4-cell renban, every 4-cell renban has one of them, so there are four of them in the corners, at most four on the ring. We need six of them on the two long renbans. Therefore yellow & orange must be the other two 159s. they can't be a 19 pair due to the x, they can't be the same digit, so one is a 5, and 5 can't go on the x either. That gives the 5 and the 19 pair as seen @24:30.

[@jimi02468]

I don't like the "Phistomefel ring" because it's something people have memorized long time ago. It would be more interesting for a new solver because then they would have to invent that out of thin air and then use it to solve the puzzle which would be more impressive, sort of like having to re-invent the Pythagorean theorem despite that normally people have just memorized it.

[@JeffreyLByrd]

I think this is the fastest I’ve ever gotten a digit in the puzzle and then had to give up because I didn’t see what to do afterwards.

[@BlueCyann]

I found the path to the break-in hard to follow, but after thinking about it I believe it's really quite simple. The two renban digits in box five can't include neither of 1 or 9. That would lead to two 1s and 2 9s in the outer 2x2s, meaning zero fives, which obviously doesn't work since you can't put two 5s in box 5. Similarly, the two renban digits in box five can't be both of 1 and 9 due to the X clue. Therefore exactly one of them is a 1 or a 9, and it's straightforward from there to see that the other has to be a five.

[@joelstevens5670]

That’s the way I used. I thought it was very neat, though someone has mentioned an even cleaner method based on the fact that a 4-cell renban must have a single 1, 5 or 9 on it. But I thought you’d be interested/amused to know that not having any 5s in the ring would actually place THREE 5s in row 5 of box 5 (since one will go in the central cell by one of the other theorems meaning two 5s would actually break box 5, both diagonals and the X clue)!! 😂😉

[@tedg1278]

This is only logic I have seen in the comments that actually works for settling the opening digits.

[@Kinada]

The way that I thought about the start of the puzzle was that each of the large renbans needs to consist of two set of four consecutive digits so the inner digits must be from 1-5-9.

[@nekogod]

The 489 in box 4 was there for quite a while. The 5's and 1's in the ring meant that one of the trio lines was 123 and the other had a 5, the xwing on 4s meant it didn't have a 4 so had to be 567. Forcing 489 into column 3 in box 4, he got there in the end, but definitely went the long way round.

[@grahamrskelly6042]

My favorite part of the solve was at about 35 mins in Simon's solve you can force a 4 into column 3 in box 4 which leads to a bunch of stuff. 123 567 and 489 in column 3 in box 4 which leads to 😊

[@bluerizlagirl]

There's a quicker way to start the break-in. If you are partitioning a 9-cell Renban into two 4-cell Renbans, the left-over digit has to be 1, 5 or 9. They obviously have to be different because of R5, and can't be 19 because of the X between R4-5C4, so R5C6 must be 5; and by the X, R4C4 (which must be whichever of 159 is not in R5C4, and lies on the Windows \ diagonal) must appear in two Renbans, which have to be diagonally opposite each other by Sudoku; and since there will be either a 1234 or 6789 quadruple along that diagonal, it has to be the Unix / diagonal to miss R4C4. But everything seems obvious once you've seen it ..... And it was a lovely puzzle!

[@stangerrits6712]

I don’t think I would ever have found the break in here, but halfway the solve I found myself shouting at the screen for Simon to get started on the renbans in box 4. There was a lot of low hanging fruit there if you do a bit of good old sudoku 😊

[@andrewdipplecomedy]

It's very hard to get the balance of a message like that right. I'm sorry to hear about the loss. Suicide is always a deeply troubling topic but I genuinely think you got the tone and the balance right. Not everybody says it, and often people don't need to, but it's nice to hear that this channel (and the associated community) are supporting, and supportive(!) of those who are struggling x

[@longwaytotipperary]

Totally agree!

