The Sudoku With Only Two Rules

** ISLANDS OF INSIGHT STREAM TONIGHT **
We're streaming tonight at 10pm UK time at this link:
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Please do join us if you can!
** TODAY'S PUZZLE **
We had to try this one because it's the work of the great Aad van de Wetering. There's more interesting logic packed into this than you can shake a stick at (and it gave our testers a lot of problems). But, if you can get your head around it, the reward is wonderful.
sudokupad.app/qB6JNbFQqL
Rules:
Place the digits 1-9, once each, in every row, column and marked region. When digit z is in cell (x, y) then digit y is in cell (x, z) and digit x is in cell (z, y).
** PATREON REWARD DAY **
Yesterday we published a new sudoku hunt, Evening Attractions, themed around Negative Constraints as our March competition.
They'll also be a bonus crossword video from Simon and his solve of Region Geometry by Emre Kolotoğlu (3hr 36min long...!) released over the weekend. And Simon's discussion video about Dean Mayer's Sunday Times crossword from last weekend will appear at 1minute past midnight on Sunday morning (which is the moment that competition has ended.)
/ crackingthecryptic
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▶ Contents Of This Video ◀
0:00 Theme music and puzzle intro
1:40 Rules
3:14 Islands Of Insight Stream TONIGHT
4:05 Patreon
4:18 Happy Birthdays
6:05 Wedding Anniversary
6:52 Rules Again!
9:45 Start of Solve: Let's Get Cracking
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[@MaierFlorian]

Simon: breaks into the puzzle. Doesn't realize he broke into the puzzle and just forgets to solve the complete chain of the rule x)

[@daniellydford6142]

It's fascinating to watch him solve an irregular Sudoku, and frustrating that he's not solving the referencing Sudoku.

[@stephenvale2624]

I have trouble following the logic in many CTC puzzles, but this one is impossible for me to follow. Sorry, but bailing on watching this one very early.

[@cjbralph]

At this point, I would be worried about an imposter taking over the channel if Simon actually finished using the logic he had worked out at any given point.

[@sainio]

Sudoku is so strong in him that just cannot help it 😀

[@Roblilley999]

Maybe it shouldn't annoy me, but niggles me when Simon doesn't finish one thing before being fixed into another. Guess that's how his brain is wired 😂 great video

[@xerodeus2337]

what a trip... 47:10 - Simon places the 1 telling him where the 8 and 6 goes 1:09:00 - Simon finally places the 8 by sudoku instead lol what a funky funky puzzle

[@SVURulez]

Thank you for the times! I ended up skipping to 1:09:00 for the sake of my blood pressure 😂

[@timdorr]

LMG: This is a hard puzzle Simon: Yes, but what if it was harder?

[@felis_timon]

It's on Logic Masters Germany? Haven't found it there

[@Daymickey]

😂😂😂 love this comment

[@HunterJE]

Having to do deep breathing exercises about Simon skipping right over placing the 6s and 8s generated by the hard-won 1s in r/c 6/8 XD

[@Turidus]

One thing we can always be sure of:Simon and Mark will find the hardest possible way to solve a puzzle.

[@steveamsp]

I keep yelling "Simon... trace out from the 1s!!!!"

[@mikescott6757]

@@steveamsp me too!!!

[@Torkav]

SAME

[@AndersAstrand]

I found an easier way of think of the indexing in this puzzle is that column N indexes where N goes in each row. And the same for the columns. So once you had all the 9s you could easily just fill in all of column 9 with the column index of each 9, and row 9 with the row index of each 9.

[@nielsdb2090]

Reading the comments makes me happy to know i was not the only one who was screaming about the 1's in r6/8 and c6/8

[@AshleyTheSwift]

I find it so strange when I find something easier than Simon does to comprehend. Ninety nine percent of the time I'm in awe of his wizardry, but every now and again I get one little smug moment like this where I understand and visualise how a rule works quicker than him.

[@noob_jr_2sjrkc]

Same, this is the first time I felt compelled to pick up and finish the puzzle myself. I think it really benefits from geometric reasoning and visualizing reflections, which I find much easier than calculating possible sums and the like.

