Computer Says "No": A New Sudoku Breakthrough
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- čas přidán 26. 08. 2021
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This is a RIDICULOUS sudoku puzzle. The computer needs about 50 sequential "guesses" to solve it and yet it has a logical path that human beings can find. This is another incredible achievement from the brilliant jovi_al - it's called Cobra Roll - and you can give it a try at the link below:
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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.
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Simon and Mark
Simon, your kindness makes me smile so much! Thank you so much for featuring this puzzle-- I had an inkling of hope that you would solve this on the channel and am so pleased you managed to get through it. No words can express how happy I am right now!
Jovial you are a legend! What the heck are you thinking?! Brilliant
I need to thank shye for being an inspiration, and my testers who managed to solve this (and the ones who didn't)!
I pointed this out in another comment, but a little easter egg I like to do is try to sneak as many consecutive digits as I can into a pattern in a classic. It took some massaging on this one! If you follow the "train" from the top left, you can see the digits from 1 to 9 in order.
A bit about the title! A cobra roll is a roller-coaster element, which I thought the givens vaguely resembled. It also has to do with loops (which this technique most certainly is) and the fact that, as shye said, it's a "roller-coaster of a solve."
Saw that it was a classic that destroyed computer solvers and knew it was one of four people. Your understanding of the base sudoku ruleset is truly exemplary.
@@jovi_al Holy smokes, what a puzzle!
Is there an official name to this technique?
Can we please get a reaction video from you so we can see the inner workings of a sudoku setter's mind when they watch their puzzle being solved. 👍
It's always fun when Simon starts putting in digits "by sudoku" in a classic sudoku without any other rules...
Lol
It is correct to say that "a human being can solve this, but a computer can't", with a strong emphasis on *A* human being, and that human being is called Simon Anthony.
Why is it correct to say that the computer couldn't solve it?
@@clumsyjester459 I solved it using the same methods that the computer did. Following those various chains all over the grid (some involving dozens of steps) is NOT guessing, as Simon keeps saying. It is logic. Just past the 17 minute mark Simon uses the same "If this is true then that can't be true" logic to prove his theory. Whoever came up with the idea of X-Wings and such had to use that same type of logic, or bifurcation to prove that the theory actually works. Anyone who uses X-Wings and such is merely standing on the shoulders of giants to help them solve the puzzle faster. I prefer doing it the hard way.
@@jimjimellell Interesting opinion. To each their own I guess. Whatever makes you have fun, although I must admit doing it "the hard way" doesn't sound particularly fun to me.
@@jimjimellell X wing’s literally require no guessing to prove they eliminated numbers from the grid. It can be thought out logically with out any guesses.
@@clumsyjester459 It is correct to say that the computer couldn't solve it without bifurcating, more accurately.
One of my favorite things about this channel is how they explain pencil marks and basic sudoku technique every single video. It makes the videos so inviting.
I recently started folloing this channel - and you are absolutely right. I love their awareness of new people watching.
24:15 "This means something"
Picturing Simon staring at a heap of mashed potatoes...
Love the reference. I think you need to be a certain age to get it, though.
This is important...
Aliens would contact Simon to represent earth for sure. He'd get my vote.
Oh, this is so funny!
Simon: Hears 5 birds chirping…
I would appreciate watching a “failed” solve video just as much as a completed one! Especially if he then taught himself the breakthrough method and explained it, then solved the puzzle.
It’s like watching Gandalf learn a new spell
"If you want to give it a try yourself..." ... No, I don't think I will.
I sign that ;-)
Same :D
:D
I gave it a try.
I just did not last very long.
:D
@@mikes_.5_cent Once Simon did the thing with 1 and 2 I immediately tried with 3 and 4 and solved it from there on quite fast (faster than he did, actually, since it took so long for him to figure out what it meant). I probably couldn't have figured out how to start out though.
"The computer needs about 50 sequential "guesses" to solve it and yet it has a logical path that human beings can find."
Guess I'm not human. :(
The word is 'can' and not 'will'. In this case, we all can only be sure of 1 human who will, and in fact already has.
@@luckystar3641 Two, because Jovial.
So we've got a Phistomefel Ring a now we DEFINITELY must call this a Jovi_al Square!
I'd suggest Jovi_al Corners.
I don't think this is a variation of Phistomefel's Ring (in the sense of permuting rows and columns). Of course that makes Jovial's achievement all the greater.