[@luketurner314]

The way I figured out the possibilities for r5c4,6 was to visualized the Phistomofel ring as 2 rows of the grid and the four Renban corners as four 1x4 blocks you have to fit in those rows. The only possible ways to fit them is with gaps at either end or in the middle (ie, 5), therefore the possible digits for r5c4,6 are 159. Then the logic continues as 23:13

[@Raven-Creations]

I echo your thoughts on mental health. It's not a sign of weakness, it's not a failure, and it's certainly nothing to be ashamed of. Although I've not suffered depression myself, I have had some basic training. Generally, I would advise against approaching friends or family. Without training, they will probably not understand that depression is not the same as feeling sad. They are likely to tell you to snap out of it, which is just about the worst thing they could possibly say. If anyone does say that to you, don't be too harsh on them. You're much better to approach someone with proper training. If you're in work, talk to the HR department. They probably won't be able to help you themselves, and if they tried to it might cause a conflict of interest (e.g. if there is a no drugs policy, and you developed symptoms after taking drugs). What they should be able to do is refer you to someone who can give you the help you need. This will also protect you from dismissal if they know you're unwell and are trying to work it out. If you're actually feeling suicidal, you really do need to call the Samaritans. Their staff are volunteers, but they are all properly trained in the art of active listening, and they understand depression. Having listened to what you say, they can put you in touch with the right people who can give you the sort of help you need. The most important thing, is to take their advice. When you're depressed, it can be hard to motivate yourself to leave the house to keep appointments. Because the Samaritans are anonymous, they can't accompany you to make sure you keep your appointments. This is where family and friends can be useful. Tell them you're having problems, and you're working them out, but you need someone to go with you to the appointment. Remember, it's your brain that's going wrong, whether by chemical imbalance, or a problem with its wiring. You wouldn't want an amateur to do brain surgery on you, but you do need to modify the way your brain works, and you need professional help to do this safely.

[@draquillin]

How I figured out the 159 in box 5: 1) Every digit must appear at least once in a corner renban, but at most twice - at most twice because they go onto the ring renbans, at least once because if there's a digit missing, it must go in box 5 in both renbans. Therefore, there must be a 1 & 9 in the corner, so there is a 1234 corner and a 6789 corner. 2) (At least) one of the corners must have a 5. There are four possibilities - 2345/3456/4567/5678. If you do 3456 or 4567, you've used 4 & 6 twice and cannot use them a third time, but you can't make a 4-cell renban without 4 or 6. Therefore, you must include either 2345 or 5678 3a) If you did 2345, then you've used the digits 2-4 twice and need a fourth renban. This can be 5678 or 6789. If it's 5678, the leftover digits for R5C4/6 are 1&9, which breaks the X in box 5. The set of corner renbans in this case is 1234/6789/2345/6789, with leftover digits 1&5. 5 can't go on the X, so 1 goes on the X with 9 and 5 goes in R5C6. 3b) If you did 5678, then you've used the digits 6-8 twice and need a fourth renban. This can be 1234 or 2345. If it's 2345, the leftover digits are again 1&9 which still doesn't work. The set of corner renbans in this case is 1234/6789/5678/1234, with leftover digits 5&9. 9 goes on the X with 1 and 5 goes in R5C6. To summarize, you get corner renbans of 1234/6789 and either (1234/5678) or (2345/6789), with R4/5C4 being a 19 pair and R5C6 being a 5.

[@RichSmith77]

You have had eight 4s in the grid for quite some time. Might be an idea to place the last one. 🙂 And he spots it as I'm typing the comment.

