Inability to see given digits is a very common condition in the sudoku community. I was very surprised at the start to see you solving a completely blank grid.
Thank you so much once again for featuring one of my puzzles on your channel! I always marvel at your kindness and your speed on picking up what the setters have laid down for you. Your solve was exactly as intended, and I'm super happy you spotted it so deftly! The title of this puzzle was not originally "Arbitrary Code Execution", but I had to change it to prevent demonetization 😅. The title of "Arbitrary Code Execution" is because the coloring and the weirdness needed to crack this puzzle open sort of reminded me of the glitchy visuals one might get while doing ACE in games like Super Mario Bros III. Yes, I am a nerd! Edit: I'm also extremely fond of the fact that r12 and r89 are entirely disambiguated with only one given digit, each! If you know anything about classic Sudoku and uniqueness, you know that this is not one of the more trivial tasks to achieve in classic Sudoku setting. Related side note: there are a *lot* of very strange and arbitrary-seeming requirements that are necessary for a Sudoku to be unique-- maybe I'll make a video on that at some point!
As a side note for anyone still wondering what Arbitrary Code Execution is: a great example of arbitrary code execution in a video game with a solid explanation for laypeople has been exhibited at a somewhat recent charity event of Games Done Quick, who happen to have a RUclips channel archiving their charity runs as well. Searching for “Games Done Quick Ocarina of Time” in the RUclips search bar will bring you to the video. It’s a technically assisted speedrun where three (or four?) players and one bot enter over a million inputs into an old Legend of Zelda game to program a new bit of code into it and then make the game execute said code. The result has been fascinating.
Arbitrary code execution is a computer security term referring to an attacker being able to run any code they want on the target computer by exploiting a software or hardware error. For the puzzle, it is likely a reference to how jov_ial managed to get the solver stuck so that it was performing complex inference chains up until near the end where it found a Y-wing, then solved the puzzle soon after.
Dear Simon ❤️ I would like to say that I too use your videos to fall asleep every night. It's not because you're boring but because you make me feel so safe. And i watch the same videos again the day after because it is so much fun. Me and my fiancee usually say "Some people watch football, we watch Cracking the Cryptic!". 😂❤️
I ran to the comment section to say this exact thing! I hate to think they might think I find them boring just because I can calm down and relax before falling asleep!
I’ve developed severe sleep problems the past few months and these guys are the ONLY way for me to reliably fall asleep 90% of the time. Without them my health in all areas would be much worse so I find it extremely soothing that they’re the way they are! I usually make it about fifteen minutes into a solve and then it’s lights out thanks to Simon and Mark. Best of all even if I wake up in the middle of the night I can count on them to help me get back to sleep!
14:35 The computer says what you've done there can be considered a "Sashimi Swordfish", which is clearly something only the best chefs would be able to cook in a sushi restaurant 😆
Rules: 05:06 Let's Get Cracking: 05:24 What about this video's Top Tier Simarkisms?! Bobbins: 2x (11:34, 11:34) Phistomefel: 2x (03:33, 04:23) Three In the Corner: 1x (19:09) And how about this video's Simarkisms?! Pencil Mark/mark: 11x (07:05, 07:09, 07:17, 07:19, 07:21, 07:31, 07:51, 13:24, 15:59, 16:14, 16:25) Beautiful: 8x (04:30, 12:35, 12:41, 14:24, 14:37, 19:20, 24:50, 25:24) Sorry: 5x (09:04, 09:52, 12:11, 12:11, 17:00) Obviously: 5x (05:46, 11:01, 12:41, 12:43, 15:34) Ah: 5x (06:36, 09:11, 12:29, 17:04, 21:19) Bingo: 2x (24:05, 24:08) Brilliant: 2x (00:28, 02:36) Fascinating: 2x (24:40, 24:43) First Digit: 2x (24:19, 24:23) Gorgeous: 2x (20:01, 20:04) Come on Simon: 2x (10:04, 11:34) Good Grief: 1x (01:34) Nonsense: 1x (23:58) Clever: 1x (19:24) Naughty: 1x (10:35) In the Spotlight: 1x (19:09) Off to the Races: 1x (15:27) Lovely: 1x (14:20) By Sudoku: 1x (17:06) Shouting: 1x (02:34) Hang On: 1x (16:47) In Fact: 1x (04:02) Full stop: 1x (20:04) Cake!: 1x (02:38) Most popular digit and colour this video: Seven (29 mentions) Blue (12 mentions) Antithesis Battles: Even (2) - Odd (1) Black (3) - White (0) Column (22) - Row (21) 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!
The fact that i did this in under ten minutes is a vindication of how much I've learnt from Simon and Mark over the past year or so! Total gratitude and just the ego boost needed on a Monday morning to kick off the week
Simon, I used to use these videos to fall asleep easier too. Your voice is pure gold and it soothes me so much. However, I can't do it anymore... Because I've learned so much from these videos that I just can't sleep until you've cracked it. Anyway thanks for the amazing content.
That was very interesting. Lot's of pencil marks but once the first digit was revealed it was fairly straightforward. Fun. I wish you would have a playlist of just Classic Sudoku.
I have fallen asleep watching CtC... but I don't find you dull, your speaking cadence is just relaxing. I do know what Arbitrary Code Execution is, but I don't understand what it has to do with the puzzle.
5:08 for me! I wouldn't have spotted skyscraper logic a couple of years ago but it's just a testament to how good this channel is at teaching advanced sudoku techniques that I didn't even have to pause before my mind jumped straight to 'this pattern must be skyscraper logic'
Some times I will fall asleep to sudoku solves because your voices are soothing. It's not that you're boring, just that even when you're excited, you're not jolting me awake again.
Sometimes I find myself hoping you get stuck because then the videos are longer and I get to spend more time watching but it is satisfying when you work things out so quickly and elegantly
I was so happy I figured this one out myself by looking at box 6, and realizing that that no matter where I put either the 9 or 8, there were two squares in boxes 4 and 5 that they couldn't go in without breaking rows 3 and 7 which meant those 2 had to be 7, and the rest of the puzzle solved quickly after that. Then Simon came in and skipped over half my logic with a better coloring method and reached the deduction so much faster. Looks like I've still got a lot to learn from the channel.