[@jikrochmal1174]

Me, a computer programmer, at the start of the solve: "uuuuh no Simon, I don't 'just get' that!" And then twenty minutes in I had some sort of reverse Dunning-Kruger moment where I felt like surely it must be much harder than just finishing the chains and solving for the desired coordinates like a system of equations because Simon doesn't immediately do that. So maybe I *did* 'just get' this puzzle actually. Yes, strange feeling.

[@J7Handle]

@@jikrochmal1174 I went on a coloring spree using just the geometry, law of leftovers and mirroring. Got 8 unsolved colors with the 6 left over as the only solved color before I started solving the actual cycles. Didn’t color the whole up to that point, but I did have over half the grid colored before I started doing the cycles.

[@BijickY]

Indexing puzzles are always hard for Simon, I believe.

[@Harry-sp3fz]

Just seen he is colouring boxes and has drawn a diagonal on the grid (great spot by him but it is not needed). I just penciled the possibilities and considered their opposites, which led to a rather simple solve.

[@paulramsay1884]

10:36 "I'm going to put a 2 in there an think about it" - Was the correct 2 placement!!! SMART BRAIN

[@belle9330]

I love how the hypothetical numbers he placed in the beginning made it's way back into the answer of the puzzle

[@heitron81]

Again Simon solving the puzzle in the most complicated way possible ignoring all the easy wins 😅

[@samueldeandrade8535]

As usual.

[@cougarfan8481]

Love the permutation math behind the x,y,z cycles here. When x, y, and z are all different values there are 3! = 6 ways to order them, meaning you get x in (y, z) and (z, y), y in (x, z) and (z, x), and z in (x, y) and (y, x). When 2 of x, y, and z are equal to each other, it reduces the unique orders in half to 3 (since x=y, x=z, or y=z). If x=y=z of course there is only one unique order.

[@CharlesGregory]

I had to stare at this for a bit (and didn't click until Simon filled in the examples) to realise that this was different to a puzzle a few weeks ago - that one was similar, but only rotated one way (XYZ, YZX, ZXY) and not six ways as you mention. I think it got easier after that. No paranoia of getting the order wrong and messing it up, because so long as x, y, and z were different, *every* combination worked.

[@pairot01]

Indeed, but the most common rule for self refential sudoku only cicles on 3 of the 6 permutations. I had to go through each transformation on paper to see it cycles through all 6.

[@twiggywales]

I often "watch" these vids whilst I work so I'm not really paying attention but today was full of many confusing statements like "I don't think green can be blue, can it?" and "Blue is defiantly not orange!" "can 4 be blue... no, lets make that purple" this is one of the most confusing videos I have ever listened too!!!!!

[@vismaychuriwala5124]

The off diagonal 1s that he had filled earlier in the puzzle could have solved a lot of digits way sooner😄

[@brianj959]

Yes, he gave up on the 1s too quickly I’m afraid. It’s always a fun and wild ride to watch the brain activity of Simon in action.

[@samvuckovic6208]

I find myself doing a THE FOUR GOES RIGHT THERE SIMON CMON then he proves to me why four does NOT go there 🤣

[@icestormfr]

Would probably have been easier when getting the 6 and 1 to NOT ignore the application of the xyz rule😅

[@kuroraiko986]

As a programmer myself, you grasp these index pivots far more readily than I do 😂

[@Xelopheris]

One way of thinking of how to do the cascade effect is to realize that every permutation of (x,y,z) comes up. (x,y,z)[1] creates (x,z,y)[2] and (z,y,x)[3], but (x,z,y) then creates (y,z,x)[4], which creates (y,x,z)[5], and (z,y,x) creates (z,x,y)[6]. That's all 6 permutations of x,y,z.

[@katiekawaii]

That makes it infinitely easier for me to understand. Thank you!

[@Pulse159]

This realization was a saving grace for me. I kept mixing up X and Y, only to realize it didn't matter.

[@pairot01]

Things are easier when you realize there's a trick to it? Huh!