[@davidhughes7174]

Great puzzle and I enjoyed your solve. Thank you Simon

[@MattYDdraig]

55:24 After a lot of misdirects and a little bifurcation i finally got there with even less hair than I started with, but the opening made it worthwhile and anu frustration was entirely due to my own failures 😅

[@bertbergers9171]

I can´t help but comment on how Simon is 59 minutes in to the video placed a 4 in box 2 (the 4th 4 looking at box 8 actually) placing by sudoku the 4 in box 8, then starts looking around goes for the X pair in box 8 fills in the 4-6 option (which he just proved to be the only solution for the pair, but did not see, because well sudoku) then the 2-8 option and before even looking on what that means his brain scans his eyes away and finds other interesting stuff and does not solve the 4-6 pair. It's become so typical Simon solving that i stopped shouting at the screen and just try to follow the logic as his brain jumps all over the shop untill we get the most intricate logic path which usually is beautifull, fill in a bunch of digits and then finally find the (in this case 4) digit which has been proven by sudoku a while ago. Simon don't change! Thank you for the invite to people to seek help with their issues. I have been there, and had i not taken the help, i would have gone into some sort of life-ending sceme which is possible here in the Netherlands for people who have lost all hope on getting out of what they are in. One more advise i like to give to people seeking help is to believe in the professionals offering the help: don't doubt their positivity and effort, they are not just there for there salary. They have chosen their path because they want to help. They do make mistakes, try and learn from them that failing is always an option, we are humans. Their advise may take you to unwanted behaviour (from perspective of the person who you where), but do believe that that behaviour will change you to the person you can be, the person who is in thouch with their emotions and can act accordingly.

[@kilrati]

What causes the "party" when you out 3 in the corner? Is it controlled by a setting option? When does it occur ot occur?

[@longwaytotipperary]

Simon sings part of the REM song “Losing my Religion” with the lyrics “that’s 3 in the corner” instead of “that’s me in the corner” when there is a 3 in the corner. It’s such a fan favorite that Sven programmed the software to celebrate! I ❤️it - it always makes me smile!!

[@Ardalambdion]

Yes, talk with someone. Either if you think people have thoughts and feelings or you yourself have. And listen with an open and not condemning mind and heart.

[@pairot01]

It's a bit clearer if you think about breaking each 9 cell renban into 2 sequences of 4 digits. You can't take 2 digits from the same 1 to 9 strip, so the digitsoutside the ring have to be 1, 5 or 9.

[@piarittersporn]

Great puzzle. Despite Simon's jump-start (Phistomefel ring), it took me a long time to solve the puzzle, but it was a lot of fun.

[@Ray-iu7hg]

45:49 for me. So cool, and you just knew it would be from looking at it 😊

[@GreenMeansGOF]

39:50 the 5 and 6 must go with the 7 as well meaning that 8 and 9 in box 3 must be on the Phistomefel ring and you also get an 89 pair in box 1

[@jonnybolton4659]

Instead of trial and error to eliminate 234678 from R5C4, instead I noticed that there had to be at least one 1 and one 9 on the ring, so two of the renbans are forced to be 1234 & 6789 (i.e. no 5s). Then if both 1&9 are on the ring a second time the other two renbans are forced, and there's no 5s on the ring. But that places two 5s in B5, so at least one of the cells in B5 has to be a 19, but by the X domino they cant both be, meaning we either have two 1s or two 9s on the ring, so its now not possible to have two 5s on the ring and one of the cells in B5 has to be a 5, and by the X domino we know which one

[@ericpraline1302]

Clever construction with a delightful start. thanks. Unfortunately I happened to glance at a comment which gave me a pointer before I started. I'd like to think I would have got there anyway. I tend to think that puzzles must get easier as you make progress but the evidence should tell me that it's not a smooth curve, and this one was quite tough at points.

[@RichSmith77]

I think the break-in becomes a little easier if you spot that the four-cell renbans in the corners each have to have exactly one of the digits 1, 5 or 9 on them. So they account for precisely four of the total of six digits (1,5,9) appearing in two sets of 1-9 on the nine-cell renbans. Therefore yellow and orange must come from (1,5,9). And it's straightforward to see they cannot be the same, nor a 1,9 pair due to the X clue, so orange has to be 5, and the X clue a 1,9 pair.