People who would describe any of you as "dull" can be pitied. :-) I often watch your videos at night time shortly before falling asleep, but definitely not because I find anything boring or "dull". Firstly it's shortly after they're getting posted in my timezone. Secondly it's the time of the day I got time to watch any videos. Thirdly and most importantly: Watching your videos really does relax me, it's almost like a meditation. Focusing on one thing and one thing alone, in a structured and calm manner.
You guys aren’t boring relaxing yes but not boring… there’s a big difference there your excitement for the beauty of how the puzzle is arranged is infectious and makes me want to get better at puzzles. I’ve learned so much from you guys
12:00 ... Simon's description of how pretty the puzzle was by making an analogy to RomCom's was hilarious. I do wish I had his wide range of vocabulary in that way.
Simon, I am a bit behind, so apolgies. But, I also use your videos to sleep with. It's not that you are uninteresting. You are fantastically so. You have an upstanding voice, relaxing with an ASMR quality. The reason we watch this stuff is there is no flashing lights, loud sounds, or distracting concepts. It's totally a compliment to have a video with just learning and understanding without having to sell something every 15 seconds.
I solved it surprisingly quickly by studying the middle 4 rows and using coloring, much like Simon. I love how Jovial telegraphed where to look with an Oddagon-type pattern in the middle (computer solvers still can't figure those out), giving us the key to breaking in. Wonderful puzzle by Jovial and great explanation by Simon.
Started doing the video alongside you - but I DID get the insight myself! I started coloring the 789s in rows 4-7, and I noticed that if r6c3 matched r5c5 and r4c9, r6c3 had nowhere to go in the 7th row. this was moments before you pointed out that same thing with r6c3=r4c9, I just got to do the coloring faster because I didn't have to be entertaining for an audience. Thanks for the video! Glad I decided to grab a short one today. :)
Whenever Simon shows a puzzle that's definitely not as difficult as the computer thinks, it seems to always involve some kind of coloring. I wonder if the computer could be equipped with coloring algorithms as well. i.e. each cell begins with a unique color, and it over time proves which colors are the same without necessarily knowing much about the digits.
Ah, but early on, the computer solver actually did use coloring, albeit candidate coloring. I use that technique often on harder standard sudoku puzzles and it can quickly solve a puzzle. The downside of course, for a human, is that coloring takes time. And that’s what makes Simon’s insight really beautiful.
@@craigshea2930 What it's lacking is not so much coloring-based logic as the ability to represent cells being unknown but equal as the conclusion of a step and input to the next. If the first thing Simon did was represented as a single chunk up to the point where an option was removed from a cell, it would involve all 15 non-given cells from the middle 5 rows of the puzzle. Simon, on the other hand, can prove that r4c9=r6c6 as an intermediate step whose conclusion he can state and reason from.
You could add it to a solver, but it's probably not going to make the algorithm faster. They work by brute force, repeatedly checking strategies from easy to hard. You can always make corner cases like this one where there's an insightful shortcut to be found, e.g. colouring forces some digits to be the same. But where do you put that on the easy to hard strategy list? Put it too low, and the algorithm won't reach it, because it'll repeatedly simpler strategies (like x-cycles in this puzzle, which is a type of colouring) to eliminate individual candidates. Put it too high, and the algorithm will waste time on proving some cells equal without that helping reach a solution.
@@sanabas1 I feel like that logic can't be correct because if you applied it to regular sudoku solving algorithms it would imply they never worked. The reason a solver can be efficient is because of the specific strategies that are programmed for it to employ. It seems to me there could be many strategies that involve coloring that are not currently employed by these algorithms.
@@willfancher9775 there are solving algorithms that run "fairly well" on a computer such as dancing links, but would be awful for a human to implement due to how much backtracking there is. The challenge is to find an algorithm which both humans and computers can use to solve easily
I'm working on my own computer solver as a hobby, and yes, this type of visual logic is very hard to program. We as humans are able to get into the mind of the setter. The way rows 3, 4, 5, 6, and 7 are set is striking and we can recognize that it must have been intentional, so we focus on it to spot some sort of pattern. A computer cannot know these things (or at least cannot recognize them easily) so it starts going through all its sudoku techniques until it finds something.
Simon, we are all still awaiting the *five* missing "3 in the corner" songs from yesterday!... I am absolutely certain they were placed there on purpose :) that puzzle must have broken a record... It's those little rituals that give order and meaning to this chaotic life. Thanks for another video!
I love the theme in minor! It sounds like a horror film. I’m imagining a 19th century Simon stick in a haunted mansion until he solves all the sudokus!
Loved watching the solve! It really felt like watching Simon try to get something for the rest of the grid out of the rows in the middle, much like you'd try to find a space of memory to smuggle your code away from your box
17:42 for me, almost decided to get a hint from the video, but in the end managed to solve it myself and I'm pretty glad because that was a really cool solution
Got it after 14:27. Had the 7-8-9s colored, but still needed the next step spelled out for me. This probably happened several videos ago (I've been neglecting the longer solves unfortunately), but I noticed Simon made his default green darker. You can do this at home by clicking and holding on the color selection screen until each color appears in an additional box, then clicking the color you want to change. I discovered this by accident.
I am so glad you mentioned this! I noticed his green got darker, and I don't remember him explaining it. My colors look so much better after changing them.
I was reminded of "Computer says no" (Cobra Roll) which was also by jov_ial. Thank you for showcasing such an amazing puzzle and for explaining the logic so eloquently.
I finished in 14:36 minutes. For a classic sudoku, that had a surprisingly beautiful geometry in it. The way the middle boxes pencil marks of 789's had to interact with the non-given cells in rows 3 and 7 was incredible to see. I wasn't expecting that in a classic sudoku, but it was amazing. I can see why a computer would struggle. Luckily, I am a human and can see beautiful geometry. I was so happy when I was able to place those 7's. Great Puzzle!
“Arbitrary code execution” is a term in computer security where an attacker can get a computer to execute some arbitrary bit of code, often by manipulating where the instruction pointer is pointing to. So I think the title is maybe a reference to how the 789 triples in the middle 3 rows “point” to the gaps in rows 3 and 6.
7:33 ... It amazes me that we as humans can see this (at least I did) while computers completely miss such a wonderful break-in. I loved solving this classic!
Surprised myself with this one. 22:20 !! The clever, clever puzzles fall if you find the right starting strategy. That usually escapes me, except for today !! Thanks for the fun.
