The Mad Miracle Sudoku

[@thoughtbyte]

Thank you so much for featuring this puzzle. It was truly a discovery. The rules are admittedly very tricky but I thought the logic of how it unfolds was wonderfully beautiful, and you showcased that brilliantly, as always. This has become a cherished hobby, thank you both for that! - thoughtbyte

[@SSGranor]

This is a beautiful puzzle. Though, I think I'll attribute my sub-40 minute time mostly to having also been thinking recently about the interaction of indexing with friendly cells.

[@mahmoudabdelghany7112]

Dude, this is awesome. I like these puzzle that are constrained with their rules and the fewest clues possible to break the symmetry. Solving this puzzle reminds me of the natural crystals that exist in nature just because mathematics allow them to. Absolutely brilliant and I enjoyed it tons 😁. Thanks for making my long group meeting pass by so quickly xD (I hope my supervisor isn't gonna read this).

[@57thorns]

Would the solve be easier using the given one and starting in box 1?

[@brettduffin8412]

I am a mere spectator

[@korayb5295]

19:40 its not friendly 6... how come he solved this puzzle correctly? even the start is wrong.... he starts with "6" in box 5... but 6 can appear on blue diagonal (r4c4 and r5c5) coz 6 is not friendly there.. why he eliminated? anyone help?

[@andrewgrant6516]

I'd hate to see what a hostile indexing miracle would look like, but if you happen to find one, please do send it to Mark to open live on the channel

[@longwaytotipperary]

😂

[@karsaanita]

Don't be fooled! It's just the indexing propaganda calling these ones "friendly"

[@jordandavenport2819]

The mind is a mysterious thing lol

[@FluffSWE]

sometimes i really dont get Simons use of colors. in 'normal' sudokus he can suddenly go crazy and color all the numbers. but in this sudoku where some cells are friendly and indexing others, he doesnt use any color at all :D Simon is totally chaos! and i love it.

[@KittSpiken]

My solve looked like a crazy quilt, hours he left the colors at home is beyond me.

[@windybeach2184]

I used green for friendly and grey for not, but I probably didn’t grasp all the logic well enough to utilise full colouring

[@masterfiddler11]

Chaotic good?

[@ElysaraCh]

I love watching Simon get increasingly angry at a puzzle like this until it starts to click and he starts solving it, almost to spite it.

[@WilcoVerhoef]

As a programmer, I can indeed confirm that at least this type of indexing feels quite natural. It only helps a bit though, this puzzle still requires a lot of the more general cryptic sudoku skills.

[@AvatarBowler]

To me, it’s mainly because programming languages like C++ and Python make use of arrays a lot, and one has to know what indexing means in order to use them properly.

[@srwapo]

I only took an intro to programming class 20 years ago and indexing felt like something I could understand, but also something that I ended up messing up quite a lot. Much like this puzzle!

[@windybeach2184]

If anyone hasn’t discovered the ‘Show row/col numbers’ feature in the app, this puzzle is the perfect time to use it.

[@michaelbellecourt3875]

I love watching Simon do indexing puzzles because it's the only time it feels like he's as utterly clueless as I always am.

[@peaoui165]

My simple way of thinking of friendly indexing this puzzle. "Take the column, put it in the row. Take the row, put it in the column."

[@matthewread9001]

My way was “if there is an x in the y position, put a y in the x position.” So a 6 in the 5th column, would put a 5 in the 6th column.

[@MaierFlorian]

You know Simon's got mad when he starts putting pencil marks in 6 cells and more at once... 😅

[@crashtextdummie]

"Somehow the Sudoku already knew" may be the most endearing sentence in CtC history. 😂 Really felt for Simon on this one, he managed to solve it without ever really grasping the index logic. Ah, to be a programmer...

[@TrabberShir]

As a very out of practice former programmer, I am going to say I thought about this puzzle very differently than Simon, but definitely not better. My total time may have been slightly better than his, but nearly half of my time was spent writing the program that actually solved it, so you could also say I never successfully solved it.

[@DWestheim]

I always do the puzzles first before watching the solve... if I at least understand the rules without crying. Today is a day where I will just watch Simon cry. :-P

[@longwaytotipperary]

😂

[@Jaze327]

I attempt most but this one was an immediate 'just watch'

[@aleksandrajanicka6949]

Now imagine trying to understand such complex rules in a fog puzzle without putting actual digits in 🙂

[@aamocryp]

that's what you have central marking for!

[@QuadraticPerplexity]

There's a thought: A fog puzzle, but the rules are hidden under the fog too...! That could support some non-local shenanigans.

[@penningmeestercgkdelft9159]

Phistomefel could definitely do that...

[@microstudy_]

i remember solving this puzzle with myxo (after bellsita asked/forced us to) and it was crazy how it resolves with just a diagonal and one digit, such an incredible discovery by thoughtbyte!

