The Miracle Sudoku Reborn

Подписаться 597 тыс.

Просмотров 81 тыс.

50% 1

** Today's Sudoku **
Doesn't this puzzle look familiar? In fact it's got the exact same digits in the exact same positions as Mitchell Lee's Miracle Sudoku from May 2020. But Mátyás Martinka has reinvented the puzzle by tweaking its ruleset! We don't know if it's easier or harder now but it's definitely interesting!! Play the puzzle at the link below:
app.crackingthecryptic.com/su...
Rules:
Normal sudoku rules apply. Cells separated by a knight's or king's move in chess cannot contain the same digit. Digits in the Nth column indicate in which column the digit N is placed in the respective row. Eg if R3C2 is a 5, the fifth column in the third row (R3C5) must contain a 2.
** Our Christmas Gift **
To all our patrons - thank you so much for your support.
We are delighted to bring you a fantastic Christmas present - a puzzle/sudoku hunt by some wonderful constructors: PjotrV, Panthera and Aspartagcus. You can access the hunt here (the password is on Patreon right now):
amgine.nl
Enjoy - and please do try to still see your families over the holidays - we know these puzzles are addictive :)
WE WILL BE RELEASING A COMPLETE SUITE OF VIDEOS TO ACCOMPANY THE HUNT AT THE START OF JANUARY ie TOMORROW!
You can join us on Patreon for as little as $2/month here:
/ crackingthecryptic
▶ SUDOKU PAD - Our New App ◀
It's OUT on Windows (released yesterday!) via Steam here:
store.steampowered.com/app/17...
You can now input your own classic sudoku puzzles into our software using our new App! The app also comes with 12 handmade puzzles from us and we're also releasing occasional bonus puzzles too. Already available on IOS and Android.
** Our Book **
The PDF is available as of today and the physical copy shouldn't be far behind. If you don't own the book then it can still be ordered here:
www.kickstarter.com/projects/...
**************************************************************
▶ OUR ARROW SUDOKU APP IS OUT ON ALL PLATFORMS!
Here are the links:
Steam:
store.steampowered.com/app/16...
App Store:
apps.apple.com/us/app/arrow-s...
Google Play:
play.google.com/store/apps/de...
▶ OUR KILLER SUDOKU APP IS OUT ON ALL PLATFORMS◀
apps.apple.com/us/app/killer-...
store.steampowered.com/app/14...
play.google.com/store/apps/de...
▶ SIMON REACTION BOARD (!) ◀
With thanks to Andrea for creating this :)
simonreacts.avris.it/
▶ CTC FAN DISCORD SERVER◀
/ discord
NEW: Guide To Our Discord Server:
tinyurl.com/CTCDiscordGuide
▶ OUR BACK CATALOGUE - ALL CATEGORISED WITH LINKS!◀
tinyurl.com/CTCCatalogue
▶ NEW CRACKING THE CRYPTIC MERCHANDISE◀
teespring.com/en-GB/stores/cr...
▶ OUR CHESS SUDOKU APP IS NOW OUT!◀
AppStore: apps.apple.com/us/app/chess-s...
Steam: store.steampowered.com/app/12...
Android: play.google.com/store/apps/de...
▶TRY OUR CLASSIC SUDOKU APP◀
AppStore: apps.apple.com/us/app/classic...
Steam: store.steampowered.com/app/11...
Android: play.google.com/store/apps/de...
▶TRY OUR SANDWICH SUDOKU APP◀
AppStore: apps.apple.com/us/app/sandwic...
Steam: store.steampowered.com/app/11...
Android: play.google.com/store/apps/de...
▶SEND US PUZZLES TO SOLVE/CONTACT US◀
crackingthecryptic@gmail.com
▶FOLLOW US◀
Twitter: #crypticcracking
@crypticcracking
Instagram (for how to solve daily clues from The Times): crackingthe...
▶SOFTWARE◀
Play the puzzle in the video by clicking the link under the video (above). We are building a website which will allow you to enter your own sudoku puzzles into the software and this is coming soon!
▶Logo Design◀
Melvyn Mainini
▶ABOUT US◀
Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships.
Thank you for watching!
Simon and Mark

Опубликовано:

30 дек 2021

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 402

@TheUnderlordITP 2 года назад

Proof for why each row has exactly one self referencing cell: Each cell that isn't self referencing forms a pair with the cell its referencing (which is self evident from the rules and is demonstrated early on in the puzzle). Since each row has an odd number of cells (9), that means each row has at least one cell leftover that can't form a pair and must reference itself. Since there are only 9 possible self referencing cells (or otherwise you would repeat a number in the column), then each row must take exactly one self referencing cell.