Tried this puzzle for ~20 minutes, and didn't feel like I could do anything more - started watching the video and stopped the video as soon as Simon pointed out that there is something interesting with r4c9, and managed to solve it from there. This is fascinating - as soon as I was pointed to the cell I needed to focus on, it was reasonably quick to find the rest Now the next step is to find these cells myself Thank you for your videos, they are always pleasant :)
If someone had presented me with that puzzle and said, "It is solvable, and it is beautiful," I would have believed them (especially if they had cited you, Simon), but I am not sure that I could have actually solved it myself. Maybe I would have been able to synthesize all of the logic that I have learned on this channel and, after some weeks of contemplation, I might have been able to do it. Maybe. Thank you for being so brilliant!
"Dull" is the wrong word. "Soothing" is the right one. I do watch the videos normally, but occasionally one goes on when I'm trying to sleep, because you have a very soothing voice.
Thank you so much for answering my question about the solve video. Maybe Ancient Wall would be great to show here on the channel as well, as you said that Phistomefel considers it his masterpiece and sharing it with a wider audience now that the hunt time is over would be awesome 😊
5:18 solve time for me on this one. Was able to determine the orientation of the 789s via row 7 and its impact on box 6 if R5C5 was equivalent to R6C3.
Beautiful. I'd never have spotted it, but was amazed to follow along and try, and it was so satisfying to finish the puzzle so quickly after that insane Jay Dyer hunt!
11:26 it's been tickling my senses that whole connection between the open spaces in boxes 4, 5 and 6 and row 7. They are somewhat interesting because row 7 connects with each at a different row. Maybe you saw part of it, or maybe remember some older puzzles that looked like this concept (don't remember said names, and weren't classic sudoku, but had the colouring at it) and tried to force it.
Aligned Pair Exclusion: Any 2 cells aligned in the same row, column, or box cannot duplicate the contents of any two candidate cell they both see. If the top gray square was a 9, the bottom orange square would be a 7, the top orange square would be an 8, the bottom gray square would be 4, and then the two yellow squares could only be 3, leading to 2 3’s in the second box. So the 9 can be removed from the top gray square.
The comment edited in is worth an upvote and a response on its own, The use of Mittens in the thumbnail deserves another, but i can't do that. And I haven't even got to the solve itself yet.
I would like to take this chance to explain why I use these videos to fall sleep and it is not because you are dull. It is because of the reason why I struggle to fall sleep, which is that I spend either some or all of my mental capacity thinking about things to worry and not relaxing so even when I am tired it takes a while to fall sleep. These videos provide two things to focus on which are the logic path you are explaining and the logic path I am trying to find at the same time. This keeps both my conscious and subconscious busy and if I am tired and in a comfortable position I will fall sleep relatively quickly. If your thought process was indeed dull then my mind would start to wander into the kinds of thoughts that make it hard for me to fall sleep. There might be other things, but those are the ones that are pretty clear to me.
The green thing at 11:26 made perfect sense to me. The green digit is the digit that goes in R7C3. We know it goes into either R4C1 or R5C2 in box 4. The unknowns in boxes 4-6 are all on diagonals. It's the negative diagonal for boxes 4&5, but positive diagonal for box 6, which is too bad. If the unknowns in box 6 were on the negative diagonal for box 6, then we would know the green digit would be in either R4C7 or R5C8 for box 6. AND, the great thing about that is that it would eliminate all places in R6 for the green digit except R6C6. It would have been a great way to start coloring your grid, which we all know is your favorite thing to do!
Simon, if it helps, at 11:30 you were attempting to establish that the number of green digits expected to be in rows 4 and 5 is 2, and if you can show that those two greens are in boxes 4 and 6, then the green digit in box 5 must be in row 6. But regardless of the orientation of empty cells in box 6, you still have no basis for eliminating green from box 6, row 6 anyway.
Great puzzle. Simon, your trick of eliminating the first 7 was very helpful and logically understandable, that I found the solution very quickly and without any further problems. I surely keep the trick in my mind.
Humankind humankind Proudly triumphant when Challenged by silicon Grinding away. Does the computer have Superiority? Jovi-al’s puzzle and Simon say “Nay!”
The diagonal 789s in rows 456 made me think of coloring and I spotted this trick very quickly and I managed to solve this in 11:21. What a great puzzle by jovi_al!
My best guess for the title is that the computer solver is doing seemingly arbitrary techniques to solve the puzzle (and bypassing the beautiful logic built in because it wasn't programmed to include this novel technique). Under that assumption, I think jovial would have then come up with a bowtie name that is an established phrase, as ACE is in the software security and glitch hunting/speedrunning domains.
Thank you, Simon, for the beautiful solve! As for your question about what you were thinking at 11:26, I might have an idea, correct me if I'm wrong: you thought for some reason that if r7c3 is green, then r7c9 is ALSO green rather than NOT green, and that led to the logic about diagonals and placing green in r6c6.
Interestingly, I only spotted the (your) yellow cell restriction after finding that (your) blue could not be 9 (hence needed to be 8) because that would lead to 8 being forced into both r1c6 and r6c6. When yellow came to my attention I actually at first thought I had broken the puzzle and was truly relieved when I realized that 4 came to the rescue.
I pulled off a fortunate guess on the 789 triples in the middle boxes and finished this one in under 7 minutes as a result. Can't say I am under 10 mins on these puzzles very often, but pretty proud of that
3:00 I confess to being one of those people. In my defence I also find it very educational and I generally solve a classic every morning. Not dull, but relaxing :)
Unlike many commenters here, CTC gives me insomnia, as I just can't help but give the more approachable puzzles a try. This one was a nice little ego boost for me, definitely an example of how I've gotten so much better at sudoku watching the channel regularly.
I love that you went to the solver to see how it would manage it. When trying to get better at sudoku, i would occasionally go there and try to see what I was missing. This did not go incredibly well. Wonder if your way of solving using a color variable instead of actual numbers would render all those crazy steps unnecessary as far as computing is concerned.
OMG! I did it! 27:11. It usually takes me 10 to 15min (and sometimes longer) for GAS. And I can hardly ever make any inroads into Simon's featured sudokus, let alone solve them. Can't believe I did this without even watching video. I used phistimophel and colouring 789s to distinguish. Is that cheating?? Gonna watch the video now to see what I should have done, but feeling pretty hyped....!!