[@davidrattner9]

Glad you got a chance to solve it and 1st hand experience what Simon did. 🙂

[@MrMusAddict]

The "simple" (to me) explanation of why the triples behave how they do in boxes 1, 5, and 9 is that you have to think about the box's friendly digit. They will always index to rows & columns of the same entropy (123, 456, 789), so you have to place the 1, 5, and 9 such that none of the entropic digits never land on the diagonal. That's why the 456 is on the same side, whereas the 123/789 are split across the diagonal; they're the only places 1 & 9 can go while avoiding placing 23 and 78 on the diagonal.

[@Anne_Mahoney]

Yes: Simon kept groping towards the entropy idea but didn't quite get there.

[@marpocky]

Also keep in mind the friendly digit has to "see" the digit(s) it's referencing. Since 1,5, and 9 land in their respective boxes in different places, their associated triples have different shapes.

[@ruminator2943]

Would you help me understand why the entropic digits can't land on any part of the diagonal? For example, why is it a problem in box 5, to put the friendly 5 in r5c4. That would put a four in the very center of the grid on the diagonal. But that position is r5c5 box 5, so it's not a friendly cell and therefore not an indexing cell. What's telling you that the entropic 4 can't be there?

[@ruminator2943]

NVM. @waffling0 answered this below. Now I can return tomorrow to proceed with the solve!

[@jaega4247]

Amazing work by Simon to fight his way through this puzzle! My own brain was clearly not made for this kind of struggle at all.

[@longwaytotipperary]

Ditto 🤪

[@penningmeestercgkdelft9159]

Correct me if I'm wrong, but I believe that the final grid even satisfies all the rules of a 1-5-9 indexing sudoku!

[@inspiringsand123]

Rules: 02:02 Let's Get Cracking: 11:13 Simon's time: 1h24m54s Puzzle Solved: 1:36:07 What about this video's Top Tier Simarkisms?! Bobbins: 1x (1:15:10) Goodliffing: 1x (18:45) Three In the Corner: 1x (41:25) Maverick: 1x (00:36) The Secret: 1x (09:27) And how about this video's Simarkisms?! Ah: 20x (04:49, 05:53, 17:44, 19:17, 20:11, 23:25, 28:21, 45:04, 45:58, 49:56, 58:15, 1:12:04, 1:16:02, 1:16:43, 1:20:35, 1:20:35, 1:23:25, 1:24:38, 1:25:51, 1:35:10) Hang On: 16x (14:03, 20:45, 22:22, 23:25, 37:10, 45:58, 50:27, 51:30, 1:06:11, 1:06:56, 1:21:14, 1:21:14, 1:21:14, 1:22:37, 1:27:17, 1:32:49) Symmetry: 10x (28:18, 29:10, 29:11, 33:23, 33:55, 48:16, 48:39, 50:01, 54:00, 1:16:55) By Sudoku: 9x (39:25, 1:07:49, 1:08:01, 1:12:27, 1:18:17, 1:19:45, 1:29:28, 1:33:16, 1:33:49) Pencil Mark/mark: 8x (31:07, 1:01:58, 1:11:20, 1:11:39, 1:12:38, 1:14:32, 1:17:18, 1:28:32) Sorry: 7x (14:53, 40:22, 56:53, 58:15, 1:04:20, 1:06:36, 1:12:18) Nonsense: 5x (35:21, 40:02, 59:56, 1:08:06, 1:26:25) Wow: 5x (33:44, 33:47, 1:07:04, 1:09:17, 1:09:17) What on Earth: 4x (02:00, 14:43, 45:38, 1:03:26) Goodness: 4x (03:50, 03:50, 47:16, 1:06:51) Lovely: 4x (07:33, 08:37, 10:53, 24:14) Plonk: 4x (52:54, 52:58, 1:20:48, 1:27:56) What Does This Mean?: 4x (03:08, 15:38, 19:12, 34:40) The Answer is: 2x (38:50, 1:17:54) Out of Nowhere: 2x (1:30:14, 1:31:42) I Have no Clue: 2x (11:22, 1:01:52) Brilliant: 2x (08:27, 08:28) Incredible: 2x (09:13, 1:32:46) Astonishing: 2x (1:37:09, 1:37:09) Bizarre: 2x (28:09, 28:12) Disappointing: 2x (1:13:02, 1:13:04) Corollary: 2x (1:17:38, 1:25:28) Obviously: 2x (27:50, 1:05:42) Baffling: 2x (14:40, 14:40) Cake!: 2x (07:48, 07:53) Good Grief: 1x (58:15) Clever: 1x (1:01:36) Naughty: 1x (26:15) Stuck: 1x (06:30) Horrible Feeling: 1x (51:40) Beautiful: 1x (1:25:10) Fascinating: 1x (1:05:57) Deadly Pattern: 1x (1:34:32) Bonkers: 1x (05:29) Shouting: 1x (10:50) Have a Think: 1x (37:34) Nature: 1x (1:10:57) Most popular number(>9), digit and colour this video: Fifteen (3 mentions) Six (151 mentions) Purple (2 mentions) Antithesis Battles: Even (8) - Odd (0) Column (113) - Row (105) 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!