[@BrokeMastermind]

Regarding Simon's commentary on the weather: once upon a time, while driving with my dad in the countryside, just as spring had begun to show; it was a rainy drizzly awful day. I was bemoaning the rain as one does when you are 9 and my dad out of the blue says "rainy days are the only days I can see green." He's red green color blind, so only when it's a cloudy overcast day is enough of the yellow from the sun drowned out that he can see green. I'm not color blind, so now on rainy drizzly days I look for the green and I'll be damned if it's not the most vibrant color in the world. Spring is coming once again in Wisconsin and I treasure these rainy days because of an off-handed comment my dad made almost 30 years ago. It doesn't change the need for a rain coat, but it does change one's perspective.

[@Silas_MN]

that's a super cool story

[@Ardalambdion]

Guessing by the length, Simon didn't get much from the last indexing Rubic's Cube indexing.

[@older-wiser-better]

That overlooked 1s hurt terribly 😢

[@Nightsorrow1]

Leave to simon to focus on one rule and forget the other. I was screaming at the screen for him to solve the 1s with xyz. 😂

[@nathanwelling4791]

The "1"s he grayed continued the puzzle naturally, but because of all of his color notes allowed him to finish faster than me still. Damn

[@noredine]

18:25 by chance, it was correct

[@LittlebeanandMe]

I came here just for this comment! 😂

[@daniellydford6142]

That's amazing. 😆

[@sampathkumar-ej7xl]

Simon deducing both the symmetry across the diagonal and figuring out the uniqueness of the digits on the diagonal using the odd number of digits was for me just masterly from my perspective.

[@foghorn51rater]

Great puzzle and entertaining video. Hilariously frustrating when you didn’t iterate from the gray ones when you found them. Not usually an early enough commenter to point things out and maybe be wrong. Hopefully you find.

[@kr12a2y]

Simon proved that the solve path isn't as linear as he thought! Good work!

[@Qazqi]

I'm surprised the testers had so much trouble with this. I wasn't expecting to get anywhere because the video's over an hour, and I did take considerably longer to notice the forced symmetry, but the puzzle is quite approachable after noticing that and reframing the rules in whatever way makes sense (which for me is "the digit in a cell tells you where in the row to put that col number and where in the col to put that row number").

[@jimi02468]

Another one of those puzzles where understanding the rules is as hard as the puzzle itself

[@kathyjohnson2043]

Maybe harder

[@user-gj5uc4yx3i]

Puzzles with this type of rule set would do well to come with row and column labels to plot digits it bit easier.

[@johnosullivan675]

You missed out on indexing the first pair of 1s that you deduced. That would have given you some 8s and 6s and resolved the 6s in box 1.

[@daleomiller]

I was shouting that at Simon for half the puzzle.

[@puritan7473]

I was wondering where he lost the time (It took me 29:39 when usually my time ratio to Simon is the other way round)... I think this accounts for most of the lost time in the end.

[@littlston5319]

Great job in getting the ones, they lead to so much more, I started marking the numbers that I followed through and doing some sudoku, love it

[@felis_timon]

Simon made it harder than it has to be. I solved without having a single thought about that diagonal-symmetry-thing. If you think about it, that rule is just the normal 159-indexing rule extended to all rows and columns. That way, you can solve this puzzle just by thinking about where which digit can go, pencilmarking the indexing cells and thinking about what these pencilmarks index in the other direction. And since 159-indexing is a standard variant, this way should be easier for most solvers

[@Harry-sp3fz]

I haven't watched Simon's solve yet but I am slightly concerned reading the comments. I have no idea why some are talking about set theory. I thought this was a relatively simple puzzle, long sure, but not complicated. All I did was pencil mark the possibilities, input the equation and see what comes out. I repeated this without using any advanced techniques.