15:20 You could just colour fours (for example with red). 489's in third row will be red-green-blue. We have to put an "yellow" digit somewhere into row 3. It can be only seven at B7 (if bottom left corner is A1 - like in chess notation).
I find your videos very fascinating, it's just your tone of voice is the second most sleep inducing I've ever heard, after the late Bob Ross. I know Mr. Ross worked on making his voice quieter, however, after his time working as a US military drill sergeant!
12:29 was my time and I must say, I'm also happy that the computer got an 8 as it's first digit, as so did I. I missed the simple trick with r3, and solved r7, first.
Did this one, yippee me!! Maybe Mark sent this to you, Simon, because you resist entering candidates in cells? I just went through the #s 1-9, entering when I could see only 2-3 cells for a #. That is when I found certain restrictions for the other #s, placing them in. Then worked out many 2 candidate #s only in some boxes, freeing up single digit possibilities. I did nothing 'fancy!' (Sorry, I'm having trouble fully explaining it.)
Well, I think I understand what you mean - probably because I did the same or at least something similar. Also the first one I have solved without watching any moves by Simon (or Mark).
When I'm stuck, I generally queue the video to a point that looks similar to what I have and try to guess Simon's logic before he can finish explaining it. This was a puzzle definitely requiring that help (I did deduce, for example, r4c4=r7c5 on my own but that was very not enough to break open the center rows)
Arbitrary code execution is an application security vulnerability when a system can be exploited to run the code of the attacker (with the permissions of the original, etc. - which is often why it is very dangerous indeed). Given how the solver behaves, maybe the idea is that it looks like the solver is just running some attacker code, not what it should be?
Simon's coloring logic was a lot better than mine. I took a round-about way of basically saying what if the center digit was 9, and then noticing that caused either row 3 or row 5 to not have a 9. 7 worked because of row 3, but 8 broke like 9 did, giving me a digit through what probably should be called bifurcation.
12:35 for me. I don't know why, but it was just intuitively obvious that the central cell had to be that particular digit, because any other candidate starts to leave empty cells all over the grid in just a few steps.
There's a pattern of 5/6 in box two and 3/4 in box eight that I was *sure* would lead to the intended break-in, but after spending 10 minutes I just couldn't get anything useful from it. I'm amazed how different the trick actually was!
The first digit I found was the 4. I noticed that if R3C5 was a 4 it would force a 4 in R9C9 and a 7 in R4C4. Then you will see that R3C1 is a 89, and looks at R3C8 and R4C1 which are also both 89 - but different from each other. Therefore there is no valid input for R3C1. Therefore R3C1 must be the 4. Still had to use Simon's logic from then on, but was pleased I got a digit at first!
After the initial goodliffing of 789 / 489, and flailing around for a while, I asked the question - can the 89 in R5C2 be different from the 89 in R6C6 (which would give me 7s in 2 of the other cells). I ended up bifurcating, and coming to the conclusion that they cannot. Once they were the same, I was able to break in - but I needed to bifurcate, and Simon was able to see this without that! Just amazing!
The really fun thing here is that while the computer rates this 380, if you place a given 7 in R6C7 this also implies the beautiful first step, and suddenly the computer thinks it's 42 (nice) and Easy.
It would have been crazy if this sudoku triggered an actual arbitrary code execution in the solver, perhaps to change the score to 'hi simon' or something along those lines. XD
It's crazy how it is simultaneously simple and difficult to spot the 789 trick and then resolve them using r3 and r7. And once you get that, it's just simple sudoku all the way, how bizarre! I have to say this has to be one of the simplest sudokus to feature on this channel but I'm not gonna forget the fact that it is very tricky to see that crack in the puzzle. And also, I have to say that the positioning of 7 in r3 is one of the cleverest things I've seen while solving sudokus.
23:36 A good time, Coloured the 7-8-9 cells in boxes 4-6, once I saw that identifying one cell would identify all of them, and suddenly I'm looking at these 3 cells that had to be identical, ruling out whatever digit it was from the 3 empty cells in Row 3, so clearly it had to be 7, since it already existed in row 3.
![Classic Sudoku: Bonus Puzzle 4: [This is STUNNING]](/img/1.gif)
Inability to see given digits is a very common condition in the sudoku community. I was very surprised at the start to see you solving a completely blank grid.
lol. (He's done it before).
Hilarious.
Thank you so much once again for featuring one of my puzzles on your channel! I always marvel at your kindness and your speed on picking up what the setters have laid down for you.
Your solve was exactly as intended, and I'm super happy you spotted it so deftly!
The title of this puzzle was not originally "Arbitrary Code Execution", but I had to change it to prevent demonetization 😅. The title of "Arbitrary Code Execution" is because the coloring and the weirdness needed to crack this puzzle open sort of reminded me of the glitchy visuals one might get while doing ACE in games like Super Mario Bros III. Yes, I am a nerd!
Edit: I'm also extremely fond of the fact that r12 and r89 are entirely disambiguated with only one given digit, each! If you know anything about classic Sudoku and uniqueness, you know that this is not one of the more trivial tasks to achieve in classic Sudoku setting. Related side note: there are a *lot* of very strange and arbitrary-seeming requirements that are necessary for a Sudoku to be unique-- maybe I'll make a video on that at some point!
That is indeed fascinating, the whole collapse with a simple deduction... just gorgeous ❤❤
As a side note for anyone still wondering what Arbitrary Code Execution is: a great example of arbitrary code execution in a video game with a solid explanation for laypeople has been exhibited at a somewhat recent charity event of Games Done Quick, who happen to have a RUclips channel archiving their charity runs as well. Searching for “Games Done Quick Ocarina of Time” in the RUclips search bar will bring you to the video. It’s a technically assisted speedrun where three (or four?) players and one bot enter over a million inputs into an old Legend of Zelda game to program a new bit of code into it and then make the game execute said code. The result has been fascinating.
@@mitnehmerrippe such an impressive showcase! i watched it just a few days after it went live :)
@@jovi_al Might we enquire what was the original title of this puzzle? :)
@@BeheadedKamikaze sure! it was called "Quick Kill", in reference to a type of speedrun strat that often gets that name :)
Arbitrary code execution is a computer security term referring to an attacker being able to run any code they want on the target computer by exploiting a software or hardware error. For the puzzle, it is likely a reference to how jov_ial managed to get the solver stuck so that it was performing complex inference chains up until near the end where it found a Y-wing, then solved the puzzle soon after.