[@apry9]

this is like a level of autism never before seen

[@albinlundqvist6102]

This is horrifying

[@spelldaddy5386]

Do one like "don't talk to Simon at parties"

[@sethstuff921]

"shouting" at 10:50 is actually shout-out not shouting. Hopefully you can continue to improve!

[@ymiros0953]

Is this comment just not collapsible for anyone else? That's kinda crazy given the length

[@KyleBaran90]

Question! How did Simon rule out the 6 from the central box diagonal about 20:00 in? Don't the rules say that the indexing only applies to friendly digits? In box 5, the 6 would be at r4c4 and in position 1 in box 5 - it couldn't possibly be friendly.

[@waffling0]

It's because if you put 6 in r4c4, it is in the same column and row as a pair of 4s which will index it (they are friendly because they are in row 4 or column 4)- they have to go in the 6th position of their respective rows/columns, which makes them occupy the same box. A similar argument applies to r5c5. And if 6 goes into r6c6, then it will be indexing itself both by row and column, so it doesn't abide by the rule that friendly digits must index at least one other digit apart from itself. So it's not about 6 being friendly, it's about the digits that index the 6 being friendly and breaking the puzzle by their positions.

[@RichSmith77]

Basically, ignore Simon's reasoning up to 23:00. He recognises himself that he was incorrectly treating 6s as friendly in box 5, but he winds his logic back and finds a correct explanation from 23:00 onwards. (The same reason as excellently explained by @waffling0).

[@ruminator2943]

Thank you, thank you, waffling! I like to understand each step before moving on, so I stopped the video. I asked the question above and have been pondering this. Such a simple explanation. A pair of friendly digits (one in the row and one in the column) need to put a digit there. Yes! ☝🏼🤓

[@Riskomul]

I was like what is he talking about with the sixes? They are not friendly...

[@DarkChasm]

🤣I almost fell off the couch laughing @3:40, that face OMGLOL.. I've now watched Simon trying to process the rules like 8 times and it's gets funnier everytime I see it. "This is the face of a man, who's brain just came to a complete halt" 😂 Mark is 100% right about one thing, it is absolutely hilarious ❤❤

[@PremierSullivan]

"Programmers love indexing puzzles"... especially C/C++ programmers. Mere mortals cannot understand C pointer semantics.

[@spacelem]

I've programmed a lot in C++ but have managed to never once use a pointer! (References get you a long way). Then again I'm a mathematical modeller, and not doing the sort of programs that need pointers. Used plenty of indices though, and more often in 1-indexed languages, so that at least makes me happy.

[@baktru]

Naah I hate this puzzle. This indexing shenanigans starts at 1, not 0 as it should.

[@Anne_Mahoney]

Real programmers use PL/I. And Fortran. 😺

[@algea_algea]

We need to see a Mark reaction video when he watches Simon open one of these "Open live" viseos

[@JonathanCorwin]

I'd also like to listen into the phone call Simon made to Mark afterwards!

[@QuarkTwain]

I can imagine Mark watching Simon make such a great number of pencil marks, and laughing maniacally

[@emilywilliams3237]

I think that understanding the rules, and working through the implications of the diagonal, were 80% of the difficulty - and you did get there, Simon, eventually, even if you think you did not fully understand what you were doing (or some of the commenters as I am writing think that you did not fully understand what you were doing). But after a certain point, indexing puzzles all seem to me to be administrative puzzles, and being watchful and careful. I was amused (and pleased) at the amount of pencil marking you did, and the careful exploration of the meaning of the diagonal and the impact of various digits when they appeared on it. It may have seemed fatuous, but the fact that you repeatedly clarified (for yourself and for us) which digits were friendly and which were not, and that each row, column, and box needed one of every digit - it may have seemed fatuous, but it is one of the things that I can so easily lose track of in this kind of puzzle. Thanks so much for not giving up on it! It was a miracle indeed.

[@oleksandrbotte7662]

I've spent last decade programming. This ruleset does not make me happy

[@spacelem]

Same, and I'm used to 1-indexed languages!

[@madsli]

Me, understanding jack shit about the rules, nodding sagely in regards to Simon's deductions: "Hmm... Yes, that makes sense"

[@Swisswavey]

No, I'm not even trying this one😂. I don't get the rules at all. I'll watch Simon's struggle instead

[@bohs2000]

Why he no color friendlies?

[@LiquorStoreJon]

I always love a good puzzle that Simon has to open live for us to enjoy!