@neil2796 2 года назад

Is there a valid possible puzzle that contains a sequential 1-9 row? If so, wouldn't that be an exception? Edit: I'm slow. While a 1-9 row is possible in a puzzle, the row/column referencing requirement isn't possible in the same puzzle.

@PhilBoswell 2 года назад

@@neil2796 wouldn't that block off any potential self-referential entries in any other row?

@alan-freeman 2 года назад

@@neil2796 I think a 1 to 9 row is possible, as is a 9 to 1 (just not in the same grid because both would have 5 in the 5th column!)

@benediktthomas 2 года назад

no, because this row would then take all the self referencing options for all digits, which would mean that the other rows can't have any self reference, but as @TheUnerlordITP showed, each row must have at least one self reference. So each row must have exactly one self reference (Thats basically what the last sentence of the TheUnerlordITP explains)

@ragnkja 2 года назад

@@PhilBoswell Yes, because every column needs _exactly_ one self-referential digit (by simple sudoku), while the rows must have _at least_ one self-referential digit because it’s a sudoku with an odd number of columns and non-self-referential digits pair up.

@tank2045 2 года назад

I literally just finished rewatching (for the umpteenth time) The Miracle by Mitchell Lee...Watching Simon gasp time after time as he trips through that puzzle just makes me happy for some reason...

@da-boi6007 2 года назад

@Mark Golbranson indeed

@kilimanjarocruz660 2 года назад

About self-referential numbers. Each row has at least one such number; That is because we have an odd number of digits per row, so it is impossible to use only pairs of referencing numbers. On the other hand, each digit can only be self-referential once on the whole grid, otherwise you would have it appearing twice in the same column. So, we have at least 9 self-referential digits (one per row) and at most 9 (one per possible digit), thus each row needs exactly one.

@christinalind2034 2 года назад

This is the channel that has helped me the most in all of 2021. Due to bad health and high risk regarding Mrs. Corona. This channel has keeped me sane. Helped me keep my brain active so it not just ended up with match 3 games and Netflix. I can never thank you enough. I haven’t been to a store more than 3 times this year but I have tried a lot of your puzzles. I hope the best for Mark and Simon and I thank both of you from the bottom of my heart. (Sorry for my bad english)

@longwaytotipperary 2 года назад

Thank you Simon & Mark for helping me get through 2021! Algorithms brought me here as I was trying to solve a newspaper Sudoku. You have opened my eyes to fantastic puzzles, supplied daily doses of humor and charm and helped me get better sleep and soothed my anxiety! CTC is now my favorite channel and I look forward to watching both of you every day. Much, much, much ❤!! 🤗

@timcolla5686 2 года назад

My first time solving one of the puzzles on this channel! And in 30:15 minutes, super happy!

@cyndisision 2 года назад

This feels like a perfect note on which to close out the year! It was the original miracle sudoku video that brought me to the channel in spring 2020, and I've watched your videos every day since then. Thank you to both you and Mark for being such stalwarts throughout a couple of truly horrendous years.

@th.nd.r 2 года назад

Beauty of a puzzle! It’s so weird to look at a finished grid without any colors but black, white, and pen-ink-blue anymore, especially with all the complex coloring puzzles you solve all the time! Nice way to finish the year. I find it incredible that two digits and this ruleset provide one unique solution, just like the original Miracle Sudoku that made me a daily CTC viewer from the day I first saw it. Great setting and great solving! Thank you for bringing a little bit of joy into my life every day in what has been a rather difficult year. See you in 2022, Simon and Mark!

@XeniaStCharlesIrisLlyllyth 2 года назад

Proof for why each row has exactly one self-referential number: because Simon said so ❤️

@maguire6813 2 года назад

What kind of creature is this?

@PauxloE 2 года назад

"Proof by authority" is usually not considered a valid proof.

@Rangsk 2 года назад

I think my proof is pretty clean: If you look at each column, it's clear that there are exactly 9 self-referencing digits in the grid because each of the nine digits must appear exactly once in their own column. Within each row, non-self-referencing digits always pair up, but there are an odd number of digits in each row, so each row must have at least once self-referential digit. But, since there are exactly 9 self-reference digits, this forces each row to take only one of them. QED.