Now the next goal is to compile a sudoku that tricks "Andrew Stewart's Sudoku Solver" into running a copy of Pokemon Yellow.
@@SirJefferE But can it run DOOM, though?
Let's run Twitch Chat through it live at AGDQ!
en.wikipedia.org/wiki/Arbitrary_code_execution
Dear Simon ❤️
I would like to say that I too use your videos to fall asleep every night. It's not because you're boring but because you make me feel so safe. And i watch the same videos again the day after because it is so much fun. Me and my fiancee usually say "Some people watch football, we watch Cracking the Cryptic!". 😂❤️
I am also currently using CtC to fall asleep for the same reason. I also watch the videos awake 🙂
You guys aren't dull at all man, you just have a calming presence :)
Exactly. They have soothing lyrical voices. And when Simon gets excited it’s the sound of happy magical beings singing in the forest! 🤗
I ran to the comment section to say this exact thing! I hate to think they might think I find them boring just because I can calm down and relax before falling asleep!
Too kind :) Thank you!
I’ve developed severe sleep problems the past few months and these guys are the ONLY way for me to reliably fall asleep 90% of the time. Without them my health in all areas would be much worse so I find it extremely soothing that they’re the way they are! I usually make it about fifteen minutes into a solve and then it’s lights out thanks to Simon and Mark. Best of all even if I wake up in the middle of the night I can count on them to help me get back to sleep!
@@longwaytotipperary love this analogy you used!!
14:35 The computer says what you've done there can be considered a "Sashimi Swordfish", which is clearly something only the best chefs would be able to cook in a sushi restaurant 😆
Love that you feature classic sudoku puzzles still once in a while. Shye and jovial are pioneers in keeping these going!!!
Rules: 05:06
Let's Get Cracking: 05:24
What about this video's Top Tier Simarkisms?!
Bobbins: 2x (11:34, 11:34)
Phistomefel: 2x (03:33, 04:23)
Three In the Corner: 1x (19:09)
And how about this video's Simarkisms?!
Pencil Mark/mark: 11x (07:05, 07:09, 07:17, 07:19, 07:21, 07:31, 07:51, 13:24, 15:59, 16:14, 16:25)
Beautiful: 8x (04:30, 12:35, 12:41, 14:24, 14:37, 19:20, 24:50, 25:24)
Sorry: 5x (09:04, 09:52, 12:11, 12:11, 17:00)
Obviously: 5x (05:46, 11:01, 12:41, 12:43, 15:34)
Ah: 5x (06:36, 09:11, 12:29, 17:04, 21:19)
Bingo: 2x (24:05, 24:08)
Brilliant: 2x (00:28, 02:36)
Fascinating: 2x (24:40, 24:43)
First Digit: 2x (24:19, 24:23)
Gorgeous: 2x (20:01, 20:04)
Come on Simon: 2x (10:04, 11:34)
Good Grief: 1x (01:34)
Nonsense: 1x (23:58)
Clever: 1x (19:24)
Naughty: 1x (10:35)
In the Spotlight: 1x (19:09)
Off to the Races: 1x (15:27)
Lovely: 1x (14:20)
By Sudoku: 1x (17:06)
Shouting: 1x (02:34)
Hang On: 1x (16:47)
In Fact: 1x (04:02)
Full stop: 1x (20:04)
Cake!: 1x (02:38)
Most popular digit and colour this video:
Seven (29 mentions)
Blue (12 mentions)
Antithesis Battles:
Even (2) - Odd (1)
Black (3) - White (0)
Column (22) - Row (21)
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!
There's no way you timestamped all this lol
@@haysan32 It's done by a bot
The fact that i did this in under ten minutes is a vindication of how much I've learnt from Simon and Mark over the past year or so! Total gratitude and just the ego boost needed on a Monday morning to kick off the week
Simon, I used to use these videos to fall asleep easier too. Your voice is pure gold and it soothes me so much. However, I can't do it anymore... Because I've learned so much from these videos that I just can't sleep until you've cracked it. Anyway thanks for the amazing content.
That was very interesting. Lot's of pencil marks but once the first digit was revealed it was fairly straightforward. Fun.
I wish you would have a playlist of just Classic Sudoku.
I have fallen asleep watching CtC... but I don't find you dull, your speaking cadence is just relaxing.
I do know what Arbitrary Code Execution is, but I don't understand what it has to do with the puzzle.
do tell
5:08 for me! I wouldn't have spotted skyscraper logic a couple of years ago but it's just a testament to how good this channel is at teaching advanced sudoku techniques that I didn't even have to pause before my mind jumped straight to 'this pattern must be skyscraper logic'
What is impressive (though not surprising) to me is that Simon solved this in less than 17 minutes--while explaining what he is doing!
Some times I will fall asleep to sudoku solves because your voices are soothing. It's not that you're boring, just that even when you're excited, you're not jolting me awake again.
Sometimes I find myself hoping you get stuck because then the videos are longer and I get to spend more time watching but it is satisfying when you work things out so quickly and elegantly
I was so happy I figured this one out myself by looking at box 6, and realizing that that no matter where I put either the 9 or 8, there were two squares in boxes 4 and 5 that they couldn't go in without breaking rows 3 and 7 which meant those 2 had to be 7, and the rest of the puzzle solved quickly after that.
Then Simon came in and skipped over half my logic with a better coloring method and reached the deduction so much faster. Looks like I've still got a lot to learn from the channel.
People who would describe any of you as "dull" can be pitied. :-)
I often watch your videos at night time shortly before falling asleep, but definitely not because I find anything boring or "dull". Firstly it's shortly after they're getting posted in my timezone. Secondly it's the time of the day I got time to watch any videos. Thirdly and most importantly: Watching your videos really does relax me, it's almost like a meditation. Focusing on one thing and one thing alone, in a structured and calm manner.
You guys aren’t boring relaxing yes but not boring… there’s a big difference there your excitement for the beauty of how the puzzle is arranged is infectious and makes me want to get better at puzzles. I’ve learned so much from you guys
12:00 ... Simon's description of how pretty the puzzle was by making an analogy to RomCom's was hilarious. I do wish I had his wide range of vocabulary in that way.