From memory, Steering Wheel is a variant of Phistomefel's Ring but I'm not 100% sure
@@BigAsciiHappyStar I don't think @jbomber44 comment was meant to suggest the Jovi_al Square was a variation of the Phistomefel Ring.
The comment was suggesting that since we have a Ring, then we should have a Square. In this case we should have a "Parker Square"... oops, soory I should have said a "Jovi_al Square".
I support the nomination. The Jovi_al Square is born!
@@BigAsciiHappyStar He’s saying that since we have a technique named after Phistomefel, we should name a technique after Jovial
@@dragonman1495 thanks that makes sense, my bad.
I find the statement "human being DO know that" very generalized and would like to see myself excluded from it.
Because this was just- wow. No. But wow.
Oooh another lengthy video for a classic, love these
I solved it the same way the computer did and there was no guessing involved, as Simon keeps saying. Following those various chains all over hell and back is a valid logical means to an end and I find it to be challenging and FUN!
It did take me 3 days to finish, but that was (mostly) because I was binge watching episodes of Stargate SG-1 and was only working on the puzzle during the commercial breaks.
I hope to see more puzzles like this on CTC.
This series of ‘logically unsolvable’ puzzles is blowing my tiny mind. I watched the ‘steering wheel’ one the other night and instantly subbed. So that’s down the rabbit hole with me then.
And you will never look back. But ... get used to shouting at your screen as you go on. 😂
Welcome to Wonderland - there is no logical escape.
I wonder if it would be practical to have a format of mini-puzzle where, instead of trying to solve an entire grid, one were given a partial set of clues (e.g. just the 1-4 in boxes 1, 2, 6, and 9, and contents of boxes 4 and 8) and told "identify all possible digits that can appear in R4C1, R4C6, R9C1, and R9C6". Although having all puzzles share the objective "place all the numbers in the grid" is somewhat cleaner than having different objectives for different puzzles, it's almost never possible for a puzzle with a really brilliant break-in to maintain that level of brilliance throughout the solve, among other things because it's difficult to design a puzzle that will fall apart without much boring slogging, but won't fall apart as a result of a lucky guess. An advantage of the mini-puzzle format is that someone who tried to use bifurcation, but didn't know how many values should be possible in a particular square, would have no way of knowing whether it was solved correctly.
Please, please. Let's have more puzzles like this one! And thank you jovi_al for creating this masterpiece.
The last two Jovi_al puzzles on the channel have been brilliant.
I am a little concerned that having decided this was too hard for me I actually spotted the corners before Simon, this could well me my sudoku high point !
After having some success as of late, I was brought low by a classic.
Not that I didn't solve it. I did solve it (and proved uniqueness) ... which is to say, I guessed the heck out of it and hit a dead-end with every guess, before stumbling over the finish line in just over an hour (60:17 to be exact). Time to watch the video and see all that I missed.
i came here after i ve watched a video of a guy solving witness in under 15 minutes..
i have to say i was even more amazed with this one!
congrats to simon, respect to jovi_al
Just like to say thank you for showing me that I can actually do a sudoku! Just got the main sudoku games today and I’m having lots of fun! Just so brilliant, so thank you again and good luck on all future solves (I’ll be rooting from the sidelines)
If you're looking for some excellent, approachable daily puzzles, check out their Discord server! The Daily Puzzle channel has some very well done sudokus, both standard Sudoku and variant sudokus. Mark has done a few videos where he tackles a week's worth of puzzles in one shot and it's really been fun solving them myself and then watching someone else go through it.
Human beings know that! No, Simon knows that! 😂 when the colours start coming in, I know I am finished!
Now I'm wondering how many breakthrough techniques are only known in arcane places of the internet. I sort of think it would be great to see some "fail" videos of Simon and Mark. Could be just as interesting as a solve.
Love the hand built classics :)
Imagine an AI with Simon's voice, taking fifteen minutes to explain how it was able to eliminate one digit by using a Unit Forcing Chain...
"I apologize, humans, if you were shouting at me 'unit forcing chain,' but it took me several hundred milliseconds to find that one."
That's a '9' to complete that column.
Highlights a row.
Can I move this beam?
...
Do you mean column?
Alternative Inference Chains are not guessing. If you read what the step does, they do the exact thing that both of you do. It implies what happens when a digit is placed and, using a few other digits in the grid, eliminates a digit as an option due to the repercussions.