[@felis_timon]

@@Harry-sp3fz Haven't read anything about Set Theory yet but probably talking about the Lore of Leftovers. That's something I used too but other than that I just did what I described in my comment. I actually can imagine it not being needed

[@inspiringsand123]

Rules: 01:45 Let's Get Cracking: 09:46 Simon's time: 1h1m34s Puzzle Solved: 1:11:20 What about this video's Top Tier Simarkisms?! Bobbins: 3x (41:11, 58:48, 1:01:53) And how about this video's Simarkisms?! Symmetry: 17x (15:14, 15:25, 18:14, 18:44, 21:52, 21:59, 27:52, 27:52, 28:17, 35:21, 37:29, 38:45, 59:10, 1:04:23, 1:05:34, 1:08:41, 1:08:49) Hang On: 11x (15:18, 17:07, 17:07, 17:11, 28:05, 46:08, 46:31, 48:03, 57:32, 57:32, 1:00:08) Sorry: 10x (06:30, 06:42, 08:21, 09:02, 10:30, 10:30, 20:20, 22:26, 29:44, 1:13:23) Ah: 10x (14:07, 14:51, 14:51, 16:04, 21:43, 27:02, 39:32, 41:25, 41:36, 51:17, 1:06:59) Cake!: 8x (04:30, 04:38, 04:43, 04:44, 05:19, 05:43, 06:39, 06:39) By Sudoku: 5x (34:46, 40:10, 1:07:08, 1:09:01, 1:10:28) Pencil Mark/mark: 5x (47:42, 52:08, 52:21, 1:06:12, 1:06:20) Beautiful: 4x (03:38, 05:32, 1:01:40, 1:05:05) Obviously: 4x (25:57, 43:47, 59:49, 1:00:37) Weird: 4x (19:09, 38:49, 52:47, 58:39) What a Puzzle: 2x (1:10:45, 1:11:17) Clever: 2x (01:11, 1:11:22) Brilliant: 2x (06:33, 1:13:13) Deadly Pattern: 2x (36:18, 41:27) Take a Bow: 2x (1:13:13) Shouting: 2x (06:17, 06:22) In Fact: 2x (01:39, 47:23) Phone is Buzzing: 2x (23:05, 33:51) Progress: 2x (39:01, 1:04:30) Wow: 2x (28:34, 1:10:45) What Does This Mean?: 2x (23:09, 49:49) That's Huge: 2x (47:20) Have a Think: 2x (08:21, 12:36) Good Grief: 1x (08:10) Apologies: 1x (06:06) I Have no Clue: 1x (03:02) Stuck: 1x (53:49) Going Mad: 1x (48:51) Epiphany: 1x (41:45) Nature: 1x (15:44) Most popular number(>9), digit and colour this video: Fifty (2 mentions) One (94 mentions) Green (78 mentions) Antithesis Battles: Even (8) - Odd (4) Row (71) - Column (64) 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!

[@davidalderson]

I've never been so happy to get to the point where I could just do sudoku.

[@gregthewalnut603]

i dont know why i listen to the birthdays every day. theyre just so *positive*

[@thomasfrewer1328]

Every time Simon says "by sudoku" it makes me think of how they'd say "by jupiter" in ancient rome (or at least that's how it's translated into english). and it makes me imagine that sudoku is some sort of deity.

[@psiphiorg]

I started this puzzle thinking that (a,b)=c -> (b,c)=a => (c,a)=b, like a previous puzzle (rotating the digits each time). Then I noticed that the rule was slightly different, and almost started over. But then I did some thinking and realized that the rule for this puzzle includes the rule from the previous puzzle and expands on it. So I was able to keep what I had done so far, and continue onward. The lovely symmetry of this puzzle allowed me to "create" some phantom regions, with the regions reflected across the negative diagonal, which allowed for some additional pairs, hidden singles, etc. I guess that wasn't technically necessary, since the reflection also allowed these to be placed in the corresponding locations in the visible regions, but on a few occasions, I found these more easily one way than the other. My time today was 45:32, solver number 52.

[@danemaple1657]

What i really like about this puzzle is it effectively gave you another rule, just it doesn't need to tell you because deducing it is part of the puzzle, fascinating.

[@st0rmforce]

What an excellent puzzle. I haven't had a go, but I can tell this is going to be beyond me

[@stephan9120]

I probably could have never found the 1's, but after Simon did not apply the rule for these, I tried to continue and everything fell apart. Very interesting puzzle!

[@samueldeandrade8535]

I will never forget this puzzle and the one with the rule "if (x,y) is z, then (z,x) is y". Both brilliant, very geometric analytical. Did Aad van de Wetering make both? I guess he did. Man, simply awesome.