Simon, I am a bit behind, so apolgies. But, I also use your videos to sleep with. It's not that you are uninteresting. You are fantastically so. You have an upstanding voice, relaxing with an ASMR quality. The reason we watch this stuff is there is no flashing lights, loud sounds, or distracting concepts.
It's totally a compliment to have a video with just learning and understanding without having to sell something every 15 seconds.
I solved it surprisingly quickly by studying the middle 4 rows and using coloring, much like Simon. I love how Jovial telegraphed where to look with an Oddagon-type pattern in the middle (computer solvers still can't figure those out), giving us the key to breaking in. Wonderful puzzle by Jovial and great explanation by Simon.
Not dull. Soothing. I watch the new videos but sometimes put on ones I've seen to fall asleep to.
The solve was wonderful but I love the coda of plugging into the machine and talking through the computer's logic as well! Brilliant video all around!
Started doing the video alongside you - but I DID get the insight myself! I started coloring the 789s in rows 4-7, and I noticed that if r6c3 matched r5c5 and r4c9, r6c3 had nowhere to go in the 7th row. this was moments before you pointed out that same thing with r6c3=r4c9, I just got to do the coloring faster because I didn't have to be entertaining for an audience. Thanks for the video! Glad I decided to grab a short one today. :)
Whenever Simon shows a puzzle that's definitely not as difficult as the computer thinks, it seems to always involve some kind of coloring. I wonder if the computer could be equipped with coloring algorithms as well. i.e. each cell begins with a unique color, and it over time proves which colors are the same without necessarily knowing much about the digits.
Ah, but early on, the computer solver actually did use coloring, albeit candidate coloring. I use that technique often on harder standard sudoku puzzles and it can quickly solve a puzzle. The downside of course, for a human, is that coloring takes time. And that’s what makes Simon’s insight really beautiful.
@@craigshea2930 What it's lacking is not so much coloring-based logic as the ability to represent cells being unknown but equal as the conclusion of a step and input to the next. If the first thing Simon did was represented as a single chunk up to the point where an option was removed from a cell, it would involve all 15 non-given cells from the middle 5 rows of the puzzle. Simon, on the other hand, can prove that r4c9=r6c6 as an intermediate step whose conclusion he can state and reason from.
You could add it to a solver, but it's probably not going to make the algorithm faster. They work by brute force, repeatedly checking strategies from easy to hard. You can always make corner cases like this one where there's an insightful shortcut to be found, e.g. colouring forces some digits to be the same. But where do you put that on the easy to hard strategy list? Put it too low, and the algorithm won't reach it, because it'll repeatedly simpler strategies (like x-cycles in this puzzle, which is a type of colouring) to eliminate individual candidates. Put it too high, and the algorithm will waste time on proving some cells equal without that helping reach a solution.
@@sanabas1 I feel like that logic can't be correct because if you applied it to regular sudoku solving algorithms it would imply they never worked. The reason a solver can be efficient is because of the specific strategies that are programmed for it to employ. It seems to me there could be many strategies that involve coloring that are not currently employed by these algorithms.
@@willfancher9775 there are solving algorithms that run "fairly well" on a computer such as dancing links, but would be awful for a human to implement due to how much backtracking there is. The challenge is to find an algorithm which both humans and computers can use to solve easily
I'm working on my own computer solver as a hobby, and yes, this type of visual logic is very hard to program. We as humans are able to get into the mind of the setter. The way rows 3, 4, 5, 6, and 7 are set is striking and we can recognize that it must have been intentional, so we focus on it to spot some sort of pattern. A computer cannot know these things (or at least cannot recognize them easily) so it starts going through all its sudoku techniques until it finds something.
Mittens - the crossover star of our generation.
Loved the thumbnail!! (I can see the resemblance)
Very very nice row 3-(4-5-6)-7 interaction! Love a nice classic!
Simon, we are all still awaiting the *five* missing "3 in the corner" songs from yesterday!... I am absolutely certain they were placed there on purpose :) that puzzle must have broken a record... It's those little rituals that give order and meaning to this chaotic life. Thanks for another video!
Oh that is clever and satisfying, thank you for carrying me through it Simon because I would never in a million years have found it myself
Certainly when I started watching I would not have seen that either but with practice I bet some day you will see it
I love the theme in minor! It sounds like a horror film. I’m imagining a 19th century Simon stick in a haunted mansion until he solves all the sudokus!
We watch and engage from start to finish with your videos, but also put them on to go to sleep, it's like cognitive ASMR.
14:00 for me. That was delightful! I love weeding out certain combinations in the middle boxes by comparing them to the gaps in rows 3 and 7!
Loved watching the solve!
It really felt like watching Simon try to get something for the rest of the grid out of the rows in the middle, much like you'd try to find a space of memory to smuggle your code away from your box
17:42 for me, almost decided to get a hint from the video, but in the end managed to solve it myself and I'm pretty glad because that was a really cool solution
17'49" for me, I feel pretty happy with it, now on to watching your solve! This was an absolutely lovely puzzle!
Got it after 14:27. Had the 7-8-9s colored, but still needed the next step spelled out for me.
This probably happened several videos ago (I've been neglecting the longer solves unfortunately), but I noticed Simon made his default green darker. You can do this at home by clicking and holding on the color selection screen until each color appears in an additional box, then clicking the color you want to change. I discovered this by accident.
I am so glad you mentioned this! I noticed his green got darker, and I don't remember him explaining it. My colors look so much better after changing them.
I was reminded of "Computer says no" (Cobra Roll) which was also by jov_ial.
Thank you for showcasing such an amazing puzzle and for explaining the logic so eloquently.
I finished in 14:36 minutes. For a classic sudoku, that had a surprisingly beautiful geometry in it. The way the middle boxes pencil marks of 789's had to interact with the non-given cells in rows 3 and 7 was incredible to see. I wasn't expecting that in a classic sudoku, but it was amazing. I can see why a computer would struggle. Luckily, I am a human and can see beautiful geometry. I was so happy when I was able to place those 7's. Great Puzzle!
29 minutes!!! So happy. Marked up 7-8-9 in 5 middle rows and just reduced by those that made rows 3 or 7 impossible. Great puzzle, good mood :-)
“Arbitrary code execution” is a term in computer security where an attacker can get a computer to execute some arbitrary bit of code, often by manipulating where the instruction pointer is pointing to.
So I think the title is maybe a reference to how the 789 triples in the middle 3 rows “point” to the gaps in rows 3 and 6.