@BanaiFeldstein 2 года назад

15:01 for me. Roping in every column and every row. Nice variation on the miracle sudoku. Two years ago, I'd look at this and go "huh???" Then I found this channel. Thanks Simon and Mark for a year plus where I couldn't accomplish anything, but I did lots of sudoku, so at least I know what I did when I wasn't doing anything.

@Rangsk 2 года назад

In fact, just the anti-king and anti-knight restrictions force roping in every band and stack.

@Waggles1123 2 года назад

@@Rangsk I wonder if there's an easy proof on that, because if so, it would make these kinds of puzzles braindead easy to solve.

@OneCatShortOfCrazy 2 года назад

I love watching your videos after I've solved it to see how much smarter your methods are than mine, and every now and then I've seen something you haven't seen yet and I feel so bloody smart for a second :D You've got me spending all day on these now!

@wolffang21burgers 2 года назад

26:30 Reason for exactly 1 self-referential digit in each row: In each row, non-self-referential digits pair up, so there must be an odd number of self-referencial digits (at least 1). From all 9 rows we must have at least 9 self-referencial digits. Each column has exactly 1 self-referencial digit (by sudoku), totalling 9 altogether. Hence, each row must have exactly 1 (taking the minimum from each row).

@tristen9736 8 месяцев назад

The thing I love most about these puzzles is seeing the pattern emerge and be able to predict based on it where digits will end up going. In this one, each digit in a row was exactly one square away from a knights move from the same digit in the row above it, ex: 7 in row 9, being one away from a knights move from 7 in row 8. It also worked out for the self referential digits.

@gmalivuk 2 года назад

It's amazing that a statement like, "A restriction on what can go in column 2 is a restriction on where the 2s can go" can be so trivially obvious given the rule set, and yet it still took me 45 minutes to wrap my head around it.

@ocirMZ 2 года назад

I can confirm I am one of the people who learned about your channel from the first miracle sudoku. As someone who never had any interest in sudoku, I am happy that the youtube algorithm decided to bless me that day

@zacharyn5520 2 года назад

I really can't tell you how much I appreciate your channel and the work you do Simon & Mark. Looking forward to seeing what the future holds for this channel!

@crystalgehrt8861 2 года назад

The Miracle Sudoku was my intro to the channel when a friend showed it to me and I took it as a challenge. I had only seen regular sudoku up until that point, but I was fascinated and excited by it. It took me a long time, but I finished, and have been a regular viewer and solver since then. The channel has definitely upped my game, and joining the pyramid hunt introduced me to even more and forced me to try for hours and hours to solve new types of puzzles because there was no Simon to save me and I tried very very hard not to ask anyone for hints. I was able to do this one with no problem. It was set beautifully, and Simon has had me in training! There was so much nostalgia in this puzzle! Thanks for opening up a whole new world of fun! I can spend hours on sudoku now and have it feel like only a few minutes!

@inspiringsand123 2 года назад

Rules: 05:55 Let's Get Cracking: 08:04 Puzzle Solved: 27:25 Simon's time: 19m21s And how about this video's Simarkisms?! By Sudoku: 10x (09:16, 12:32, 13:36, 15:00, 19:55, 20:27, 20:32, 21:54, 25:13, 25:57) Stuck: 4x (04:31, 04:52, 16:29, 17:02) Gorgeous: 4x (13:00, 21:08, 23:50, 24:59) In Fact: 4x (00:59, 03:20, 14:18, 24:14) Beautiful: 3x (11:15, 19:59, 27:25) Extraordinary: 3x (01:02, 01:09, 05:16) Obviously: 3x (00:52, 01:28, 14:43) Useless: 2x (24:30, 24:30) Lovely: 2x (17:56, 22:55) Incredible: 2x (02:13, 03:00) Shouting: 2x (04:19, 05:43) Approachable: 2x (02:27, 02:30) Alexa: 2x (11:51, 11:53) Sorry: 1x (11:53) The Answer is: 1x (04:13) Out of Nowhere: 1x (20:46) Ridiculous: 1x (00:50) Of All Things: 1x (21:57) Alacrity: 1x (25:54) Whoopsie: 1x (21:19) Wow: 1x (21:58) Most popular digit this video: One (54 mentions) Antithesis Battles: Low (5) - High (1) 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!