[@IroAppe]

It's cool that the rule works into the same direction: For example "4" is 5 cells down, so you place a "5" 4 cells down. And the "4" is also 7 cells to the right, so you place a "7" 4 cells to the right. It makes the rule easy to execute once you understand that.

[@christermagnusson8526]

My brain melted when he got digits in the grid and didnt use the index rule to get further.

[@piarittersporn]

The complicated rule completely twisted my brain. For a simpler method, I drew a table with the 3 symbols square, triangle and circle (3 times each) on a piece of paper and was able to quickly re-enter xyz in it with a pencil without confusing my brain. So I was able to work my way through from digit to digit until I could finally continue primarily according to normal Sudoku rules. That was really very helpful and absolutely stress-free. With Simon's method it would take me ages to solve the puzzle. One thing is now clear to me: thinking can sometimes be exhausting. 😂

[@KennethBouman]

Having MATLAB as my third language really helped me out here. I was surprised how quickly it fell apart after the halfway point! Brilliant puzzle, Aad!

[@Wakaflockabach]

I'm confident this would have been at least 30 minutes shorter if he'd have just used the God damn 1s lmao based on these comments, glad I wasn't the only one yelling at the screen. I swear, only he could solve this without using those 1s....Simon, Simon, Simon...

[@ffets-SEP]

Wow, this was exhausting, but following all the (x,y)=z rules plus a bit of sudoku made it quite easy.

[@BryanPlonk]

Hi Simon! your favorite plonker here :)

[@bossdoorpodcast]

I did make a short attempt at this, but no thanks! I don't know if I CAN do this, but I know I'm not going to spend the hours it would take to find out lol. Simon is a better man than me!

[@RMDillinger]

I was screaming at the screen to use the 1s in 8,6 and 6,8 from 48 mins - brilliant deduction to get those numbers and then didn't use them lol

[@RhiannonAgutter]

After looking at this on the day of release of this video and being like, nope, I came back to it today with new inspiration and did it in 42:40!

[@ChakatStormCloud]

I really enjoyed this one, though my bread and butter for the early part was reflecting regions across the diagonal and saying "this region has 6 in it, so wherever it lands across the diagonal can't be a 6."

[@oliverwalden4334]

Interesting, how different the solving paths can be, though I only watched half of the video. I got the ones just as Simon found them at the start, be I worked on them, quickly getting all of c/r 6, then some coloring gave all the sixes and nines and then most of the rest was sudoku and symmetry. Nice puzzle, really enjoyed it. Now, please, someone solve region for the stars!

[@koenth2359]

As a father of three, working long hours, of course I know the law of leftovers 😊

[@Jh-zx9sm]

Love a good Aad van de Watering puzzle, went to put this on in work and turned it off so i could try it myself once i got home, took me 55 ish minutes love indexing rules just hate abnormal region rules :(

[@rojoloco9268]

Long time viewer, first time solver, what a wonderful puzzle

[@elevensalor]

The only way I can keep track of these x/y/z ones is to draw a little grid on a post it and stick it to the monitor. I just cannot keep it straight without seeing it every time.

[@HunterJE]

Another way to look at why a digit on the falling diagonal gives the values for three cells instead of six is that it causes some of those six to land on top of each other...

[@alexm495]

Yes it was frustrating to see Simon not extend those 1s, but I think his instincts are to focus in on digits that are important to the solve, in a way that goes beyond my abilities; but then he gets too focused and forgets to pick the "low hanging fruit" as he calls it. A case of his advanced solving skills leading him astray while overlooking the basics. Let's be forgiving folks!

[@benjaminrealy5661]

45:43. Easily deduced the mirror line. And within 10 minutes realized the mirror line had to contain each of the digits once. Went back and forth between notation and colours and as colours eliminated notations it solved itself enough to do standard sudoku without having to worry too much about xyz (but it did help in some cases) Lots of thinking, but not too difficult. 10/10

[@sirgeremiah]

Simon immediately recognizes 4 new digits as "given digits". At least he'll be able to see these!

[@richbuckingham]

You can also break-in just using coloring in the bottom right as you know which cells correlate across the diagonal and must be unique per box, row and column, this quickly gives you only a single color on the 1 in (9,9) which matches (6,8) and (8,6) and you're away in no time.

