Expert Sudoku: The Basic Techniques Used By Champions
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- čas přidán 1. 03. 2019
- We take a look at a BEAUTIFUL human-created Sudoku requested by one of our viewers. This puzzle is an excellent test of your mastery of basic techniques.
We would be very grateful to any viewers who might consider supporting us by becoming patrons of the channel on Patreon. Our page can be found here:
/ crackingthecr. .
If you have a puzzle you'd like to see us solve, please either email or tweet it to us at:
crackingthecryptic@gmail.com
or
@crypticcracking
#crypticcracking
#sudoku
I laughed out loud on this:
“My fluid intelligence is not taking me that far by the moment”
LMAO, so I had a troll clip of Pee-Wee's playhouse on another tab, totally thought I was reading the comments of that. Made this comment even more perfect.
4:04
I wonder what Simon there, would think of the puzzle Simon solves today?
Thank you so much for doing this for us beginners. Although I started Sudoku 7 years ago and currently doing some very difficult to ultimate hard puzzles but I never forget my starting with you 2 guys. I think your methods are perfect and easy to follow. Of course with persistence in doing, one can advance himself tremendously. Thank again. You're the BEST.
‘Sometimes you have to brute force it’
I’m punching my screen it’s still not working
What does brute forcing it mean? He says that on several videos
@@moimeself1088 you dont use logic. Just try every possibly combination.
I wish i could like this comment, but unfortuantly doing so would get rid of the amazing number of likes it has.
@@danielmajer1905 thank you
Εληννηκα
Are these techniques named? I'd love to see a video dedicated to specific techniques with multiple examples
First is called fiancetto
Edit: wrong game
X Wing and Hidden/Naked Pair are the techniques he used here that are beyond basic row/ column/ box logic.
I actually just played enough to figure these techniques out, and I made up my own names for them lol
@@illustrationism same
The technique at around 7:00 with the 3s in the three blocks 3, 6 and 9 - I have seen this called the mallet on-line
Thank you SO MUCH! I've only recently gotten into solving sudoku puzzles a few months ago after finding your channel and I've had the darndest time solving the expert level puzzles. I used the Snyder system you talked about in this video and it worked WONDERS! I think I may have over cluttered my puzzles with pencil marks but this simplified method helped a ton. I also just learned the naked single and x-wing logic which helped tremendously as well. Much love from the U.S. !
i've been playing with highlights this whole time and just turned it off, now im realising how hard this damn game is
I just watched the 4 digits sudoku video and I succesfully completed the puzzle myself after that and now I can predict some of your moves in this video. Amazed myself actually. Thanks for the great lessons!
Checking out older videos from the channel. I appreciate the patience with which you approach showing how the logic works, and the evidence that Snyder notation is very helpful. I also appreciate how far the channel has come - but the character of the channel is well demonstrated by these roots. Thanks for all that you have done, Simon and Mark, to grow the channel into what it is today and to promote the hand-crafted, elegant puzzles that are the hallmarks of CTC.
This has been by far the most helpful puzzle I have seen on the channel. I am new to this whole mess and I am the guy that penciled everything in. I will endeavor to learn this snider method. Videos like this have shamed me into not supporting you on Patreon. I will fix that oversight today. Be well.
Day 6 of quarantine...
(Thank you for the techniques btw!)
this is so true lmao
Same here lol
True
Same
I’m late to the party lol
loved the beautiful puzzle, and also your very clear explanation! Even when you were in puzzling frenzy and on solving high, you take enough time to explain what you are doing. Brilliant, thanks!
I like to sequence through all the numbers two or three times filling in forced cells before making any pencil marks. This often eliminates many squares reducing the number of time-wasting pencil marks.
I am a huge fan of Sudoku and have been playing since it started spreading worldwide. Did not look at tutorials or videos out there and have been exploring techniques myself. It is nice to feel validated that those techniques that I've practiced over the years are actually named and well rooted in the Sudoku community as well. Looking forward to more videos like these to learn
Late to this video but I noticed after finding the 3/4 pairs in C7 and R9 you had 3 corners of a unique rectangle and the remaining corner's only other option was a 5 which would also unwind the pairs since there would be only one position left for a 3 in box 6. Love the vids, I've learned so much from you guys!