[@sillyking1991]

SO the way i thought about it that made it a little easier to picture. at least parts of it. was that any digit that was friendly by virtue of its row/column had to appear in the analogous place on its opposite. so like the 4 in column 4 had to be in the analogous position on row 4. This is because the 4 in row 4 and the 4 in column 4 both reference the same square. so they much be paired with the same number. in other words. if R4C7 is a 4. then R7C4 must also be a 4. knowing that, then you can determine that those numbers can never be appear on hte rows/columns within the box that they both reference to.

[@Anrui_Ishi]

Even watching Simon work through the logic of this puzzle I was still very very lost.

[@chessburns]

Often i can follow his logic but wen i cant i rewind the vid several times in order for it to sink in. Try it n see if that helps :)

[@borreholic7238]

So now after the fact looking at the solution... except for boxes 1, 5 and 9 where they would have ended up on the diagonal, in box 2 the 2 is in row 2, the 3 in box 3 is in row 3, etc.... I'm sure you are some wizards out there who knew early on that had to be the case. In other words, it's only in boxes 1, 5 and 9 that friendly cells index two other cells. (I'm a complete newbie, so sorry if there's 100 ways of saying this in a clearer way).

[@skulldoxbox2]

Weird way to look at it is if RxCy=z and is friendly, then RzCy=x and RxCz=y. Don't know if this will help anyone, but that my math way of explaining the rule in my head.

[@longwaytotipperary]

That’s perfect 👍🏻!

[@MartinFindon]

These rules are designed to make you weep, trying to get your head around them is like trying to pat your head and rub you stomach. Love the video thumbnail!

[@Squishy3757]

If you’re familiar with indexing the explanation is very simple. A friendly digit becomes an index for both the row and column in which it is located.

[@craigfjay]

I don’t find these rules simple at all- the rules say that it must reference “at least one” cell other than itself, but then the example show it must reference both cells- not just at least one of them

[@zachswanson6643]

It's a negative constraint on digits referencing only themselves: so you can't put a 1 in r1c1, for example. But digits can reference only one other digit, for example a 2 in r2c4 only indexes to a 4 in r2c2, since the other direction points at r2c4.

[@stevieinselby]

@@craigfjay I think the "at least one cell other than itself" is there to stop you putting a 1 in r1c1, a 5 in r5c5 and a 9 in r9c9 - those cells are completely self-indexing on row, column and box, and so those digits would be valid entries without that bit of the rule. It took me a while to figure out that all friendly cells must index their row _and_ their column _and_ not be completely self-referential.

[@RichSmith77]

​@@stevieinselbyDoesn't it stop any digit on the diagonal being its own row/column number? E.g. a 2 in r2c2 would be referencing itself in both row and column, and not referencing any other digit.

[@DiMono]

This puzzle is a beast. I'm glad I took the time to solve it. Thank you for featuring it.

[@George4943]

Indeed, Simon, indexing takes a change in point-of-view about meanings of numbers. An index is an ordinal. 1st, 2nd, 9th, etc. An index of n means the nth position in a column, row, box, or position in a box. Contrast with cardinals. You can add cardinals: 2+3=5, but not ordinals: 1st + 3rd is not 4th.

[@abcde_5949]

17:55 I was thinking that these self-indexing numbers could still exist, as long as they are labeled as "unfriendly". Apparently that wasn't the case.

[@karsaanita]

I don't know why, but these indexing puzzles are way more doable for me than some of the more typical sudokus. Maybe because the difficulty in these originates from the rules and not some clever trick that I can't find most of the time :D

[@oregonexpat]

Simon, I hope you weren’t too upset with Mark. We see that He does have a definite knack for picking out the puzzles 🧩 that fall just a bit outside your comfort zone. But it makes for truly excellent viewing, letting us sit with you and anticipate, and kibitz, and chide you as we hear your thoughts while you „puzzle it out“. Great fun, and all thanks to Mark for being your devil!

[@MrAsymmetry_]

I think my programming experience allowed me to intuitively get a much quicker start than Simon, and realize that along the diagonal each cell only had 6 possibilities (i.e. box 1 can't have 123 on the diagonal and similarly in box 5 and 9 with their respective digits) But even so, this was brutal, I find it very difficult to visualize this kind of indexing in my head (I usually have to draw or print a matrix when programming to fully get my head around it) and I was soon slowed down and unsure how to progress in this puzzle. I had to get a few hints from Simon to get it finished :P

[@RealNovgorod]

Only in the diagonal boxes (1, 5, 9) the friendly numbers index 2 different cells (within the same box), while in all other boxes they coincide with their row numbers and therefore only index into the diagonal line. Is that a coincidence or a necessary consequence of the rules?

[@longwaytotipperary]

Now I see that!😲

[@berlinflight_tv]

While this puzzle is far above my current weight class, the video still was an eye-opener for me in terms of which solving skill I’m still lacking: Simon is so good at questioning and verifying his hunches and intuitions to make sure that he doesn’t go down a wrong path. I often neglect to do that, and so I frequently manage to do an initial break-in only to end up taking a wrong turn and breaking the puzzle. On this one, though, I wouldn’t even have been able to spot the break-in.