Edit: If you go through the entire sequence of steps, it never uses the trial and error. Therefore, no guessing involved.
Implying and guessing is the same thing actually. I think the line between them is defined only by the amount of how much you use it
I wouldn't say implying and guessing are the same. A chain is often just like when we have a bunch of 3-or-4 cells, and color them, and make a deduction based on 'this cell sees both a green *and* a purple, so it isn't a 3 or a 4' or the like.
@@Henrix1998 They could be similar in some regard. We could theoretically argue that these chains are like a short version of bifurcation, but then we could also spark the conversation that bifurcate just means to split, and has been a modification of that definition that means to guess. But also, according to Simon and Mark, it's only bifurcation if you write it down, which to me is somewhat irresponsible to have a definition as such. Whether you guess in your head or show your work, it's still guessing. But when they do it, more often then not, it's something that dis/proves that something can or cannot be that, and that they have enough logical information to discern it. And when they do it, they make an implication that x digit cannot be here because there would be no place for y/z in a few moves. So I wouldn't exactly say they are the same, but in some instances could very well be.
There's a fat grey line between guessing and looking for alternative inferences. Depends on who you ask. Someone just commented that doing an alternate inference chain in your head is not guessing, but writing down the exact same chain to test/prove your elimination is definitely guessing. Go figure.
An alternate inference chain is NOT guessing. it is a logical technique that examines the candidates within and between cells that tells you which of two choices must be true without any guessing. It is the epitome of pure logic. Sudoku Swami has some excellent videos on this esoteric logical technique.
I admire your genuine modesty and the fact you call a spade a spade….. nonsense is nonsense….
' forced square quadriples'...... processing that...
You know, if someone manages to program one of those sudoku solvers to be able to do geometric solves like this one, and the phistomofel ring varients, then the solver will become all powerful.
"A series of esoteric guesses" - Wasn't able to make any progress after 20 minutes aside from the series of very interesting looking pairs in Box 3, very intrigued by this technique - And, indeed, was able to figure out what the technique meant during Simon's discussion about it and then the puzzle pretty much solved itself within around 10 minutes. Lovely puzzle, and a very good explanation of the logic by Simon that made it crystal clear what was going on before he himself figured it out.
Completely off-topic, but I can't help but wonder if Simon would change his mind on never wanting to do another audio puzzle involving bird sounds following yesterday's stream if someone like Phistomefel were to design one.
Since we have a blind associate on this channel and given that we have a comment about audio puzzles, both of these get me to wonder: could one set the audio equivalent of a sudoku? I'm musically incompetent, so I'm not the one to say, I guess. But what does come to mind is ... a sudoku is about one might say, broadly speaking, a spatial arrangement of 9 types of elements repeated 9 times over. So an "audiodoku" would exhibit (say) a temporal arrangement of 9 x 9 elements. Unfortunately, and this is where the idea founders, we only have one temporal dimension to us, alas! Yet we know from recursion theory (for example) that we can represent pairs as single elements (i.e. reduce calculations of Q to N, so ...?
Me: listening, all happy because solving is going on and it sounds tricky.
Simon: Sorry, I realise this is the most inarticulate thing anyone has listened to in their life...
These are some of my favorite videos on the channel. Just the childlike joy from Simon as if he was discovering Sudoku again.
jovi_al: awesome!
I ended up doing trial and error with the 23 pairs and then the 14 pairs and getting them both wrong in first attempts. But I solved the puzzle. Simon's break-in was amazing to watch.
Trial and error with 23+ pairs sounds exactly like what the sudoku solver was doing.
24:00 One thing it means is that, due to the 34 pair in the square's upper-right corner, one places an 8 and a 5 in the middle block.
31:50 The puzzle doesn't collapse so much as gradually weaken now. I first ruled out 3, later 2, from the lower-right corner, leaving 14.
34:00 I stand corrected. The puzzle collapses for Simon.
End: Congratulations! It was a great puzzle.
Another corker of a classic! Thank you, jovi_al and Simon!
Also interesting to point out with the symmetry, if you read the digits from box 8 and box 4, on the diagonal, you get pairs of numbers. 5-6 6-7 7-8 8-9
if you follow the "train" from the top left, you get all of the digits in consecutive order :)
this is an easter egg i try to put in my classics, seeing how many consecutive digits i can place in a row!