The song choice at the end when you're on a roll solving the puzzle is an accurate representation of how my brain feels when I finish a difficult puzzle. I swear its like I'm winning carnival games.
thanks for creating basic solving techniques... I'm learning so much!
Oh wow - actually followed along with this, thanks to practising on the cracking the cryptic app :)
I am going to have to try this technique. I usually fill in all the pencil marks and gradually eliminate combinations, but he's right how the busy-ness of all the pencil marks obscures good patterns.
So looks my panels with every number pencilled in may have been holding me back :D
MisterHughes You look like the guy in the video lol
There's just no way to make sense of all of that information quickly xD
Excellent explanations! Thank you.
Awesome noting technique, thanks for the tip
I was trying this puzzle before watching the rest of the video, and I actually did find the trick with the threes through process of elimination on row 9 - the threes could only be in the bottom row of the bottom right 3x3 square because they were essentially ruled out from every other open position in row 9 (after finding the 1 in the bottom left 3x3)
This IS beautiful, thank you!
I am enjoying going back an re-solving the puzzles in these older puzzles with newer techniques. I was astounded that the first number I got was the 1 in R8C9 using the Phistomefel Ring. That made the 3/4 pair in box 9 easy to find and we were away.
For some reason, this popped up in my feed. I remember the old pre-lockdown stuff. You great pair have come on leaps and bounds. Love you both.
EDIT: The software really has come on leaps and bounds. Well done.
Very clearly explained and enjoyable to follow
Wow, that was wonderful. Thanks!
New to sudoku but IMO when you play at this level you've gotta master the logic shortcuts or it will take 30-40 mins or longer or never to complete a puzzle. That's where I'm at, with intermediate skill level puzzles, but I typically have to do repeated iterations of missing numbers in rows/columns vs 3x3 blocks. I should use the notations but it seems to slow me down. The trade off is a faulty memory that can't retain the numbers I need to test. Tantalizing!!
Really appreciate this video. Very helpful!
Thank you so much. I learnt something new from you.
Time to look back. Today I watched again this 2 year old pre-web-interface episode of CTC (a suggestion from youtube) and I can conclude some differences to 2021:
Almost the only difference was that mostly classic sudokus wehre in the focus, because of the software. No variants like Arrows, Sandwiches, Anti-Knight, Little-Killers, XY, X-Sums, Snakes, Palindromes, Kropkies, Renban or German Whispers Lines... We had much, much more given digits!!! And not to forget, the Set-Theory (Phistomefels Ring) was not developed so far. However, every episode was entertaining and instructive, so i learned something about X-Wings, Swordfishes, Empty Rectangles or Bent Triples... Thank you, good job, well done M.&S.!!!
At 8:00 I don't see how you knew the 7 when into column 8 of row 7. Couldn't it have also gone in column 9 on that row?
Look down column 8 and you find there's only one place the 7 can go.
@@joshuazucker No. Two places in c8; rows 3 and 7. Nvm, my mistake😨, the 3 8 pairing eliminates 7 in row 3.
I love CTC's solving style so much I made a video on my channel where I
analyze each step of this solve. In addition to explaining the
strategies used, I add a couple of pause the video moments and some
alternate solving paths, similar to how someone analyzes a chess game.
i liked that recording of entertainer at the end. I always like when you can hear the pedal movement on the piano. i just wish you let it go to completion
Guess I've been doing it right all this time, but one interesting note: before marking the 2's in the center, I would have made marks for 2's in row 6, even though (later) it would have shown that I was placing a mark for a number in a location that was never really "valid."
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@@austurhlid too political buddy
Great puzzle ! Great learning !
I played sudoku for the first time since young baby where I could never even solve a medium one, and I solved a super-hard one in the newspaper in just 30 minutes! I thought I made up my own technique but it was the one used in this video
Sad
@@gabrielcuneta7256 haha how so?
@@EricSmyth4Christ nvm
You did make them up, just that those techniques were already known
I taught myself these methods as a kid. I became obsessed with sudoku; still am 😎
7:26 for me after importing and building the candidate list, with no hints. Not a bad puzzle!
Really helpful, thanks a lot
I can improve my move now
Muhammad Nabil ur gay
@@ariff9477 after you mention it, it really sounds gay.
dude change ur profile picture
@@ariff9477 weebs can play sudoku too ya know
lol
yeah i also noticed nyt loves putting pairs in their hard sudokus! now i know what to do about it
Thank you!