@azland00123 2 года назад

Had to go back and watch the original miracle sudoku. Still absolutely amazing.

@3dprintingmeathead332 2 года назад

I got the miracle soduku app on steam the other day. Made it to level 21, it's getting tough now. But it's really helping me out this holiday season. I am going through diagnosis for aspbergers at 37 years old, while simultaneously purchasing a company and a house. Having so much to think about and plan is tiring. Getting lost in your puzzles really helps refresh my mind. P.s. I'll admit I haven't done many handmade sodukus, and honestly I find them harder because a human made them and I don't think like the average human due to my condition haha! Happy new year!

@stephenjames2951 2 года назад

Because there are pairs of indexes there is always one number left over that has to self index. Since you can only have the same number once in each column each row has to have a different self indexed number.

@-BooBoo 2 года назад

Beautiful explanation!

@chitraagarwal8259 2 года назад

What a wonderful start to the new year! Very elegant puzzle.. It's a huge testament to Simon and Mark that this feels genuinely approachable!! Wish both of you and all other followers of the channel a happy and safe 2022.

@davidstorrs 2 года назад

Happy New Year, Simon and Mark. This channel has been a source of happiness throughout the 'interesting times' of 2020. Thank you for all that you do.

@traegrovez5110 2 года назад

My girlfriends Christmas present to me was a large sudoku puzzle book and on the back was a note saying that she had subscribed me to the CTC patreon! By far the best present I’ve ever received❤️

@twosometwosome3698 2 года назад

On the idea of the "striping" Simon points out. The flip-side (or corallary) is in the rows. In any given box, the 1 will always be paired with the 2 and 3; the 4 paired with the 5 and 6; and the 9 paired with the 7 and 8.

@Saryna 2 года назад

That is not correct for any 1-5-9 type Sudoku with all columns. If you ignore the Anti-Knight/King restriction and just do the last part of the rule set you can very easily create grids which have no roping at all. I did some logic. You know there's always going to be a 1 in column 2, a 2 in column 1, a 3 in column 2, a 2 in column 3 and so on. So each number is already forced to pair up with its neighbors at least once for each. 2 1 X X 3 2 X X 4 3 and so forth. Then the addition of Anti-Knight and Anti-King forces most digit placements exactly 3 rows apart, resulting in X being 123 as well, so you get 132, 213 and 321 in this grid. _I will try to reply with an image link containing an example for that not being the case without the chess restrictions but if RU-vid filters it there's nothing I can do (and most channels have links filtered)_

@jaymontana2708 2 года назад

This puzzle is the first time I've been able to complete one of these fully on my own. Only because you have given me the tools to do so.

@JakeRoeder 2 года назад

This took me a bit to wrap my head around the rule set, but ultimately (and after 2-3 dead ends due to faulty assumptions) I was able to solve this one. The solve path is wonderful and me being able to solve this one without any hints at all feels like wonderful proof of my growth in solving thanks to this channel and the GAS puzzles in the discord. Thanks to both of you for creating such great content and special thanks to the setters and the CtC community!

@markbennet9058 2 года назад

You also have vertical and horizontal "roping" in this puzzle. The self-referential number in each row and column occurs because 9 is even - it wouldn't necessarily happen in a monstrous 16x16 grid.

@bobblebardsley 2 года назад

(I think you mean because 9 is odd 😋)

@harshitchauhan5162 2 года назад

It has been a great year for me since I joined this channel, seeing you and mark introducing the community to such a vast variety and beauty of sudokus! Here's to a very enjoyable time a hopefully a fantastic year ahead for you guys🍻.... Happy New Year to you and everyone :)

@BobertJoe 2 года назад

So looking at the way the final grid is laid out, you can see exactly why the two digits are both the minimum number required, as well as all that is required to get a unique solution. You could think of this, not as a 9x9 grid, but as a 3x3 where each row consists of a block of A{123}, B{456} and C{789}, and each column consists of {ABC} x3. By placing a single A digit in rows 5 and 6, you force an A into row 3 in box 5. The specific column those two digits are placed in fixes the order of those digits, as well as giving enough information to reach up and down the grid. Interesting puzzle, even though the patterns made my own solve more trivial than it should have been.

@RicardoMorenoAlmeida 2 года назад

I noticed the 123, 456, 789 pattern, about halfway through, but I didn't want to fall into a trap of solving with that, so I went through with the logic. I think I would have felt somewhat cheated had I gone down that route, even though it would have been a much faster solve.

