Improve At Sudoku: What To Do When You Get Stuck
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- Опубліковано 10 сер 2019
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▶ABOUT US◀
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. We're also "cryptic crossword" aficionados. Mark is the eleven-time winner of The Times championship and Simon is the former record holder for most consecutive correct solutions to The Listener crossword. We hope we can help your puzzle solving while also introducing you to some of the world's best puzzles.
Thank you for watching!
Simon and Mark
Whenever he says 'we've got some cool logic going on', I know I'm either going to learn something or be lost...
i usually find it going the other direction
Pencil me in the Lost column
@@oswaldcornelius638 I can usually follow the logic after he points it out, but can never spot these situations in puzzles on my own. Usually end up underlining candidates as if they were set and running until I get a contradiction, then removing the assumed candidate. Not fun, not efficient, and nowhere close to elegant. It allows me to finish some puzzles I'd never otherwise be able to though.
Seeing Simon work on them and find this type of thing makes me really wish I could train my mind to recognize stuff like this...
@@RealRuler2112 I missed the logic on how he chose the 7 (over the 5) in the first place. Also the concept of an "empty rectangle" that contains values in it eluded me. Still, more value than not in these videos.
@@oswaldcornelius638 I might be able to help you with the empty rectangle concept... Look at the upper-left block at 9:30. Since there's a 1-2 pair in the middle left and middle right cells of this block, 7 can only go in the top row or middle column. Either way, it eliminates 7 as a possibility in the upper-right cell of the upper-right block because of the 5-7 pair in the row just below the middle.
If 7 is in the top row, it's obvious that 7 can't be in the upper-right cell of the upper-right block. If the 7 is in the middle column though, it forces the 5-7 on the left to be a 5 and this forces the other 5-7 in that row to be a 7; this 7 also eliminates 7 as a possibility in the upper-right cell of the upper-right block as it's in the same column as the right 5-7 pair.
How to determine that you're going to use a 7 for this involves recognizing this type of pattern, which I can't do. =(
I have a request. Can you pick a relatively hard puzzle and solve it on camera without explanation so we can see how fast you do it without walking us through it at the same time. Then walk through it!
that would be fantastic!
You can turn your PC sound down.
@@StarGazer568 it's not about his voice or something, but about: how fast would he solve it without wasting time for thinking how to explanate it to us 😉
@@CATAZTR0PHE Good point!
@@StarGazer568 even if we did that, we would have to cut down some "explanation" time which can vary the time by a bunch, also while he explains, he might see something that we don't, and he might have to process how to explain that too.
If he didn't explain, probably he would be faster and that is the question, how fast can he solve one without explaining most of it to us.
I'm sure you either get the point now, or I'm just rambling.
That empty rectangle thing is super interesting. Became pretty clear how it worked once you try to put a 7 in the non-pencilmarked box. But it's one thing to understand how a trick works. It's another beast entirely to be able to spot it
skysthelimit112 Very true. I completely understood the logic of the trick, but it would have been almost impossible for me to actually spot it unless I was given a hint that I was supposed to use it at all.
thats the sole reason it is a 'hard' sudoki i think. Because I got stuck, watched the video until that point, and then everything went smoothly again.
@@angelmendez-rivera351 Absolutely. The logic on these is straight forward, but trying to find it (especially when you don't even know if any thing IS actually there) is crazy.
When basic Sudoku fails, I typically put a great deal of effort into finding x-wings, y-wings, empty rectangles & skyscrapers....but, well, found 1 x-wing once which turned out to be entirely useless.
Watching Simon pick them up "so easily" is phenomenal.
Ah well....I'll get better. I hope. One day!
It does get easier with practice. It helps too if you can highlight every cell where a digit can go first. Then these patterns pop out at you more clearly. At least until you become more proficient at it.
It also helps to really understand the patterns and their permutations. For the empty rectangle scan for an L, T, or + pattern of a digit (including rotations and inversions) inside a box that restricts it to a single row and column. Sometimes it can be tricky since you really only need two off-center digits to create multiple variations. Work through them all.