[@joelstevens5670]

Hi Rich. Just wanted to thank you for your regular helpful comments, especially for any missed steps or tidying up difficult pieces of logic. They’ve rescued my solves on a number of occasions (especially in Mark’s videos, due to his more common use of complex logical chains)!! I’m a keen solver and Maths lover, as you can probably tell! :)

[@RichSmith77]

@@joelstevens5670 Thank you for your kind words. It's nice to know my contributions are appreciated. 🙂 I like to read the comments and answer people's queries when I think I can. I'm nowhere near the level that Mark and Simon are, or indeed many of the regulars who post amazing times, as I tend to be a bit plodding in my own solves. If I can think of the right question, I can usually reach the answer, but thinking of the right question to ask at the right time tends to be what slows me down 😉.

[@joelstevens5670]

@@RichSmith77 You are most welcome. I’m very much along the same lines (try to help where I can, though in my case I end up using about 100 more words than necessary/unintentionally giving people information that they maybe didn’t need)! 😅 What you say about solving is very relatable. I’m normally drawn to questions I didn’t actually need to ask and I always find I’ve missed some simple piece of sudoku in the process which could have spared me half an hour of extra logic! But such is the task of solving sudoku variants and I wouldn’t change a thing (well, maybe the number of 2-3 hour solves due to misreading/mis-applying the ruleset). 😉

[@CrackingTheCryptic]

Yeah that's a lovely way of looking at it. Very nice!

[@bethanyhunt2704]

Could have done box 4 from the other direction. 5 has to be on a short renban, so once 4 is in c3, and one renban is 123, the 5 renban has to be 567.

[@Robert_H.]

For the fact that the Sudoku went on for over an hour, the logic was surprisingly easy to follow to solve it.

[@anaayoung9142]

What a puzzle! Very smart one. Happy to see you talking about Men's mental help. In a world where the most suicidal humans are men is very very very important to talk about that! This is very kind of you!

[@masu33]

43:20 It would have been easier to just say 5 should be on one of the lines (as it is already on both of the middle lines).

[@TheJuicyTangerine]

54:57 for me, I got stuck on finding the 1234 quadruple in column 9!

[@alienrenders]

What an amazing puzzle! I didn't have much time the first time I tried it. Came back to it today and it was actually not that difficult (just under 40m). Some clever logic in this one. Just need to think about the groups of 4 that are possible.

[@simonscott87]

I’m trying to explore another set-theory aspect of this puzzle. Given we have the digits 2-9 in the horse shoes in row 8 and 9. Does that not imply that the cells in between has the digits 1 through 9 plus a single one in them? I wonder if that could have helped early in the puzzle..

[@Gonzalo_Garcia_]

18:39 for me. Great puzzle!!

[@ahouyearno]

That fist pump on the three in the corner. I love Simon enthusiasm

[@bouchecaro]

Thanks for the Birthday shoutout! Always makes me happy :D For cake we went with cookies and creme ice cream cake this year.

[@istvanmagi473]

The logic that Simon used to exclude 2 was bad, right? It only worked because Simon used adjacent corners, and he never checked for diagonal corners.

[@martinepstein9826]

Yeah, he didn't explain this but the real reason it doesn't work is because in this case you only have one five in the corner 2x2s when you need two fives.

[@parkerbond9400]

It would have been fine if he had taken it one step further. Once you have 2 of 6789 the last 4 line phistomofel ring box would need to be 543+2, which would break.

[@SenselessUsername]

Indeed bad... If you put them next to each other -- e.g., top left corner 67 above 89 but top right corner 89 above 67 it breaks sudoku because X-wing on 6789 breaks the second box (all four need to be in the middle three of the third line, that's what he referred to). But as Martin E says: even if on the opposite side of a diagonal, since we have two full 1--9sets minus a 1 and 2... one corner must be 1234, two corners must be 9876 (these are the only ways to include the three 'extremes" 1-9-9). Which then leaves your fourth corner with two fives (as well as a 3 and 4) which breaks sudoku.