@Noircogi 2 года назад

I kept waiting for Simon to realize this. I think in this case Mark would have because he's talked about the ribbon solution before.

@PauxloE 2 года назад

But what in the rules forces that we have those 123 / 456 / 789 blocks?

@RicardoMorenoAlmeida 2 года назад

@@PauxloE I'm not sure the rules DO mandate that pattern, which is why I didn't use it to solve the puzzle. It might be the case because of the indexing, but further analysis would be necessary.

@pantheracheshire 2 года назад

Actually what's really interesting, is that not only do you get one self-referential cell per row, there's exactly 1 per box as well (same reasoning) . :)

@sammiddleton7663 2 года назад

I don't agree that the reasoning is exactly the same. There is exactly one self-indexing cell per column by classic sudoku and as each row contains at least one self-indexing cell because there is an odd number of cells, there must be exactly one. To extend this to the boxes, you must leverage the logic explained by Simon at 11:20 to force each box to contain at least one self-indexing digit as follows: For each box, consider the numbers that index its columns (one of (1, 2, 3), (4, 5, 6), or (7, 8, 9)). These must be placed 1 in each column of the box, otherwise that column number would be repeated in the box*. If one of those digits is not self-indexing, then it must form a mutually indexing pair with another of those digits, forcing the remaining one of those digits to be self-indexing. As such, each box contains at least one self-indexing digit and because the column logic means there can only be 9 self-indexing digits, there must be exactly one self-indexing digit per box.

@sammiddleton7663 2 года назад

* in the more general form of this logic, repeating a low (1/2/3), medium (4/5/6) or high (7/8/9) in the same column and box forces repetition of the column index in a box, but not necessarily the box in which the low/med/high repetition in a column occurs.

@Boxkid351 2 года назад

@@sammiddleton7663 you have 9 boxes, 2 digits in each box are being swapped. 9 cannot evenly be divided by 2, therefore a single number lands in its own box.

@your_nightmare 2 года назад

It took me three hours to solve it but it was really fun!! Thanks😁

@whitetiger1518 2 года назад

Another Happy New Year to you both and many thanks for keeping me sane. I was shown the original miracle sudoku, and have been addicted to the channel ever since. You are my most watched channel! Many thanks for being a beacon of sanity and safety in very weird times. Peace safety and health to both of you and your families for 2022 and beyond. Fiona

@glennmelven3414 2 года назад

That was a great puzzle. Managed it in 38 minutes. A miracle for me to finish a Simon video in less than 2x video length.

@vikingslayer34 2 года назад

What an awesome rule set. I vote for more of these puzzles! My hats off to you Matyas and Simon.

@LEEBLISSY 2 года назад

1:32:12 for me. PHEW that was a great sudoku, very satisfying to finish. I have a great difficulty finishing these sudokus, but I knew I could finish this one if I just kept going. and I didn't make any logical errors that made me give up 😅 I'm still relatively new to the sudoku scene so I'm pretty slow!! but that was very fun! I did the first two miracle sudokus before I think but I dont think I was able to finish them? once I remembered the indexing rules for this one though I was able to just go row by row and fill in the things I missed, so I think this one might have actually been easier! stunning job mátyás martinka !!

@meganlove5681 2 года назад

Absolutely loved this puzzle! Very approachable and fun. Loved the original one as well, both excellent puzzles

@martinyyt 2 года назад

Haven't watched the video (yet) but I did solve the puzzle - 122:39 over a couple of days with a re-start or two - my first ever solve of a Simon puzzle, and I am pleased as punch. I realised about halfway through that the puzzle was roped/striped but still struggled a bit with the logic. Finally, colouring 89 pairs helped me figure out what to do - thoroughly chuffed that I used a Simon "trick" to get to the end.

@carolinefreeman4546 2 года назад

I solved this the same way you did the original miracle sudoku - with colours. It took me a lot longer than your method for this puzzle but I'm still pleased that I managed it.

@sane9875 2 года назад

Absolutely brilliant Simon!!

@shovalis 2 года назад

I'm excited even before watching the video! This is indeed the puzzle that got me to start following you! :D

@jeffreysherman8224 2 года назад

About 60% through my crack at this puzzle I noticed that there is a pattern to the columns. Every column has the exact same order of digits only each column starts on a different digit because of normal Sudoku rules. "Simply beautiful!"