[@Pulse159]

Took me just short of 2 hours. I was very stuck for a while. resorted to set theory when I had a full column and row to get moving again. I ended up using a color to mark any numbers I got through sudoku or set so I could go back and resolve the X,Y,Z rule when i got stuck. Very fun puzzle. I was very concerned when I kept confusing X and Y at the beginning, only to realize after a while that it didnt matter. You can resolve every combination of X, Y, and Z not just the pattern given in the rules.

[@RichSmith77]

Arghhh, I almost had it. I had the symmetries worked out, and lots of cells coloured, but missed the crucial point that each digit would appear only once on the diagonal. I needed that hint from Simon, and also to ask the question where 6 could go on the diagonal. Solved it from there.

[@bangbangfan2184]

Aad is my favourite setter. His puzzles are normally very clever, but approachable. I have even completed some of them myself. Phistophemel, qodec and Totally Normal Cat puzzles are great too but they tend to be so far out of my level that I have trouble even following Simon's logic at times, let alone completing them myself.

[@taliesintown9710]

You might find it easier Simon to write down your digits for the index rules! Get a piece of paper and draw three columns, and label them x, y and z and write the index rule to remember it, that way you can cycle through and see it more visibly in front of you. You did a puzzle with a similar rule set i think a few months ago and you struggled with it there as well, so maybe this’ll help you. Perhaps you can create a second screen and write it there for viewers to see as well. Now I shall fall asleep to this video! edit: my brain has kept thinking and i think this kind of rule set could benefit from being written in a slightly different way: “When digit z is in rXcY, digit y is in rXcZ and digit z is in rZcY.” this way it is in sudoku notation because co-ordinates can be written differently like in graphical notation which is what i thought of first.

[@daniielah.7569]

43:08 The break in was super satisfying, seeing Simon lose track of the logic chain from the break-in was not ^^'' Still, love this channel, got into Sudoku thanks to it

[@stangerrits6712]

1:01:46 It’s probably not part of the intended, more straightforward solve path, but figuring out that green is 9 is a very clever deduction indeed!

[@user-on1yq5gq6z]

If I may suggest a simpler approach: The 1 pencil marks in row 8 can be quickly whittled down to columns 5 and 6 (column 8 is excluded by the diagonal not being able to contain an extra one). Now reflect around the diagonal and ask yourself whether 1 can be in row 5 by looking at the region surrounding that square and asking where 1 goes in that region.

[@andrewcook4873]

Created coloured boxes as the mirror images of the given boxes to help me know where all the overlapping sets are. I managed to whittle it down eventually. I got a completely different solve path so the solution isn’t as linear as all that. I think the difficulty for me was applying the rule, I never really got my head around the application of it and had to read the rule again every time I got a concrete digit so it went very slowly.

[@Gonzalo_Garcia_]

23:17 for me. Wow, what a cool idea. Loved the puzzle!!

[@RecreationalCynic]

I understood the rules and how to apply them, but got stuck for a while because I didn't realize that the diagonal had to be a set of 1-9. Once Simon pointed that out in the video the rest of the puzzle just unravelled itself for me

[@SVURulez]

I'm so glad I glanced at the comments early on in the video because that emotionally prepared me for the trauma of Simon failing to make use of the only rule after getting the first digit 😅

[@fatercoelho7476]

going through the conclusion of the rules would be helpful. going by the iterations you would get: if (a,b) = c then: ac = b. therefore: ab = c cb = a cb = a ca = b cb = a ba = c bc = a ca = b ab = c removing the duplicates: ab = c implies that ba = c ac = b ca = b cb = a bc = a making sure to always resolve those rules any time you place a new digit makes this quite simple

[@jonniboye6399]

For some reason I struggle a lot with these types of puzzles just keeping the logic in my head. It's not that complicated, but I find myself failing so hard and having to go through the mental exercise of figuring out what cells are referencing each other for each instance.

[@Timlagor]

I got the 8 and 6 in column 1 early by considering the implications of where we knew 1s could be but didn't know the remainders trick.