Lovely play with the 4s in row 9. I had to replay that a couple times before it clicked.
Do you ever get to the point where you are stuck and play a guess?
thats called bifurcation, it's a technique often used competitively but it isn't considered part of a logical solve path so simon dislikes it and there are 2 excellent videos showing mark doing a puzzle with it and then simon doing the same puzzle without it( albeit in about 4 or 5 times longer). If you haven't seeen them alrady I believe they are called something like "hwow to cheat at sudoku" which is marks one and "how NOT to cheat at sudoku" which is simons.
Really amazing at 12:32, hard to find that 3/4 pair at row 9, I never think about that possibility, really amazing bro, that's what we say "logic".When you figure out 3/4 pair, other numbers in row 9 are definitely clear
Feels good when you get ahead of him happens rarely
Wow beautiful job
Me da mucha alegría que aunque yo no sepa inglés puedo entenderlo perfectamente, lo e resuelto mentalmente y no me equivoqué en ninguna, me hace feliz saber que soy bueno en algo
19:46 hahahahahaahh I relate to making all my mistakes when the puzzle is already mostly solved.
Please write a book, ive been searching for a decent one for what seems like forever. Cheers
You could switch between pencil marks and normal numbers if you’d click on the right mouse butten. It’s a bit faster
Great tutorial solve. Looks lile ive been working on harder ones. Seems beyond this technique. Like picking the least disruptive square for a pair. Picking by the least progress made?
My logic at 11:36 or sooner is that the 2 in C9 and R8 (with your deduction about the 34 pair) means that the only spot in the bottom right box for a 2 is R7C7 (in my solve I had the 2 pair noted in C8 R5/6 and C7 R7/9 next after the 7s got placed)
how did he know the 3 and 4 have to go together?
@@kailyndonnelly06 It's a pretty long sequence! The places the 3s are penciled in R6 and R9 eliminate the 3s from the rest of column 7 (that's an Xwing). Then the 4s that are placed already in R4 and R7 eliminate a couple of possible 4 locations from column 7, and there's already a 4 in the top box. So, there's only 2 spaces left in column 7 that the 3 and 4 can go in, so those two spaces have to be the 3 and the 4.
@@joshuazucker thank you so much!
Lots of great stuff in your video. Thanks.
I'm stuck on how you determined the 3-4 pairs in column 7 by using these numbers found in the top right box column 8??? I found the 7s right off the bat but got stuck soon after. Any help is appreciated because I bet the method you used would be helpful in future puzzles.
I don't think you actually need that 3-8 pair in the top right box to figure the 3-4 pair out. I'll try to explain, timestamp is 10:15 for convenience:
Look at row 6 and row 9 and try to put a 3 in there, it can only go in col7 or col9 in both rows. Which means you have two possible combinations: a 3 in row6col7 and the other in row9col9, or a 3 in row6col9 and the other in row9col7. Either way you have a three in one of these two spots (row6col7 and row9col7 are the ones we're trying to put the 3-4 pair in).
Then you look at column 7 and try to place a 4: rows 1/2 are ruled out because of the 4 in row2col8, row 4 is ruled out because of the 4 in row4col2, and row 7 is ruled out because of the 4 in row7col3. This means a 4 must go in either row6col7 or row9col7 in that column.
So in these two cells you know for a fact one is going to be a 3 and the other one is going to be a 4 and you have your pair.
I hope the explanation wasn't too messy :)
@@AmaranthRBY hey why did he pick 3 and 4 pair specifically? Why only those 2?
@@nirmalsinghbuttar7095 It's just something he noticed, this is one of the harder things to learn when doing sudoku. The ability to look at the grid and realize that the 3s and the 4s had that specific restriction in that specific place
@@AmaranthRBY got it. Thank you. :)
Simon is a true Entertainer so the song is an excellent choice ! Nice alternation to KV545 for once...
I already knew this but I still enjoyed the video
Even if you don't find the 34 pair in C7, there is a simple forcing test with the 4's in the middle right 3x3 block that will get the puzzle going.
No matter which position is chosen for the 4 in that block the 2 in the bottom right block gets forced into RC77. In one case the 4 punts it there and in the other case a forced 3 punts it there.
Resolving that 2 is all that is needed to crack open the puzzle.