@shmockette7158 2 года назад

This is my favorite puzzle! Thank you.

@saphirelynn2000 2 года назад

That was a beautiful puzzle. I loved the organization of the numbers in triples with each other. I had a feeling that it was going to be that way early on. It definitely made me smile to see the pattern of numbers.

@Rich-je9fy 2 года назад

First one I finished all by myself. Great puzzle, thanks for sharing !

@jonbrowne8334 2 года назад

Excellent puzzle and enjoyable solve! Happy New Year!

@stevezag4145 2 года назад

What a fun puzzle! Thank you, Mátyás Martinka!!

@boydegg 2 года назад

22:31 woop woop!!! Amazing how Mátyás can use the same puzzle start for a new kind of puzzle. Brilliant.

@DanielColborne 2 года назад

I did it! Wow that was good fun. I had many "aha!" moments with this one. I didn't need to resort to bifurcation or help from the video. I can't wait to see how Simon gets on with it and how quickly he makes me feel less intelligent. Thank you for another wonderful puzzle and for keeping me sane through the pandemic. Focusing on puzzles has been an immense help. I wish you and Mark all the best in this new year.

@DLT739 2 года назад

Indexed cells pair with each other, so there are an even number of cross-indexing cells in each row, meaning there must be at least 1 self-referencing cell in each row, and therefore at least 9 in the whole puzzle. Any self-referencing cell in a column contains that column's number and can be the only self-referencing cell in that column, so there are at most 9 self-referencing cells in the puzzle. Therefore there are exactly 9, 1 in each row and column.

@TorreGD 2 года назад

Great video! One thing we noticed was that in each box, each row only contained low values, high values, or medium values. I think you said something about this at the beginning, but this realization alone allowed us to solve this puzzle in like 8 minutes.

@RO8s 2 года назад

Well, it turns out I like Miracle Sudoku! That is the very first time I have followed the link to the puzzle and succeeded. Ever. For the very first time I get to experience the sheer complacency of watching Simon solve a puzzle I have already solved. I had no idea of the inner glow that proceeds... And no poxy double-inverted triple-off-set Y Wings in sight...! Oh, the joy...

@davidhughes7174 2 года назад

A genuine miracle, because I also solved it with alacrity. Thank you for your wonderful solve Simon and Mátyás Martinka for your twist on the original miracle.

@faddy91 2 года назад

A really beautiful final grid. Roping in rows and columns AND the same posiiton in each box contains a complete set of the digits 1-9.

@Meanslicer43 2 года назад

I managed to finish this in in just over 35 minutes. Which I am admittedly proud of. I absolutely love miracle puzzles as well

@avantredguard565 2 года назад

Brilliant puzzle! Writing this before watching your solve because it's not often I complete a puzzle without help. What a beautiful looking puzzle, excited to see if you and I went about it the same way. It was a fun constraint, but not one I imagine will see a lot of use in future puzzles since this might be the only thing you can do with it.

@katam6471 2 года назад

It was when I watched the original Miracle Sudoku and Simon said "It's like the universe is singing to us", that I fell i love with the channel. :-)

@ALLU800 2 года назад

Amazing video and an amazing puzzle! In just a few days of binging your videos I was already able to solve this one on my own in 36 minutes.

@BozoTheBear 2 года назад

Loved this so much, thanks Mátyás!!

@Poldx 2 года назад

Great Puzzle! Dunno if anyone noticed, but not only is this puzzle created in a let's call it "roping manner", but also when you look at columns, EVERY column of the finished grid has exactly the identical sequence of digits in it, which is rather cool if you ask me :D

@JasonPeltier 2 года назад

It's cool that each row in a block is restricted by low, middle, and high digits. And also to keep the logic from breaking, two of the sets of low/middle/high sets have to cycle through the 1st, 2nd, and 3rd rows in each block in each set of 3 columns, while the 3rd set has to reverse. It's like a positional striping that is opposite from the actual numerical 3-digit column striping.

@TheHunterMPG 2 года назад

That was lovely! Happy New Year to CtC, more in 2022 🙂

@literalstardust445 Год назад

I noticed that the rows within boxes are contained to be low, medium, or high. its beautiful

@maxmarshall7123 2 года назад

The rows are fascinating - it's only sets of (1,2,3) (4,5,6) and (7,8,9)

@sillvvasensei 2 года назад

I think it's fairly common in anti-knight sudoku, either by column or row.