7:33 ... It amazes me that we as humans can see this (at least I did) while computers completely miss such a wonderful break-in.
I loved solving this classic!
Surprised myself with this one. 22:20 !! The clever, clever puzzles fall if you find the right starting strategy. That usually escapes me, except for today !! Thanks for the fun.
16:33 found it hilarious you did not spot 7 :). The logic was incredible up to this moment. Looking further into it the puzzle just collapses,
Flippin' 'eck, I solved it. The suggestion here that colouring was the key was all the extra help I needed. Quite astonished!
I always enjoy watching you tackle difficult puzzles and finding your way to a solution. Your SudoKu-solving skills are impressive.
Tried this puzzle for ~20 minutes, and didn't feel like I could do anything more - started watching the video and stopped the video as soon as Simon pointed out that there is something interesting with r4c9, and managed to solve it from there. This is fascinating - as soon as I was pointed to the cell I needed to focus on, it was reasonably quick to find the rest
Now the next step is to find these cells myself
Thank you for your videos, they are always pleasant :)
If someone had presented me with that puzzle and said, "It is solvable, and it is beautiful," I would have believed them (especially if they had cited you, Simon), but I am not sure that I could have actually solved it myself. Maybe I would have been able to synthesize all of the logic that I have learned on this channel and, after some weeks of contemplation, I might have been able to do it. Maybe. Thank you for being so brilliant!
"Dull" is the wrong word. "Soothing" is the right one. I do watch the videos normally, but occasionally one goes on when I'm trying to sleep, because you have a very soothing voice.
Thank you so much for answering my question about the solve video. Maybe Ancient Wall would be great to show here on the channel as well, as you said that Phistomefel considers it his masterpiece and sharing it with a wider audience now that the hunt time is over would be awesome 😊
Absolutely lovely!! So simple and elegant and yet difficult to find and so beautiful all around! Take a bow jovi_al, take a bow Simon!
What a stunning classic
5:18 solve time for me on this one. Was able to determine the orientation of the 789s via row 7 and its impact on box 6 if R5C5 was equivalent to R6C3.
Oh wow, that's a brilliant spot. Well done!
@@Alex_Meadows Thanks!
Beautiful. I'd never have spotted it, but was amazed to follow along and try, and it was so satisfying to finish the puzzle so quickly after that insane Jay Dyer hunt!
Thanks for the input, especially the explanation of your pencil marks
11:26 it's been tickling my senses that whole connection between the open spaces in boxes 4, 5 and 6 and row 7. They are somewhat interesting because row 7 connects with each at a different row. Maybe you saw part of it, or maybe remember some older puzzles that looked like this concept (don't remember said names, and weren't classic sudoku, but had the colouring at it) and tried to force it.
9:03 today, not normally a big fan of classic sudokus but loved the logic on this one! Enjoyed the Mittens shoutout as well.
could not let myself go to sleep until i got my daily dose of simon solving a puzzle. finally i’ve been saved.
Aligned Pair Exclusion: Any 2 cells aligned in the same row, column, or box cannot duplicate the contents of any two candidate cell they both see. If the top gray square was a 9, the bottom orange square would be a 7, the top orange square would be an 8, the bottom gray square would be 4, and then the two yellow squares could only be 3, leading to 2 3’s in the second box. So the 9 can be removed from the top gray square.
nice
The comment edited in is worth an upvote and a response on its own,
The use of Mittens in the thumbnail deserves another, but i can't do that.
And I haven't even got to the solve itself yet.
I would like to take this chance to explain why I use these videos to fall sleep and it is not because you are dull. It is because of the reason why I struggle to fall sleep, which is that I spend either some or all of my mental capacity thinking about things to worry and not relaxing so even when I am tired it takes a while to fall sleep. These videos provide two things to focus on which are the logic path you are explaining and the logic path I am trying to find at the same time. This keeps both my conscious and subconscious busy and if I am tired and in a comfortable position I will fall sleep relatively quickly. If your thought process was indeed dull then my mind would start to wander into the kinds of thoughts that make it hard for me to fall sleep. There might be other things, but those are the ones that are pretty clear to me.
The green thing at 11:26 made perfect sense to me.
The green digit is the digit that goes in R7C3. We know it goes into either R4C1 or R5C2 in box 4.
The unknowns in boxes 4-6 are all on diagonals. It's the negative diagonal for boxes 4&5, but positive diagonal for box 6, which is too bad.
If the unknowns in box 6 were on the negative diagonal for box 6, then we would know the green digit would be in either R4C7 or R5C8 for box 6.
AND, the great thing about that is that it would eliminate all places in R6 for the green digit except R6C6. It would have been a great way to start coloring your grid, which we all know is your favorite thing to do!
How are you ruling green out of r6c9, in the hypothetical case of a negative diagonal of unknowns in box 6?
Simon, if it helps, at 11:30 you were attempting to establish that the number of green digits expected to be in rows 4 and 5 is 2, and if you can show that those two greens are in boxes 4 and 6, then the green digit in box 5 must be in row 6. But regardless of the orientation of empty cells in box 6, you still have no basis for eliminating green from box 6, row 6 anyway.
12:15 for me - I wasn't sure where to start, so I just penciled in 789 in the middle rows and tried filling numbers in until they fit.
Great puzzle. Simon, your trick of eliminating the first 7 was very helpful and logically understandable, that I found the solution very quickly and without any further problems. I surely keep the trick in my mind.
Humankind humankind
Proudly triumphant when
Challenged by silicon
Grinding away.
Does the computer have
Superiority?
Jovi-al’s puzzle and
Simon say “Nay!”
Months late to the party here, but I thought this video was hysterical. Simon has a great sense of timing and comedy.
Simon is John Henry holding the machines at bay. Loved the video and the puzzle 18:40 for me
I am impressed that Andrew Stuarts software could figure it out at all, but well done Simon.
The diagonal 789s in rows 456 made me think of coloring and I spotted this trick very quickly and I managed to solve this in 11:21. What a great puzzle by jovi_al!
My best guess for the title is that the computer solver is doing seemingly arbitrary techniques to solve the puzzle (and bypassing the beautiful logic built in because it wasn't programmed to include this novel technique). Under that assumption, I think jovial would have then come up with a bowtie name that is an established phrase, as ACE is in the software security and glitch hunting/speedrunning domains.