@@jovi_al Aren't there two little trains? One 1-9 boxes 1-2-4 and one 1-8 (with a surplus 8) boxes 9-6-8? Thank you very much for a beautiful learning opportunity for me (translates as: needing help by video)🤗!
@@jovi_al missed that somehow!! BTW awesome sudoku, I'll come back to it in a couple months one I've done some training!!
@@jovi_al Pretty much a N00b here, but I did spot that 1-9 train upper left... guessing that the shape is what inspired the name of the puzzle?
Simon,
In its simplest form, aligned pair exclusion basically says the following. Suppose you have two cells that share a row, column, or box - that is, they “see” each other. Now suppose these two cells can also “see” an entire group of N cells that between them share N+1 candidates (an almost locked set, or ALS), and the two original cells also share candidates with the ALS. All aligned pair exclusion states is that the two “starting” cells cannot contain a combination of digits identical to one of the cells in the ALS, since this would leave that cell in the ALS with no possible candidates.
Fabulous puzzle and an unbelievable solve! Well done to both of you!
So cool you were able t solve it Simon. I really enjoyed the logic and appreciate your presentation of it. Thanks to Jovi Al for the great new puzzle!
Computers
15 years ago, I wrote a [classic] Sudoku solver program in C++ that can solve any puzzle astonishingly fast. I couldn't find a Sudoku that the program couldn't solve in less than 20 microseconds (you read that right, that's 20 millionths of a second). Same for this puzzle -- 17 microseconds. But the algorithm was basically an optimized brute force, or bifurcation. That's what computers are exceedingly good at. I mean mind-boggling good, and fast.
But I remember the feeling after having done it. Sure, I accomplished getting a correct program to solve quickly, but what a let-down. I discovered it was no fun at all. What makes puzzles fun is not getting the correct solution, but the series of small victories along the way as you apply your own brain to it.
Simply Sick... congrats to all who were able to solve it!
awesome puzzle and awesome solve!
What a satisfying solve!! Sadly, it wasn't me who solved it. But watching the genius of jovi_al and Simon was satisfying enough.
Congratulations to both of you.
This is next Level.
This seems so lovely, I am happy to share in the excitement
thats sooooo beautiful omggggggg
Usually I can barely follow the logic at all, but I was able to see the 1,2,3,4 quite quickly which was pretty cool. I was sitting here like Simon. It’s right there. You got this
Thank you, Simon.
I had to watch it a second time to figure out how the 1,2,3,4 thing worked.
Thank you.
I attempted to do it how the computer does it, labelling out all of the possibilities for each number with the pencil marks, and I must say it is much more difficult to notice the 1234 square with all information available than it is to break it down step by step. When all information is available you see overlapping possibilities for those squares that are differnet numbers, making the trend of the 1234 boxing almost impossible.
That person would eventually create Skynet.
Nomination for this construction is referred to as a "Jovi_al Frame"
What an incredibly brilliant puzzle. I was utterly unable to advance until Simon started thinking about the corners - and from there, I got it. I think I was kiiiinda getting close to that on my own, but would never have reached it for real, as I was focusing on entire columns or rows, and one digit at a time. This is really an unexpected strategy, and surprisingly clear once you see it.
utterly stunning setting.
This is a great "series." Keep them coming!
"That's five in the corner. No that doesn't get a song" whahaha I had to stop the video cause I laughed too hard
I want to see MANY more of this type of puzzle
Myst! I have done them all and i spittle stay awake deep into the night to see you work through myst, riven etc!
What a happy smile he just has at the end ^^
What a sublimely telegraphed technique! Kudos to jovial for this incredible puzzle, it was a joy to watch Simon solve it. c:
incredible that Jovi_al can keep producing wonders of logic. Thank you Simon for highlighting the wonders of sudoku again.
So maybe im not a human being, i could never spot that in a million year.
The solver you used in illustrating it has been upgraded apparently. It doesn't have to go through such a complicated rigmarole, at least for this puzzle. Techniques are restricted to: Naked Pairs/Triples; X-Cycles; Fireworks; Hidden Singles. The puzzle is still ranked as Very Hard Grade with an overall score of 356.
These new rule classics are my favorite.