@AngryViking234 2 года назад

23:01 that was a really nice re-imagining. Considering how familiar I am with 159 rules it surprises me how long it took to get comfortable doing it with every cell.

@Raye938 2 года назад

Great puzzle. My explanation: A self referential digit must occur in every row because there there are 9 in each row and they have to pair off. This means that at the end there will always be one without a pair which means it pairs with itself.

@jwill294 2 года назад

1 self referencing digit because there are an odd number of digits. Great video as always thank you

@FelipeRodrigues-vj1zb 2 года назад

I love how every row is also separated by low, mid and high digits. A very special setting indeed.

@Roblilley999 2 года назад

It's lovely how all the columns end up as blocks of 1,2,3 4,5,6 and 7,8,9

@trainsinpoland 2 года назад

Happy New Year Simon to you and to your family.

@nady2296 2 года назад

35:13 what a nice ruleset! It took a little bit of time for me to fully understand it but then I didn't get confused so that's great :) I love the logic used at the beginning of miracles sudokus. Knight and king's moves are always fun and the new rule was a powerful one (it has too if we want to solve the puzzle)

@AdamGaffney96 2 года назад

36:26 Really proud of myself for finishing this one so quickly as I felt like my brain was melting the entire time trying to make sure all the rules were being accounted for every time I got a new digit. That was incredibly fun though, and despite one 10 minute sticking point with no progress I was basically just going and all the logic flowed nicely.

@bobblebardsley 2 года назад

One slightly cool thought about miracle sudokus: Because by definition they have very, very little given information, they *must* have a very restrictive rule set in order to have a solution. Therefore anyone who can understand the rule set has a very good chance of being able to solve the puzzle, if they take the time to apply the rules, there's usually nothing too challenging in the puzzle itself. Making it a miracle everyone can share in, which is very cool indeed.

@agar0285 2 года назад

"And exactly" is probably the reason why Alexa started saying stuff. It's pretty similar to "Alexa" when said relatively fast

@OutstandinglySteve 2 года назад

In each column there are the numbers from 1 to 9, which means that the first column always contains a 1, the second column always contains a 2 etc. Since that number always refers to its own column it is technically self referencing.

@deadboy4735 2 года назад

This rule with columns is quite helping! It'd be so difficult to find all possible solutions with only two known digits as normal sudoku!

@CMLachky 2 года назад

Great Puzzle!! Very fun to work out the trick, but once you have, it unfolds rapidly.

@HunterJE 2 года назад

I wonder how many different solvable puzzles it would be possible to make with the same givens and different rulesets? Would probably be hard to impossible to set but would be neat to see a puzzle collection with a bunch of first-glance identical puzzles...

@MarushiaDark316 2 года назад

Sounds like it'd run into Godot's Incompleteness Theorem rather quickly as how many possible ways are there to define a rule? Case in point, can I have a rule that says, "Digits cannot repeat in a cage unless your name is Phistomefel and it's a Tuesday in February?" Technically, that has a solution, albeit a very narrow one. In theory, you could have infinite such rules.

@lDanielHolm 2 года назад

There has to be one self-referencing digit in each row because there is an uneven number of digits in a row, and in order for a digit to reference another, it has to pair off. So 4 pairs and 1 loner for each row.

@Gonzalo_Garcia_ 2 года назад

11:39 for me. Happy new year, thank you so much for having been such a big part of 2021 for me.

@michaelawilliams 2 года назад

Remarkable puzzle!