[@laurv8370]

oh dear... i was screaming to those gray 1s for half a week.... :D

[@crazypantaloons]

Something about the rule makes it symmetrical. I did it by accident enough to know that was true, but I never quite placed the flip flop.

[@LarkyLuna]

I love doing these solves because I can sit down and do math beforehand lol You have a triple (x, y, z) and two transformations, one is turns into (x, z, y) and the other (z, y, x) You can reach a permutation of (y, x, z) by doing T1->T2->T1 You can prove that you can reach any of the 6 permutations of x,y,z and every digit is in a cycle of 6 digits (with repeats)

[@deelkar]

106 minutes, and I needed to get to Set Theory to "get" it. after that it was pretty smooth sailing.

[@Harry-sp3fz]

I managed to solve it in 68:34. It isn't a "difficult" puzzle but it is time consuming going through the equation over and over again. I actually had to say it out loud every time. I enjoyed it but I don't think I will do another one of those unless their is some other rule set added on.

[@jeremydavis3631]

I'm not sure the rules were clear enough. While it doesn't matter whether we think of the coordinates as (row, column) or as (column, row) because the rule is symmetrical across y = x, what does matter is where we put the origin of this coordinate system. Since the coordinates are called x and y, it seems likely that someone will interpret them in the same way as we're taught to interpret rectangular coordinates in school and say that (1, 1) is the bottom-left corner. That would lead to a very different, almost certainly broken, outcome.

[@goldcakes]

Okay, so (1,1) is top left. I was searching the comments for the answer to this

[@ServantOfSatania]

Spent 30 minutes doing nothing before going to sleep, waking up with the right mindset to actually look into the logical extent of the rule and solve it in 20 more minutes

[@Raven-Creations]

The symmetry is caused by applying the rules to the productions. In the end, given xyz, all permutations of xyz are generated. I.e. xyz, xzy, yxz, yzx, zxy, and zyx. If x=y, this reduces to xxz, xzx, xxz, xzx, zxx, and zxx, removing duplicates leaves xxz, xzx, and zxx. If z=x, it reduces to xyx, xxy, and yxx, and a similar picture emerges if z=y. That is, the unique digit occurs in each position in the triple, one of the permutations lies on the negative diagonal (strictly speaking, since row numbers increase as we descend, it is really the positive diagonal, but I'll go with the convention). If x=y=z, the cycle is self-referential and no new cells are generated. This all makes it much easier to propagate the digits, with none of the head scratching over which digit goes where. For instance, I worked out that R6C8=1. It's then just a question of permuting the three numbers, so R1C6=8, R1C8=6, R6C1=8, R6C8=1, R8C1=6, and R8C6=1. Using this, I was able to solve this quickly without colouring, although I did shade the cycles that had been completed, just to keep track of digits which had not yet been through the cycle process. When considering where a digit could go, I also shaded the cells it couldn't, which made it easier to see where it was restricted, and since the pattern of restricted cells must reflect, it was possible to quickly narrow digits to one or two cells. Colouring the digits made no sense to me. It just made keeping track of things much harder.

[@leeannadimoulas5163]

This puzzle was... So weird. Once Simon showed the break in via the diagonal symmetry, I paused to solve for myself, forgot to use the rule (x,y,z) and just used the symmetry line. Took so much longer that way lmao. Finally finished it by separating the 3,4,5 triples I had left using -gasp- the intended rules and solve path. 🤦 So any goofs you made Simon... Couldn't have been that bad. (Re-solved, which obviously gave me an advantage, in 40m and it was so so much more straight forward using the actual rules. 🤣🤣🤣)

[@karsaanita]

Another colouring puzzle! 🎉

[@adipy8912]

First I thought it was the same rule for the miracle Rubiks cube sudoku 2 weeks ago where 3 digits makes a cycle, but in this sudoku there's a ix between 3 digits makes a cycle and 6 digits making a cycle.