[@joelstevens5670]

This was actually quite unusual. Simon’s initial logic was sound as what he was saying (if you listen carefully) was that you can’t have a 1, two 9s and two 5s in the ring as that would transpose to the blue cells, forcing two 5s onto the same line. However he got distracted by the 6789 repeat problem (which was needed but only later on), then corrected himself, only to go back to his initial thought which was clearly an assumption as he’d just pointed out. So yes, the way he used to proceed was slightly inaccurate. There were actually a few other ways though so it didn’t matter too much and he did at least point towards the right train of thought. I think Simon can also be forgiven the minor slip up given his tendency to prevent others from making false assumptions, myself included.

[@LiquorStoreJon]

Well, this puzzle looks tough! I think I will sit back and let the pro solve this one :D

[@TheSpotify95]

8:28 That can't be 5, because if they sum to 10, then it must be 5 & 5, which cannot appear next to each other under standard Sudoku rules!

[@ServantOfSatania]

45:54 for me... wait a minute, that's palindrome not renban!

[@FrancisFjordCupola]

Figuring out the trinomenoes in box 4 could have been much easier. We know one of them must contain a 1. And that only fits the sequence 123. Now because of sudoku the 4 in box 4 is forced on the line. But the lines cannot contain a 5. Thus the 5 must be on a trinomeno and it cannot go down to a lower number so the second sequence is 567. And the numbers in the third column in box four are therefor 489.

[@dannstarrjp]

42:20 thats the most complicated way of saying 5 must be on one of the 3 cell renbans by sudoku 😂

[@robert-skibelo]

Please, if you know you're going to use a theorem, could you prove it in the rules section so that non-beginners can skip the proof easily? It would also be good if you could do the same for the various secrets of renban lines, whisper lines, yin-yang, etc. too. A second advantage if you did this would be that the duration of the solve section would be more meaningful and more useful to compare with one's own time.

[@Tabu11211]

lmao I googled difference of squares after watching the sudoku video on numberphile before figuring out what your channel was and this popped up. Was like, OH ITS THE GUY!

[@diederikvandedijk]

Grey could have been 1, meaning the horse shoe cells on the negative diagonal could have been selected from 2345.

[@RichSmith77]

If grey was 1, then 5 and 9 would be the renban digits in box 5, missing from the two sets 1-9 in the Phistomefel ring. So there would be two 1s on the Phistomefel ring. Therefore two of the 2x2 corners would be 1234 sets, one would be 6789 and one would be 5678.

[@diederikvandedijk]

@RichSmith77 Yes, that't right, but I didn't get that from Simons reasoning in the video. (At least not the first time i watched that part. Probably my bad.)

[@RichSmith77]

@@diederikvandedijk I think it gets covered by Simon in the explanation from 26:30. The grey digit is an extreme digit. That extreme digit appears twice in green. So it appears in two of the corners. If it's a 1, then 1 appears twice, and we will have two 1234 sets in the corners. Those 1234 sets cannot appear on the negative diagonal, due to five cells on the negative diagonal then being from the four digits 1234.

[@stangerrits6712]

I think during the second part of the solve, all the colouring is not really beneficial for scanning the grid

[@barefootalien]

After 8 hours, I am finally admitting defeat to this puzzle. D: Now to see where it went wrong... Ah. I was assuming a symmetry along the diagonals in the 2x2 boxes that didn't really exist. Funny thing is, I learned that lesson at least twice...

[@JasperJanssen]

Twan is normally the Dutch spelling of Toine, as in Antoine.

[@jonathanwest6266]

Seemed obvious immediately that the middle digits were from 159 cos you need 4 4-digit sequences that are comprised from 2 sets of 1-9. Only 1,5,9 can be omitted from either pair of them.