You know what, I think I will NOT try this one myself before watching
Very impressive ... Bravo !
have seen the video twice and i have no idea how to solve it. I understand the logic, but I would never think of it during a solve.
yes yes yes!!!! so thrilled you found the trick here, it really is something magical :D
Wow Simon. You made the grid come alive by spotting that 1234 combo. Spotting something that others dont and making it seem like it is no big deal is Simon.
Beautiful puzzle.
That solve was epic.
Simon saw the symetry but didn't see the string of digits 1-9 in upper left part of the grid which looks pretty nice
He spotted the 1234 at top left and at bottom right, which turned out to be useful.
another way of looking at it is dividing to 2 sets of 1-4 and 5-9 (with 2 colors) then it just solves itself
Seriously amazing.
I did notice that as soon as you had the weird square quadruple pencilled, you completely ignored the colouring from that point on. Wouldn't have made much difference, but simplified a few spots along the way
I'm always impressed how you can find these logical patterns, but also constantly surprised that you don't follow through on your early logic when it can still help. In this case you place an 8 and a 5 on coloured squares. The colouring logic immediately allows eliminations from r9c6
Simon vs the machine
No variant sudoku is as daunting to me as a standard sudoku that Mark or Simon deem hard.
I gave it a go, made some pencil marks, fiddled with set theory, showed I could get somewhere with bifurcation but the bifurcation didn't point me towards any logical path. So I started watching the video. Once Simon highlighted the 12 possibilities and turned to 34, I realized what was going on and solved it, but that's with Simon doing 90% of the heavy lifting. Still pretty proud of the 10% I did though.
Wow, what a solve and what a puzzle! And it actually seems a bit of a consolation to me that computers and machines will never really take over the world, as long as they can't even do something that a human being CAN do: use intuition, spirit, serendipity perhaps, to grasp this classic sudoku. Is there actually such a thing as artificial "intelligence"? Or should we say that computational force is dumb and blind and just gives back what real human beings have been putting into it?
I'm going to do a bird tweet puzzle that makes a sudoku so be careful if you want win?. Still loving your stuff(All of it. Everything else too. You have kept me and my family sane. I want to say a massive Thanks again for your time. I love CtC that much I want to put it on the big screen in my Aunties home. She migh like
She might not get it but she is a fan too. Respect guys. You all make me have a great day, everyday so keep that for us if you can because we appreciate it. Take care and much love from STOKE. I like oatcakes
You know it's bad when you're all the way to step 35: Death Blossom
It was those same four corners that were key to breaking the puzzle the other day. The other puzzle feels like it played "forward" and this one "backwards" for the same technique.
I'll play the computers' advocate here since I think this whole situation is very unfair for them, just think it from their position:
"I can solve any sudoku hundreds of times faster than any human, but they are putting medals on themselves because I can't solve this one puzzle using the one thing humans find easy, and without letting me use the things computers are good at"
I mean, that's like putting a boxer against a kickboxer, but you ban them from using their arms, and then when the boxer against all odds wins every single match but 2, the kickboxer acts all victorious and they get the gold medal 🙄
If machines ever become conscious, they are gonna hate us for sure
Actually the program managed to solve this puzzle without brute-forcing. Yes, it used some techniques that Simon referred to as guessing, but I think Simon as well did that. Based on the symmetry of the puzzle and given digits he guessed what digits to color. It was the symmetry that made him guess while the program had its own factors that helped it make guesses.
Simon was directed by the numbers to look at which part of the puzzle to check. If you reorder this puzzle so that the forced quad isn't 1234, he would probably have given up. Still, I wouldn't give up on computers, they could implement these "human" techniques as well. It is still simple, deterministic logic.
@@pharazfadaei1323 I think some of the techniques Simon derides here are essentially analogous to some of the coloring techniques he uses. Not shown on screen using colors, but the basic principle is the same. On the other hand, programs don't presently use geometry to prioritize their search for situations where such techniques would prove useful. If one had e.g. swapped columns 5 and 6, and arbitrarily permuted the digits 1-9 so that the key digits for the corner of the "square" weren't 1, 2, 3, 4 but instead 2, 3, 6, and 8, I doubt Simon would have been nearly as successful.
Never before have normal rules applied to such an abnormal sudoku.
Just one word: amazing!
@2:48 ....'Sudoku expert' must know everything!
A sudoku that computers can't solve but humans can? I always knew I had a brain like a computer.