[@kinourik7979]

It's the first time i try a sudoku just because of that 1 in r6c8 XD it was fun and in fact was a chain of rules at some point it was just sudoku xd

[@penningmeestercgkdelft9159]

What a fascinating new application of the (x,y,z) indexing rule! In fact, when (x,y,z) are three different digits, the number of permutations will be 6 and that's the number of new digits you can get. When (x,y,z) contain two different digits, there are 3 permutations, and when x=y=z there is only one. Moreover, any pair of cells (x,y) and (y,x) are never in the same region, otherwise the irregular sudoku rules would clash.

[@Quintinohthree]

I'm wondering if these rules prevent any grid which has an (x,y,z) tripple (which must be on the diagonal). I think if there are, they come in sets of three, as each reduces the number of cells referred to by two (from three to one for that cell) and that will need to be compensated with an extra set of six digits each referring to eachother, which will eat up three (x,y,z) tripples. Now how that would be possible or not, I can't exactly figure out.

[@MattYDdraig]

16:48 Breaking in was a challenge but getting 3 or 6 cells for every one makes rapid work once you get going. Very clever design to make it all work though.

[@DaveLeCompte]

it's unfortunate that (x,y) is interpreted as x=row number, y=column number, and not x= horizontal coordinate, y = vertical coordinate

[@NicD]

Yeah, they're confusing letters to use with standard matrix notation. (Luckily it makes no difference in this case.)

[@DaveLeCompte]

I'd use i,j,k if I were using matrix indices, and x,y,z, if I were talking about coordinates@@NicD

[@timdunkley9173]

Just over 13 hours without spotting the symmetry.

[@RMJ1984]

Its funny how human brains work. Because this puzzle seems so simple compared to many of the others long complex puzzles with 10-20 lines of rules.

[@christopherswanson5849]

i think the rules should be explicit that (1,1) is in the top left corner, and that the ordered pair is read (row, column). i honestly thought it was ambiguous on purpose and began to solve as if i needed to prove this information.

[@Pulse159]

I thought this as well, but interestingly it doesn't matter if row or column is X in this puzzle. Because of the way the pattern propagates around the board, every combination of X, Y, and Z is always used.

[@christopherswanson5849]

that is true! however, the location of (1,1) changes the puzzle completely; e.g. if (1,1) is in the bottom-left like a math graph, the two 6s at the start become a 4 and a 6. rulesets like this one usually read "if rXcY is Z, ..." and because the wording here invoked mathematic notation, i assumed that meant that in order to assume ANYTHING, the necessity for specifics with math notation applied @@Pulse159

[@Dr_Trey2001]

You could have gotten the 1 right off the bat when you penciled the 1’s in row 7 and column 7. That leaves you a naked single in r6c8

[@faddy91]

I think the rules are mathematiclally simple but not the easiest thinng to visualise. If you think of it as like 159 but referencing every row and column. For example once Simon has all the twos he should be able to fill in row 2 and column 2 simply by looking at the indexing

[@vulkandrache1928]

What are all these pencil markings good for if it takes you 10 minutes to use them?

[@dwdei8815]

Seeing as there has to be a norm for the way round (x, y) coordinates are given in variant sudoku, what a pity it is (row, column) - i.e. vertical then horizontal, the opposite to the (x,y) cartesian coordinate system we're much more habituated to. Everyone who has ever drawn a graph, that is. It does my head in.

[@olivier2553]

When trying a solution becomes a bifurcation? Around the minute 58, Simon tries 9 in R5C7 and it implies 9 is in R2C3 which reflects in R5C4 by the law of left over and is a conflict. At that step, 9 is green. I think that by effectively writing 9 in the cells during the deduction would make it more visible than just highlighting the cells and Simon could have seen that more readily. But is that bifurcation? Simon managed to do the same deduction a little while later with the yellow colour, but the deduction was already there to be taken but I am not sure it is allowed to "try" it on.

[@Beosker]

As a coder, can confirm that I get indexing is easy for me to understand

[@PathOfShrines]

Really cool idea. I found this a little less brain-melty than the one a week or so ago. 45:43.

[@CrypticCL]

Is it unreasonable for me to have felt confused and want to clarify the origin? In the standard cartesian plane, the positive digits are found 'above' and to the right of the origin. i.e. 1,1 would be the bottom left cell. But here we are to assume that it's like reading a book - i.e. that 1,1 is the top left cell.