[@psssht8998]

I have been waiting all day for the video. Got a tub of ice cream and ready to be at awe of simon solving the sudoku

[@logiciananimal]

Any other logicians in the house? I wonder if the "given items in grid" vs. "rules" trade-off is similar to rules vs. axioms in formal systems. I wonder how that could be studied. (There is an older book, purely on classic Sudoku, called _The Hidden Logic of Sudoku_)

[@robertleifeld225]

When Simon begins his video, he uses 99 percent of internet bandwidth. No bandwidth remains for Mavrick so he Flys his aeroplane near Simon's window.

[@MattCarlyle-e6q]

Simon's allergy to thinking about box-friendly numbers first was both maddening and amusing :)

[@jazzlittle184]

I really didn't find the solve fun to watch as I could not see the logic, even while watching and listening to Simon try to explain it to me. I still can't see why Simon was treating a 7 in r8c8 as friendly. And I feel like Simon almost explained that many times but it was not easy to follow. 😭

[@lizzyvv447]

I got to the point where Simon was at 1:08:10 faster than him... and then I got completely stuck and watched the video instead.

[@kenadigwe2917]

I dream to once a member of the ranks of lunatics 🫡

[@BryanLu0]

In box 9, the 9 is friendly, which determines the 8 and the 7 since it's in row and column 8 and 7 so it refers to a 7 and 8 in row and column 9.

[@PauxloE]

Getting a grasp on this (I wouldn't call it break-in) took a while, and then it was careful elimination, spotting triples and quadruples, etc. Total time 145:21, solve counter 236. Fun fact: most boxes had 3 friendly digits, except for 3 boxes, which had (only) the digits appearing 3 times in total. (As usual, after solving this I don't have time left to watch the video, so this goes to my long list of CtC videos I need to watch.)

[@PauxloE]

→ For this puzzle I found it really helpful to enable the row/column numbers in the options of the tool. → I used coloring to mark (potentially) friendly digits - one color per digit. (I switched to a color scheme without black/gray, to have 9 actual colors available.) - e.g. in the situation at 1:02:50, I had shaded the 1 in box 1 as friendly, the potential 1s in box 2/row 1 and box 4 column 1 (half-colored), the 2s in box 2/row 2 and box 4/column 2, the 3s in box3/row3 and box 7/column 3, the two 5s in box 5 and the two 9s in box 9. (I also marked the cells a friendly cell pointed to (apart from itself) with a circle in a similar color. Not sure if that's for everyone, though.

[@Halfrando]

Solved in 98:58, very proud of this one for me:) Probably spent a good 20 minutes just running the ruleset around my head until I could remember what they meant haha

[@kluaoha731]

I had to stop and reread the rules every time I considered a digit for a cell that would make it friendly.

[@Mannol26]

I wasn't even gonna try to do this one on my own.. but the logic Simon prior to 52:57 was correct, only in a reverse way.. putting a 7 in the ninth column isn't friendly, but the logic is that the 9 in that row needs to be friendly in the 7th column to put the 7 there.. and the same goes for the 7 in the ninth row, the 9 needs to be in the 7th row of that column..

[@longwaytotipperary]

🤪

[@RichSmith77]

He could have saved himself a bit of time by first considering 5 in box 5, and then 9 in box 9. Both had only two possible positions, and both restricted 4s, 6s, and 7s, 8s in their respective boxes. There was then no need to also think through the indexing restrictions for 4s, 6s, 7s and 8s in those boxes.

[@TheClawNinja]

Brain overload. And I've only read the rules so far.

[@Stereomoo]

84:00, took me a long time to figure out anything to do, but then it got easier from there. Amazing that a puzzle this simple in terms of rules & the initial 1 can have a relatively followable solve path.

[@giladooshlon]

Took me over 2 hours but somehow got through it eventually. Amazing construction

[@dab1810]

A somewhat simpler method of explaining Simon's starting logic: a "proper" indexing cell cannot be placed on the line, because then it will only index itself. However, because of the nature of the cells on the line, they become "pseudo indexers", i.e. they tell which columns and rows have X number. Therefore, you cannot have a friendly number indexing to a cell that is on the line in the same 3x3! Definitely needed Simon's help getting this logic started, but it works without fail and is extremely restrictive of three numbers per box wherever there is a diagonal line

[@tman9641]

Please record that phone call to Mark!!!!! ❤❤

[@SkylersRants]

I'm completely in awe of you Simon. I still don't even comprehend how the rules even work. Why can you say one cell or another is or isn't friendly? No clue. Hat's off to you.

[@RoderickEtheria]

What's interesting about this is you have generally symmetric constraints producing a non-symmetrical solution.