But in the first place how can we be sure that they were a 3/4 pair? Why not a 3/8 pair?
@@oikosu
The question is where the 4 can go in the middle right hand block. Starting at 11:00 … there are 3 possible squares -- RC67,69 and RC59.
In force testing we try the positions and note the forcing results.
If you put the 4 in one of the C9 spots, the 4 in the bottom 3x3 will be forced into RC97.
If you put the 4 in the C7 spot (RC67), a 3 gets resolved in that 3x3 to RC69 which forces a 3 into RC97.
So no matter where you put the 4 in the middle block, either way you end with a 3/4 in RC97.
There were only 2 possible spots in the bottom 3x3 for a 2 -- RC77, 97. And you've just eliminated RC97 as being a possible 2 as the forcing test tells you it has to be a 3or4.
There is now only one spot left for the 2 in the bottom 3x3 -- RC77.
@@lawrencekallal6640 Thank for your explanation, it's very clear! Now I understand why it must be a 3/4 pair there.
6:13 3 at E3 and 33 in Box 8 makes 33 at J7 and J9 in row 9. Now there's an x wing on 3 in Boxes 6 and 9.
I met a guy who could solve hardest sudoku puzzles from the newspaper without putting possible numbers into boxes or even get stuck anywhere he'd just go around putting numbers into boxes until it was done. He was like a savant. At first I thought he was playing a joke until I saw it completed error free. Myself I can do all mid level puzzles and some higher up level ones but struggle with the hardest ones. Then I saw some of your videos that have rules and one or two or even no starting numbers or that have cages or special rulesets for certain blocks. Hell I hadn't ever heard the word orthogonally until it was a rule for adjacent numbers. Sudoku has more facets than I ever thought it could have.
Good stuff Andy Murray.
George Mariolis ahahahahaha
what program do you use for working sudoku?
I have another approach: always start with the rows and columns (can I place a digit by logic alone), then I take the numbers 1 to 9 one by one (dito), then I do what you say, start with placing pencilmarks.
They start of with finding the obvious ones too. They don't go 1-9 as it may take longer, and stick to finding numbers where they have the most chance.
I use these basic techniques to solve an expert level sudoku every single time. Just gotta be precise with marking the numbers.
Thank you man
is really nice to see a well made sudoku, most of the time I try with free apps so always in the expert level I end up with a lot of pairs, but not logic to choose, so I have to brute force a path to find if is the right one.
Oh that explains the issues I'm having, so pretty much they require bifurcation or else there is no way?
@@aaronmarquez5596 isn't that there is no way is like with an empty rectangle, just that you have to continue like 3 or 4 steps ahead. like today I did and empty rectangle I try with a 6(it wasn't one): vertical limit a 4 that limit a 2 that give me a 15 pair that give me a 4; horizontal another path to get the 15 pair and get the same 4. And that solve the puzzle, normally that wouldn't even be called empty rectangle XD but guessing I think.
Thanks!
Thanks so much Kameswari B - we really appreciate it :)
At around the 10 min. mark you say we need to find a 34 pair. You have in column 8, a 38 pair, and the number 4. You then say we need to look in col. 7. How did you determine we needed to look for a 34 pair in column 7? How did you know we needed to look for a 34 pair, and then why column 7 and not column 9? Please explain the reasons for this?
I'm wondering either.
Same question I had.
I think that because there is going to be 3 and 4 in column 7 some order and you can limit possibilities just in two cells and column 9 had too many options for 4 to get 34 pair on that column. Bad english sorry.
@@arsenaali7794 Thanks you !
I like the music!😄
Great work Simon. Where did you get your sudoku solver? You use it with great ease.
Sudoku Guy, it’s Duncan’s Sudoku Solver.
That was my first thought! Great solver - big helper!
I got deeper into sudoku just before the quarantine - and I AM SOOOO HAPPY! Thank you guys for amazing tutorials and solving puzzle videos! 🌞
I am new to your channel and am curious about the app you're using. I like it better than other's I've seen.
Can someone please explain how he got the #7 in row 7?