@sammiddleton7663 2 года назад

Because I felt like doing some maths, I worked out that there are 945 possible rows in an indexing sudoku and an additional 1675 that obey the indexing restriction but cannot be part of a valid indexing sudoku (the 1 row where all digits are self-indexing, 36 with 1 pair of mutually indexing digits, 378 with 2 pairs, and 1260 with 3). This compares to the 9!=362,880 possible classic sudoku rows. In general, if you have an indexing row of length k containing n mutually indexing pairs, the number of possible rows are k! ÷ (k-2n)! ÷ 2^n ÷ n! and the total number of indexing rows of length k is found by summing this formula for n from 0 to floor(k/2) inclusive. The generalised formula can be found by considering a mapping from a permutation of k digits/an arbitrary row to an indexing row with n pairs of mutually indexing digits where the first n pairs of digits are the n mutually indexing pairs and the remaining digits are the self-indexing digits and considering the ways the permutation can be transformed without changing the resulting indexing row. These are: permuting the self-indexing digits ((k-2n)! ways), swapping any number of the pairs (2^n ways) and permuting the pairs (n! ways). As each column contains the digit that indexes it exactly once, each digit is self-indexing exactly once. As each row and box contains at least one self-indexing digit, each must contain exactly one. If we place the self-indexing digits column by column, the 1 can go in any of the 9 rows then the 2 in any of the 6 rows not in the same box as the 1 and the 3 in the 3 rows not in the other 2 boxes. This repeats for 4, 5, 6 and 7, 8, 9, giving (9 × 6 × 3)^3 = 4,251,528 possible ways to arrange the self-indexing digits in an indexing sudoku. Additionally, the 945 rows valid in an indexing sudoku can be divided into 9 groups of 105 by the digit that is self-indexing. This gives an upper bound of 105^9 × (9 × 6 × 3)^3 or approximately 6.596E24. This is completely useless because the number of valid classic sudoku grids is only approximately 6.671E21.

@fulltimeslackerii8229 2 года назад

interestingly enough, the N colum rule (and perhaps all 159 puzzles) create the disjoint subset constraint as well. the difference being that a disjoint doesn’t give you the other half of the pair when you find a digit!

@Zach_Bliss 2 года назад

I was here from the beginning!

@josephdlist 2 года назад

This was such a fun puzzle and a wonderful way to end the year. The reason you can only have one self-referential digit is because there’s an odd number of digits in every row. Therefore, the digits pair off and leave one odd one out. Furthermore, if you put three or more self-referential digits in a row, you would be short on another row which would result in repeated digits in a column.

@thedavecwright 2 года назад

Oh, loved it. Just under 71 minutes for me. Proper puzzle. 😁

@boostbast5331 2 года назад

You need an even count to divide a grid into pairs. A normal sudoku grid are 9 by 9. To divide it into pairs, you need to get a number on every row and every column who is self-referencing, and exactly 1.

@joemelnyk2230 2 года назад

Bloody Marvelous!

@sherylkoenigsberg5421 2 года назад

Fun one to end the year!!

@mikepictor 2 года назад

That was the video that got me into your channel.

@rochib21 2 года назад

*There are exactly 9 self-referencing cells* Proof: Firstly, there can't be more than 9 cells because that implies atleast one self-referencing cell (SRC) must repeat in a column which breaks the rules. Also there can't be less than 9 because then there will exist atleast one row with no SRC, but that is impossible since 9 cells cannot be divided into exact pairs. Extra: This mathematical property is famously called the *Pidgeonhole Principle* used widely in the field of combinatorics. It basically says that if you were to put _n_ pidgeons in _m_ holes where _n_ > _m_, there must exist atleast one hole containing multiple pidgeons.

@jimmyh2137 2 года назад

Oh nice, i did this one before myself and i remember loving it! It took me quite some time to solve because i was kind of new to the modified 1-5-9 rule (i did one 1-5-9 sudoku before, maybe 2 others max but never on every column)

@waficlabban8658 2 года назад

I love how every row of every box had a 123, 456 or 789 scrambled

@tylerwilson4085 2 года назад

EDIT 2: Thank you to the responders for my silly oversight. EDIT: the reason each row must have a self-referencing index is because 1) there is an odd number of digits in each row, so we need at least ONE self-reference since they come in pairs and 2) you cannot have > 9 self-references because of sudoku (there would be duplicates in a column somewhere), and 3) there must be one and only one self-reference per row because if there were an odd number > 1 of self-references in a row (say 3), there would have to be another row with the same number of self-references otherwise you'd run out of pairs to index. This breaks #2 above of being > 9 total self-references.

@quentind1924 2 года назад

Do you know the normal sudoku rules ?

@rdtg1359 2 года назад

You can't have two 2's in the same row or column ... by normal sudoku rules.

@logiciananimal 2 года назад

Another astonishment. Fun to see the 987654321 row!

@thomashughes8800 2 года назад

Tom here. Each row will have one self referencing number because each reference is made in pairs, or groups of two, an even number. Each row however is made up of 9 numbers (1 set of 1 to 9). This means THR each row will have at least one self referencing number because there will always be at least one number left when taking away any selection of pairings.

@WyanetStarJ 2 года назад

Since every row has 9 digits, you can perform of them only 4 pairs which makes eight total. The 9th digit is left over and has to reference itself. That brave one 😊