[@jenisjourneys9215]

101:40...I understood intuitively that 1,2,3 couldn't appear on the diagonal in box 1; 4,5,6 in box 5; or 7,8,9 in box 9...but I needed Simon to explain the logic of why and the next step to me (thanks, Simon!). I'm not sure I fully understood the indexing principle, though...I had to backtrack from incorrect solves 3 or 4 times. But definitely seeing my Sudoku & logic skills start to improve!

[@nidoking042]

Around 1:14:30, when you put the 8 in box 1, I went in a bit of a different direction, coloring the 456 along the diagonal and looking for contradictions. If you consider row 1 column 2, it can't be 7 or 9. Regardless of which way round you put the 1 and 2 in box 9, there will be both a 7 and a 9 looking at that cell. So it's the third 456 in box 1, which places that same digit in row 2 column 9, sorting out the 9 in that box, and there's a huge cascading effect from there. I also worked out pretty early on that none of the digits on the diagonal could be friendly at all, but I don't remember exactly how I arrived at that conclusion. Probably an extension of the backwards indexing logic - a friendly cell on the diagonal would be indexed from both directions and thus can't point back to the indexing digits. I think it's impossible for a friendly cell to index another friendly cell, but I don't think I'm up to proving that.

[@randysavage1011]

Fun fact, Simon wears red more than any other color.

[@penningmeestercgkdelft9159]

In fact, when coloring all the friendly digits after finishing the puzzle, you'll find that the resulting pattern is symmetric around the positive diagonal (from r9c1 to r1c9). In fact, box 1, 5 and 9 only contain one single friendly digit each, whereas all the other boxes contain three friendly digits each. The latter boxes furthermore contain all the digits that are friendly with respect to rows or columns, whereas the boxes 1, 5 and 9 only contain a digit that is friendly with respect to its own box.

[@accident12123]

1:00:00 I found it interesting you didn't try to start here. I'm more a novice so I guess I just saw the given and asked where can that eliminate possible friendly digits. From watching your solves i think your more seasoned solving ability has givens helping along the way and not the break in.

[@JaymanOttawa]

It was very interesting watching you use extensive pencil marks during this solve. I'm looking forward to your next video when you get back to belittling others for doing the same!

[@konstantinzelikov4903]

I didn't understend on 43:30 Simon puts both 2 and 3 in cells and not 2 or 3.

[@steve470]

Here's a restatement of the rule: friendly cells index in both their row and their column, and they do so separately. Consider the column that the 1 is in. The 1 is in the second cell, so a 2 must be in the first cell. Now, consider the row that the 1 is in. The 1is in the third cell, so a 3 must be in the first cell.

[@konstantinzelikov4903]

@@steve470 but this is not the rules of this puzzle. I still don't see any problem if 1 indexing only one of that cells.

[@steve470]

@@konstantinzelikov4903 "All friendly cells are column and row indexers, and they must index at least one cell other than themselves." Note the "and": they all index in *both* column and row. The second half of that sentence just means that you can't have, for example, a 4 in r4c4, because that would be indexing itself in both its row and its column.

[@konstantinzelikov4903]

@@steve470 thanks. Finally i understand the rules. Puzzle is not as hard as I thought.

[@grahamrskelly6042]

That was really really hard, such a good puzzle though. I did have to watch the intro to get my head around the rules, I am not a programmer but maybe slightly better programer then Simon... But his scanning is way faster then mine.

[@SimonToth83]

I managed to solve the indexing part easily, but then got completely stuck on basic Sudoku and just couldn't crack it. 🙁

[@icedbear]

I was shouting at Simon SO loud, that I almost woke up my father. Who's 10 miles away. In a cemetery.

[@jeanbarque9918]

Isn’t Simon wrong with the 6 in box about r4c4 an r5 c5, a 6 it would be a friendly digit.. so why shout it count for something.. ? And the 4s of r4 and c4 aren’t necessarily in box 5.. which … nonsense.. please someone explain

[@atpx8]

decided to try solving this one myself, which ended up taking just a bit over 165 minutes. brutal, but brilliant

[@LarkyLuna]

I think those digits are called friendly because every time you a friendly digit index something, that indexed digit is looking right back at it friendly 4 in column 5 putting a 5 in column 4 But a friendly 5 in column 4 would put a 4 in column 5 They index each other in pairs always So the logic always works backwards as long as it's looking at a true friendly digit

[@BryanLu0]

Digits are friendly only by the fact that they share row, column, or box number (sometimes position) This is a standard naming convention The fact that the indexed digit also indexes the indexer is a result of indexing. If you think about 159 sudokus, column 1 tells you where the 1 goes in the row, or the 1 in the row tells you what goes in column 1.