Since 3 and 8 got paired in row 1 and row 3 in column 8, either 3 or 8 would be in either of the boxes and vice versa. So 7 can't be placed in column 8 and column 7 too as there's already a 7 down there. So 7 can only be in column 8 which results in 7 being placed in the 7th row column 8. Hope u understood 😊
At 7:50, how did you know that the 7 could only be placed there? It could be in the top box where you shadowed 8 and 3? Thx!
because thos two boxes is taken by both 3 and 8
@@garrilrumampuk1811 Why couldn't the 7 go in the 9th column instead of the 8th? No conflicts there. He doesn't explain this at all. He just does it with no explanation.
Wondering the same thing
@@soundsgoodtome He's analyzing column 8. Can't go in row 1 or 3 because there's a 3-8 pair, can't go in row 4-6 because there's a 7 in the box, can't go in row 8 because there is a 7 in row 8 already. Only option left for column 8 is row 7.
@STEVE7 TeeBeeCee Every column needs each digit. In this case, he's examining column 8 for a 7 digit. It cannot go in the top nonet (3x3 box) because row 2 is taken by a 4, and rows 1 and 3 are a 3-8 pair (which he has "pencilled in" in small grey text). It cannot go in rows 4, 5, or 6, because that nonet has a 7 in it already, and you can't repeat digits in a nonet. And row 9 is taken by a 6. So it can only go in row 7 or 8, but row 8 already has a 7 digit, so it can only go in row 7.
What software do you use for this? I want to up my skills in solving and I think doing it in sw will really help me
I don't think it would.
I know and use these techniques almost by default because sometimes I forget to use them!!😣😬
Recently got into Sudoku and it's really interesting.
7:58 How did you know that a 7 could go in THAT cell and not in column 9 row 7 OR column 9 row 9?
Edit: 19:10 How did you know it was a 1 in that cell instead of below the 8 next to it?
I'm thinking the same
For the one at 7:58; because there needed to be a 7 in that column, and it couldn't go anywhere else in that column. Therefore it must be there.
19:10 same logic, the missing numbers in column 8 are 1, 5. The 5 couldn't go in row 4 because there's already a 5 in that row. Therefore it must be a 1.
@@ColdIntruder1 But couldn't be the 7 in that column in line 3?
@@ColdIntruder1 19:10 the fact that he 'explains' there's a 9 and 6 throw me off there. thanks for the explanation there
7:58 look at the top right square. 7 can't be in the 7th column because there is already 7 in this column and can't be in the 8th column because he already concluded that there is 3, 4 and 8 so it must be in 9th column, therefore in the bottom right square 7 can only be in the 8th column.
At 10:30 in the video (after finding the 3s in column 8), why did 3&4 get picked/identified as the next hidden pair to find?
I understand the technique used after that, but not why that particular pairing was picked in the first place.
I know it's a late comment, but that's just what he noticed at the time.
what program is he using
G'day,
I worked this system out before seeing it on CZcams. another thing I do is place a DOT instead of the small pencil marks numbers (on paper).
You are so cool
Well I'm doing that from now on...
Wow! Nice job. How do we go about sending in user puzzles?
You can email us at crackingthecryptic@gmail.com or tweet to us at @crypticcracking
So where do we get to have a go at it before The Big Reveal?
What tool do you use ?
Where I can set and delete candidates.
Fun puzzle
I like your channel
I am trying to follow your logic and technique for solving this puzzle. I am at a loss as to how you came to the conclusion as opposed to an assumption for row 9 column 7 at approximately 12:20 in the video. You state that no numbers other than 3 or 4 can be used in the square. At that point in the puzzle I still see the #2 as a very valid possibility. I know it is eventually shown to be the correct decision. I can't seem to find that logic this soon in the puzzle. Thanks in advance and I am looking forward to your explanation.
I might not be him, but I think I might be able to help. At that point in the video, he has discovered that both squares (row 6 and row 9 in column 7) are the only ones in the column that can contain such numbers. That means that each one of them HAS to contain one of either number for the column to be complete. Therefore, no other option can be placed in them besides the 3 and 4 pair.
Did that clear your question?
hello sir, can you explain at 19m03s why column8 row 4 can only be 1 due to 9 and 6? thank you
what kind of sudoku program are you using i love the interface
does anyone know exactly why there must be a "7" in row: 7, col: 8 @ 8:00?
There must be a 7 somewhere in column 8 and this is the only possibility!