11:25 It's okay, Simon. Hard classics drive me mad, too XD
Thank you, Simon, for the beautiful solve!
As for your question about what you were thinking at 11:26, I might have an idea, correct me if I'm wrong: you thought for some reason that if r7c3 is green, then r7c9 is ALSO green rather than NOT green, and that led to the logic about diagonals and placing green in r6c6.
23: 33 here. That was pretty neat!
Interestingly, I only spotted the (your) yellow cell restriction after finding that (your) blue could not be 9 (hence needed to be 8) because that would lead to 8 being forced into both r1c6 and r6c6. When yellow came to my attention I actually at first thought I had broken the puzzle and was truly relieved when I realized that 4 came to the rescue.
I pulled off a fortunate guess on the 789 triples in the middle boxes and finished this one in under 7 minutes as a result. Can't say I am under 10 mins on these puzzles very often, but pretty proud of that
3:00 I confess to being one of those people. In my defence I also find it very educational and I generally solve a classic every morning. Not dull, but relaxing :)
Unlike many commenters here, CTC gives me insomnia, as I just can't help but give the more approachable puzzles a try. This one was a nice little ego boost for me, definitely an example of how I've gotten so much better at sudoku watching the channel regularly.
I love that you went to the solver to see how it would manage it. When trying to get better at sudoku, i would occasionally go there and try to see what I was missing. This did not go incredibly well. Wonder if your way of solving using a color variable instead of actual numbers would render all those crazy steps unnecessary as far as computing is concerned.
OMG! I did it! 27:11. It usually takes me 10 to 15min (and sometimes longer) for GAS. And I can hardly ever make any inroads into Simon's featured sudokus, let alone solve them. Can't believe I did this without even watching video. I used phistimophel and colouring 789s to distinguish. Is that cheating??
Gonna watch the video now to see what I should have done, but feeling pretty hyped....!!
15:20 You could just colour fours (for example with red). 489's in third row will be red-green-blue. We have to put an "yellow" digit somewhere into row 3. It can be only seven at B7 (if bottom left corner is A1 - like in chess notation).
I find your videos very fascinating, it's just your tone of voice is the second most sleep inducing I've ever heard, after the late Bob Ross. I know Mr. Ross worked on making his voice quieter, however, after his time working as a US military drill sergeant!
12:29 was my time and I must say, I'm also happy that the computer got an 8 as it's first digit, as so did I. I missed the simple trick with r3, and solved r7, first.
That was it (@15:28)
That sorted the corners from the Phistomefel ring.
[1s ("Aces") included]
Cool 😂👍😎☕️☕️
Did this one, yippee me!! Maybe Mark sent this to you, Simon, because you resist entering candidates in cells? I just went through the #s 1-9, entering when I could see only 2-3 cells for a #. That is when I found certain restrictions for the other #s, placing them in. Then worked out many 2 candidate #s only in some boxes, freeing up single digit possibilities. I did nothing 'fancy!' (Sorry, I'm having trouble fully explaining it.)
Well, I think I understand what you mean - probably because I did the same or at least something similar. Also the first one I have solved without watching any moves by Simon (or Mark).
6:31 found the break immediately. Wouldn't call this a mittens' level of puzzle, but would stump a lot of newer solvers.
When I'm stuck, I generally queue the video to a point that looks similar to what I have and try to guess Simon's logic before he can finish explaining it. This was a puzzle definitely requiring that help (I did deduce, for example, r4c4=r7c5 on my own but that was very not enough to break open the center rows)
Arbitrary code execution is an application security vulnerability when a system can be exploited to run the code of the attacker (with the permissions of the original, etc. - which is often why it is very dangerous indeed). Given how the solver behaves, maybe the idea is that it looks like the solver is just running some attacker code, not what it should be?
Wonderful puzzle! Wonderfully and entertainingly solved!
Got to cherish you again using the same word twice. 😁
@@davidrattner9 ☺️☺️
Simon's coloring logic was a lot better than mine. I took a round-about way of basically saying what if the center digit was 9, and then noticing that caused either row 3 or row 5 to not have a 9. 7 worked because of row 3, but 8 broke like 9 did, giving me a digit through what probably should be called bifurcation.
12:35 for me. I don't know why, but it was just intuitively obvious that the central cell had to be that particular digit, because any other candidate starts to leave empty cells all over the grid in just a few steps.
There's a pattern of 5/6 in box two and 3/4 in box eight that I was *sure* would lead to the intended break-in, but after spending 10 minutes I just couldn't get anything useful from it. I'm amazed how different the trick actually was!
The first digit I found was the 4. I noticed that if R3C5 was a 4 it would force a 4 in R9C9 and a 7 in R4C4. Then you will see that R3C1 is a 89, and looks at R3C8 and R4C1 which are also both 89 - but different from each other. Therefore there is no valid input for R3C1. Therefore R3C1 must be the 4.
Still had to use Simon's logic from then on, but was pleased I got a digit at first!
After the initial goodliffing of 789 / 489, and flailing around for a while, I asked the question - can the 89 in R5C2 be different from the 89 in R6C6 (which would give me 7s in 2 of the other cells). I ended up bifurcating, and coming to the conclusion that they cannot. Once they were the same, I was able to break in - but I needed to bifurcate, and Simon was able to see this without that! Just amazing!
The really fun thing here is that while the computer rates this 380, if you place a given 7 in R6C7 this also implies the beautiful first step, and suddenly the computer thinks it's 42 (nice) and Easy.
It would have been crazy if this sudoku triggered an actual arbitrary code execution in the solver, perhaps to change the score to 'hi simon' or something along those lines. XD
It's crazy how it is simultaneously simple and difficult to spot the 789 trick and then resolve them using r3 and r7. And once you get that, it's just simple sudoku all the way, how bizarre! I have to say this has to be one of the simplest sudokus to feature on this channel but I'm not gonna forget the fact that it is very tricky to see that crack in the puzzle.
And also, I have to say that the positioning of 7 in r3 is one of the cleverest things I've seen while solving sudokus.
Not dull but soothing.
23:36
A good time, Coloured the 7-8-9 cells in boxes 4-6, once I saw that identifying one cell would identify all of them, and suddenly I'm looking at these 3 cells that had to be identical, ruling out whatever digit it was from the 3 empty cells in Row 3, so clearly it had to be 7, since it already existed in row 3.