[@Raven-Creations]

After studying this for a bit, I came to the following deduction: for a box on the diagonal, the digits for the rows/columns in that box must not be friendly by row or column, nor on the diagonal. For instance, in box 1, 123 are restricted. 1 can only be in R3C2 or R2C3, 2 can only be in R1C3 or R3C2, and 3 can only be in R1C2 or R2C1. The given 1 places the 1 in R2C3, which places the 2 and 3. This puts 1 in C1 in R4/5/6, so R1C1=456, and so R1C4/5/6 = 1, and R3C7/8/9=1. I got the 123 in box 1 pretty quickly, but it got really tough after that, mainly just trying to work out where to look. Then it suddenly collapsed, round about where you were at the 1:20:00 mark in the video. I'm normally fine with indexing puzzles, but for some reason this just didn't click with me for ages, and I kept having to double, and triple check I'd not made a mistake. I think it was probably the way the rules were phrased, which seemed backwards to me.

[@bryandenijs7661]

Question: At 1:03:40, Simon says: "If a 1 is in R4C4, it puts a 4 in R1C4 and in R4C1. If a 1 is in R5C5, it puts a 5 in R1C5 and in R5C1. If a 1 is in R6C6, it puts a 6 in R1C6 and in R6C1. ", but why is that? The 1 isn't a friendly digit in neither R4C4, R5C5, R6C6, right? So why is it indexing the 4's, 5's or 6's? And then he says: "Whatever digit you put on the diagonal, it's going to cause mirroring." It just don't understand why. He says the 3 is not possible on the diagonal in box 9 because you have to put 7, 8 or 9 in R3C789 (which is not possible), but why would it put the 7, 8 or 9 there? The 3 is not a friendly digit in box 9, or am I missing something?

[@christianschmid1440]

One day I want a flashback which explans mavericks background story. Am I watching too much anime and therefore expect every reoccuring person in a video to have a tragic background? Yes... yes I do.

[@RichSmith77]

After three hours, I though I'd solved it. I certainly had a solution. It was only as I started watching Simon's solve that I realised I'd relied on a completely unjustified "deduction". Soul crushing. I'd done okay in the initial part, finding the 1 in box 1 and the restricted positions for 456 in box 5, and 789 in box 9. I'd also restricted a few other digits, like 4 in the top of box 4 and 6 in the bottom of box 6. I'd worked out there was only one friendly digit in boxes 1, 5 and 9 (the box number), and three friendly digits in every other box, and what those digits were in each box. For some reason, that I cannot now explain, I decided that none of those three friendly digits within the same box should share a row or column! This remarkable (and very wrong) incite allowed me to "solve" the puzzle. It turns out that none of the friendly digits in a box do share a row or column, so my solution ended up being correct. But my method for getting there was wrong. At least, having recognised I made an erroneous assumption, I went back and re-solved it without the assumption. But only by exhaustively bifurcating down paths I knew would be wrong, until I reached contradictions. Not very satisfying.

[@bait6652]

Its nice to know when u struggle(even tho u discover what ur suppose to see) , u can always come back to the channel to see the trigger only to find out their 30min in and struggling....then u watch them break the puzzle only to realize u missed/forgot one of the rules (self-pos on diagonal not alloweed)..wasting away 20-30 or hr Found the 2spots for box1:1 ...forgot the additional rule :(

[@flobiish]

@54:53 If you put the 9 in r7c8, the 8 goes in r7c9 because the 9 is in box 9 and thus friendly. It's the box number that determines the order between boxes 1, 5, and 9. The 456 in box 5 are on the same side because 5 is the middle digit of the trio so it is in rows/columns 4 and 6 and those are on the same side of the diagonal as the 5 pointing at them. The 1 causes a jump across the diagonal because the 1 (the box's friendly) is in rows/columns 2 and 3 which are on opposite sides of the diagonal. Same goes with the 9's effect on box 9's digits, but you'll figure out where they go later in the video (I assume, I'm actually still paused at this timestamp). I'm enjoying the solve, but I'll admit I'm having less trouble getting the indexing...probably because I'm a programmer. You will find the 8 next to the 9 in box 9 and the 7 is across the diagonal.

[@OlafDoschke]

I'm not sure your discovery of the inverse nature of the indexing, of cells being indexed, was making it simpler, especially on the marked diagonal. Just take a look at the positive diagonal, too. It's populated with 159 only. And if you take the time to mark all friendly cells by box, row, and column you will notice only very few are not self-referential. That makes that puzzle hard. If there were more cells like the 1 in box 1, the 5 in box 5, and the 9 in box 9 (again159) there would be more cascading effects. Those were the only cells indexing two other cells. It's not astonishing because each row's friendly cell must self-reference itself within the row. Each column's friendly cell must self-reference itself in the column. And that's also the reason there can't be friendly cells on the marked diagonal as they would be self-referential twice. The only other digits theoretically possible on the diagonal would be by box-friendliness, but they'd cause double digits within their box.