[@Rach881101]

48:29 for me. Beautiful puzzle!

[@eddieharwood7788]

What a puzzle. I found the break in hard but managed it okay, then I just missed simple bits of sudoku and ended up watching Simon's solve to see that I completely missed the 23 pair in row 9 which cracked it. I thought Simon strangely didn't use the 3 cell renbans in box 4 until he'd moreorless fell into what they were when there was nothing left. I got that they could only be a 123 and a 567 very early although apart from giving the digits in column 3 this did not prove to be a great breakthrough.

[@SamuraiPipotchi]

The simple brilliance of the logic leading to the middle 195 tiles is so satisfying. Edit: I feel like the way I did it was much simpler than this

[@tedg1278]

At 20:00 you show that having 2 sets of 6789 in the blue is problematic if they are in the same row or column and state that you can have them if they are on the diagonal opposite corners. The entire reason for having for having the 6789 in the blue cells is to test the concept of a 2 in the yellow cell. You then eliminate the 2 from yellow without ever expounding on why having the 2 sets of 6789 in blue on diagonals would fail. I can't see a reason it would fail immediately.

[@KevinSheedy-rt1db]

1136:55 for me. Great puzzle!

[@AndreAy1975]

Solved it with much help from the video.

[@srwapo]

42:45 + 52:30 on my phone = 1:35:15, horrible time! I peaked at the video twice and both times for something simple that I should have figured out by myself (why r4c4 couldn't be a 1 and not seeing the 4 in Box 1 undoing the 24 pair in Box 3). Wasted like 30-40 minutes just not seeing those two simple things.

[@CauchyIntegralFormula]

100m38s. I ended up having to make assumptions for the sake of contradiction quite a few times, which I dont like, but it worked

[@nickjayyoung7662]

Can anyone remember which video the "nori nori" came from? I enjoyed this video nonetheless.

[@data261]

Is there a way to do this without using the phistomefel ring?

[@guamAPEX671]

Yelling at the sceen - "There can't be a 7 on the 3 cell line in box 6 because there already is a 6!"

[@dudbike]

Are you sure you are not Canadian? You apologize a lot for things out of your control. Love the vids!

[@honeyspiderii]

The 5 in box 4! 🤯

[@karlmortenlunna2417]

Very nice puzzle. 25:56 for me.

[@andremouss2536]

15:18 Why doesn't Simon use the Phistomefel sequel about the central cell (which may be the only missing digit in the ring, if any) ?

[@donaldsnyder1543]

As far as I know , that only works when you miss out a digit. Since there was a 1234 , 2345 and 6789 sequence none are missing.

[@TheSudsy]

i just watched Simon thinking for 5 minutes (not realised i had paused video) doh!

[@imblackmagic1209]

thanks for sharing!

[@yungariesx]

Thank you for reading out Jae’s birthday message! Love you Simon 🫶🏼

[@incoxide]

19:46 Why can't the repeat 6789 renbans be in opposing corners eg top-left and bottom-right in his example?

[@incoxide]

Simon actuallys goes on to say exactly that it is possible, and then immediately rules it out in the next breath! what the?

[@incoxide]

Ok I worked it through myself, and it seems that under the 1,2 combo in the middle box, you always end up having three repeats of the six (at least). Simon apparently saw that in his head, but never explained it out loud, other than to say that "it just doesn't work" - which was true.

[@F1r1at]

Like how can Simon not see a simple logic with 1s and 5s in boxes 4 and 6, but also be able to tell the really hard thing with 195 in box 5?) I, sadly, could not do this puzzle, because did not get that logic x(

[@puritan7473]

Simon again insists on an incredibly circuitous route to finding the easy 5 in the middle box - surely if was far easier to see that having to use two groups of 4 digits out of each 9 meant the unused digits in the middle box could only be 1, 5 or 9 and therefore there has to be a 1,9 pair on the X and the other one is 5 !?!