What a brilliant piece of logic from jovi_al! My suggestion for the name of this new technique is "Symmetrical Hemisphere Quadruple".
Another great puzzle! I had no idea where this could have gone even from the start - but I suppose that isn’t very hard to do when i can barely spot a skyscraper haha
I've watched so many videos on this channel and only just realized I wasn't subscribed. It really does help to remind viewers to subscribe lol
Myst, what a throwback
Ah, a good old red|blue, orange|green pair between the corners. Love to see a puzzle like this set and solved!
This is the ultimate proof that computers will never be smarter than us (or at least smarter than Simon). They are faster, but not smarter! Amazing solve, by the way and great puzzle and new technique!
Should be able to program the , these digits cannot be, logic , if you can step through the logic found.
The only thing I can help with here is the name... "cobra roll" is the name for a particular shape on a rollercoaster track, and I can "see" that shape in the placement of the given digits.
First "6" was (r1c5) then a "6" is given (r2c1). Next was "8" in r4c5. (I dont think that technique has a name yet, but i don´t know, and I did not a guess. I call the techniqe for "Highway")
10 minutes in total and it was solved.
Skill-level was 10,6. (40191).
Simon you have one 10,9 (58057) in your mail wainting for you.
Wonderful! The computer solutions look like cave art! 😄
Alternative inference chains are not guessing. You start with the logical principle that if there are only two instances of a candidate in a particular house, then one of those instances must be true and the other must be false. That is called a strong link or strong inference. If I can eliminate A, then I prove B. You then consider that if for the candidate that turns out to be true, all other candidates in that cell and other all instances of the candidate in question in the same house must be false. That is called a weak link or weak inference. If I can prove A, then I eliminate B. You can use this principle to prove that only two instances of a particular candidate can exist in a particular house, where it would otherwise appear that there could be more instances of that candidate there. That allows you to make eliminations. It starts by making an observation, then making an assumption based on that observation, yes--but so does science.
Now, if you write anything down during the process, or if you carry the chain all the way to completion or failure of the puzzle, THEN you're guessing.
So.. doing a chain in your head is not guessing, but doing the exact same thing on paper is? How so?
@@ceevio_art
The difference is whether you use anything more than what’s true no matter what the “starting cell” of your chain is. Concluding that “A eventually leads to B, and Not A _also_ eventually leads to B” is not guessing, but entering the intermediate step(s) that aren’t the same in both cases _is_ guessing.
@@ceevio_art It's a bit of a technical thing. If I start writing numbers in the grid as if I know they are true when in fact I do not, it approaches bifurcation, especially if you carry the puzzle all the way to completion or fallacy.
@@ceevio_art PS: Here's how I got my first two digits: We have a 35 pair in r5c2. Now if that cell were a 3, then we would get a 38 pair in the upper row of the center block, which kicks out the possible 5 there, meaning 5 would go in r6c5. That leaves only r1c6 for a 6, which would give r2c1=6, r2c3=5, r2c7=3. Now, if we return to block 4 where the chain started, we see that a 5 could only go in r4c1, giving r4c8=2. But that leaves a empty cell at r3c8. Therefore our original supposition is wrong, meaning r5c2=5.
Next, if r4c8=5 then r6c5=5, which we know from the previous chain leads to r2c7=3 and therefore r3c8=2. This tells us that we have strong link in between the 2s in r3c8 and r4c8. One must be true, therefore 2 can go nowhere else in that column but rows 3 and 4. That eliminates 2 from r6c8, and the only other place for a 2 in row 6 is column 2, therefore r6c2=2.
AICs are no different than looking several moves ahead in chess. Of course in a live chess game you aren't allowed to shuffle pieces about the board--you make one move and stick with it. You have to do the calculations in your head. Think of Sudoku the same way. You can't just go slapping numbers down until you pass or fail, and then change your mind if you fail--but you CAN think out the consequences of a particular entry before you make it, and draw a conclusion as to whether that entry would be correct.
This is again another patterning technique I must try to figure out for myself.
Without getting into anything too spoilery regarding The Witness, I hope you see it through all the way. There is so much to discover, and some of its most lovely puzzles lie in what some might call the "post game". You seem to be having a lot of fun with everything that isn't birds, after all.
Solving starts at 6:43
That was just wow.
Don't worry simon if you don't solve it you are a computer.. that not so bad..
I've just not been so upset because of inability to solve this puzzle yesterday evening.