[@andrewnelson2525]

I immediately focused on 1's in box one and got three digits in short order. Then I focused on the diagonal and made consistent headway. Unfortunately I mis-indexed something somewhere and got hopelessly tangled up, and had to restart the puzzle, and the total solve took hours. So according to Simon I'm a genius (for knowing where to start), and according to Mark I'm a numpty for all my mix-ups. Actually, a genius numpty is a pretty fair description -- I'll take it!

[@moocowpong1]

The whole first hour is Simon explaining the rules to himself.

[@ukdavepianoman]

A real slog this one. The final grid has some interesting properties - RxCy + RyCx = 10 almost everywhere...except for some 159 combinations. Given the symmetrical nature of the ruleset perhaps not too surprising.

[@timcotton1782]

The better description of the indexing is: For every friendly digit X in position RYCZ, RXCZ=Y and RYCX=Z. Programmers prefer to re-state linguistic descriptions as formulae and equations...

[@coreydixon9713]

Well, it took me 4.5hrs over the course of 2 days, but I somehow managed to solve this one! I nearly had a huge blunder when I had somehow not placed a 9 as a possibility in the central cell and thought I had found a 7 there. But something felt off and I double checked my work. Funny how one slip can cause a defeat. Glad I could conquer this amazing puzzle!

[@DavidCollison]

Taking my love of the channel as a given, I think this video is also a great demonstration of how the ability of Simon (and Mark) to unwind from a mistake is an especially valuable logical skill and is especially impressive while being recorded on video.

[@benwhite5734]

One quirk of the puzzle is that the digits 2, 3, 4, 6, 7, 8 in their respective boxes must be doubly friendly in their respective rows, and the 1, 5, 9 in their respective boxes must _not_ be in their respective rows. A consequence of this is that once the 4 indexer on the diagonal is locked into being 379, it must be 3 because the 4 in row 4 must be in box 4.

[@srwapo]

About 2 hours 15 minutes with a bunch of peaking at the video. And making a spreadsheet that helped me keep track of where the digits could go. And turning on the conflict checker. This one was super tough for me, but I felt like I could do at least some of it once I sat down with some free time. There was a lot where you had to keep track of multiple digits several steps into the future to see if they worked or not. I could ALMOST feel how they worked, but it was just too much to keep all in my head at once. Probably would have taken me about twice as long without help from the video.

[@Kira_Nakasashi]

Sometimes when I get stuck, can't figure out where to go next, and I have a lot of pairs, I assume one number in the pair and start filling it in with that assumption (Like, in a 12 pair, I assume it's a 1 and see what happens from there.) until I reach an impossible answer with what I have. If I don't get anything and have followed all the logic, I do the other number in the pair and follow that as well. Usually that will help me figure out which of the pair set is the correct one because I'll eventually reach something impossible by the rules.

[@gooseberry41]

149:20 for me. Rules are not that complicated actually when you get used to them. But I got completely lost in the middle of the solution trying to disambiguate 456 placement in box 5 or 789 in box 9, spent most of the time for that.

[@tralomine]

I finished this one faster than you (for once (yes I'm a programmer)) and I find it a funny to see you struggle to understand every implications of the rules

[@Coyotek4]

I was able to place the 1, 2, and 3 in box 1 (and assorted pencil marks) ... and that was it. Got completely stymied and had to watch much of the video to see what I missed (mostly how the cells along the marked diagonal had to themselves be indexers). Too tough for me. :(

[@altreusplays]

Your first 1 didn’t break because it was the only one that was friendly once: the others were friendly twice (by row or column); and in position 1, friendly thrice! Of course, there are two safe positions for 1 in box 1, but the given digit excludes one of them by sudoku.

[@Pete7396]

@58:35 Simon says that box 2 cannot have 2's in the 3rd row because that would force 3's into the 2nd row, but that is incorrect. The rules state that a friendly cell must index "at least one cell other than themselves", not "they must index every cell". So a 2 in r3c4 could index a 4 in r3c2 and then you could put any digit you like in r2c4.

[@nagualdesign]

40 minutes in and I'm baffled by your reverse 'logic'... 🤔

[@mstmar]

consider my brain melted. my solve looked pretty much like simons except a bit longer (at 126 mins) and in slightly different order, but each piece of logic was the same. one thing i found a bit helpful was reversing the logic on the friendly indexers. basically saying if there is a the Xth cell in the row/col with a friendly X is the col/row number of the friendly cell.

[@hyperactvehuman]

@22:01 why did he assume that all the numbers on the diagonal are friendly? Or where ever the six is on the diagonal is friendly. Edit: he corrected it 30 sec later.

[@Malakree]

Watching him essentially prove that a digit cannot be friendly by virtue of it's row/column while in a box which contains the indicated diagonal, then spend 30mins not realising he's proved that is a bit irritating. How he can simultaneously see such esoteric points and then be blind to the obvious proofs/corollaries is mindboggling to me.