@@joshuazuckergreat explanation josh
See the top right matrix...see the 3/8 3/8 pair, good! Now focus on the 8th column...well basically that rules out any other number as we know a 3 and an 8 are definitely filling them two boxes. The right middle matrix underneath has a 7 which rules out a 7 anywhere else in that column quite obviously
So by process of elimination in the bottom right matrix a 7 can only live in the box he has placed it. Took me a while to figure it out so hopefully it makes sense to you now
I have a personal problem with sudokus. After I was trying to learn finding and using the triplets I found myself struggling with using basic "I miss X in this row/line/block" method, and even moreso with simple "if I place X then Y will happen which means X is right/wrong" thinking. Should've worked on all the skills together I guess.
Does anyone know what program is this, or if there any similar ones? Exactly like this one, where you hoover over a cell and can chose any of the numbers. The only buttons outside the board here are the "little" and "big". Usually in other games, you have instead the number "from 1 to 9" and have to pick one at a time. Thanks
Can someone explain what's the logic behind 7:58 where he placed down 7. Couldn't there be 7 in row 3 as well?
That's exactly what I'm confused by. To the right of the box where he placed the 7 and the very bottom right corner box are both possibilities I would have thought...I cane here to find out exactly these kinds of moves and I'm only more confused. Explains nothing
What does 3 and 7 have to do with anything from removing that cell for being a 2 at 15:14
Nothing in that circumstance. His logic was that if either one of those had been a 2 instead he would have been able to lock the 2 in column 4 and 5 there by solving the column 6 location for 2. Instead he had to go a different way
Why do the 3 and 4 have to be paired in column 7 as opposed to just be present but not linked?
Same doubt here..
10:30 In column 7, both 3 and 4 cannot go in any of the other places. The two places where they are pencil marked are the only two places in column 7 where they can go. That means if one is 3 then the other must be 4 and the other way around, and therefore they form a pair: no other digit can go there.
3 mistakes in the endgame
so relatable that it all goes wrong when you relax the tension haha
didn't understand how did you able to eliminated the 2 at 15:20, can help me understand pls?
19:02 I understand 1 is the only number that can go there. But I would like to know how did you spot that, since you spoke about 9 and 6? I'd like to know the way to spot that.
Only 1 and 5 left in column becuz he found 9 and 6. Therefore, he can see that row 4 already has 5 so it has to be a 1.
@@UserIsM Oh now I get it. He was actually filling up that row with 1, 9 & 6 and found that 9 and the 6 couldn't get there. Thanks mate.
I love Sudoku, and I play it quite often, I was hoping to find a new technique or maybe even an idea to finish sooner, but I just couldn't follow the arrow to the mouse moving all over and him talkin I just couldn't keep off of where he was and what I was to do, I hope those who are able to keep up do learn something
wow very good you can solve a hard soduko
My stumbling block was the 34 hidden pair in c7 :(
Me too…I still don’t get that logic
@raybuttigieg1343 There are some different points I can make about the approach used. Firstly, if you identify a number of candidate numbers that matches the number of cells they can occupy, you can think of them as partially found. For example, if we find a 8,9 pair in a column, then we know they won't appear elsewhere in the column, as there are only two places these numbers can go in this column and we've found them both. The other part of the technique used in the video is that numbers don't repeat in a 9x9 square. If the possible positions of the numbers in a 9x9 square are found, we know that they won't be found elsewhere in that 9x9 square, and as each row and column also has to have all the numbers without repeating them, we can eliminate possible positions for numbers. For example, if we find that the number 3 must appear in a square in either columns 5 or 6, we know that it can't appear in the same square in column 4, so the number 3 must appear in column 4 in a different 9x9 square. I hope this helps, but I'm happy to try to explain this again if it didn't make sense.
0:48 This statement has aged poorly.
Why
Yeah, why
Sir really helpful videos of yours. Can u tell me the sudoku software you are using in your laptop . Because I want to download the same software in my laptop or maybe be the name of the software Thanka
I found it, It's called Duncan's SuDoku Solver
@@FMuscleZ28 thanks buddy
I could follow him only till 16 min, I lost him afterwards while he was finding 2.
15:35 In column 4, because of the '2' in row 1, the only place to put 2s are on the row 4 and 5. 16:19 Since column 4 and column 8 locked their 2s in row 4 and 5, the only place to put 2s in the center-left group is row 6. Because of the '2' in column 2, the only place to put '2' in the center-left group is in column 3.