Then follow both branches, in both directions, and see if they line up with a naked pair in another chute. If there is one, then it can be used to eliminate the digit in the corner both paths point to.
There are several good sudoku tutorials out there, both here and on other sites. Take the time to work through them. You'll find yourself improving rapidly.
@@davidh.4944 Excellent advice, thanks. I'm handicapping myself by using limited software (doesn't allow a distinction between corner marks & candidate marking).
However, that's offset by some automated highlighting. Software complications aside, yup....I'm gaining skill.
I need more advice (like yours) on the "finding/spotting" and less on the "how they work, what you can eliminate" (Simon tends to focus on the latter.)
As for tutorials....once in a while. I don't take this all too seriously. Once in a while, I'll look around for some, but, well....not everyone's a great teacher, nor video maker, nor Sudoku solver....and it kinda takes all 3.
8:20 Plot Twist: He actually got stuck himself and secretly called his friend to help him out.
Xdd
It couldn't have been Mark, he would have gone straight to bifurcation ...
The Empty Rectangle totally baffled me on the first explanation but I watched it again and understood. That was the key that unlocked the rest of the puzzle for me. I have been working these puzzles until I get stuck and then watch the video for a single clue that pushes me forward and then I continue on my own until I get stuck again. It is a great way to learn and I appreciate the wonderful lessons!
Exactly the same for me!
I still cant understand it ;-;
@@KattLover5412 @EnchantedOcelot the 'pointing' was confusing to me but basically the 7 could only go in those 5 highlighted places in box 1. So it was atleast 'pointing' downwards in column 2 or pointing rights in row 1. Either way, the the top right corner could never be a seven, because of either a 7 in row 1 or seven in column 9, which was caused by the 57 pair in row 6. Hope this helps!
Same!! I was literally able to solve the rest of the puzzle after that, (except for getting ‘stuck’ bc I completely missed where I could’ve filled in a super easy cell😅)
@@lucvandijk3006are you good at sudoku?
"An empty rectangle is just a fancy way of saying a number can only point in two directions." Thank you so much, now I finally understand what an empty rectangle is and now I can start implementing the technique in my solves!
Yes, I also finally completely understood empty rectangles due to this solve and I'm very grateful for it. I also got stuck on this puzzle using only Snyder notation, so I sort of wish Mark had gone as far as he can with only using Snyder first and then showed what you start looking for at that point. But he's a World Champion and as soon as he sees what's going on, he asks if you'd like to stop and try to see what he sees and just goes for it. Maybe in the long-run that will be better for me, but I don't yet know how to notice these things at the point he does.
ugh, can someone explain? I have no idea why did he assume 7 would be there. its quite obvious the number only restricts cells horizontally and vertically, but why he inferred the number is there?
@@cla2008 the other two "empty" cells are a 1 2 pair. so the 7 would either land on the top horizontal line or in the middle vertical line
@@ceelar right, thanks. that bit I missed.
He was just trying to see if he could make the two 57 pairs affect the same block. By sending the 7 up the column into block 1, it would then affect row 1, and the other matched pair of 57 could also "see" and affect the cell at the end of row 1 (column 9). That way both of the 57 pairs could affect that block. He chose the 7 because he could play it in block 1. He couldn't play the 5 because there is already a 5 in block 1.
I think an easier way to describe the logic at around 9 minutes is that regardless of where you put the 7 in box 1, the top right corner of box 3 cannot contain a 7.
Now it makes sense to me!
yes. took me a while to understand, until i looked at it like that
Your explanation makes sense! Thank you. He could have not bad any harder to understand, you made it easy.
Is there a way you can train me in sudoku? I will pay for two hours session!!!
Excuse my possible bluntness here (I'm still to understand the empty rectangle), but if, hypothetically, we were to put the 7 in the cell in column two row three then in box two we now have only one place to fit a 7 since we already had marked two locations with the Schneider notation earlier.
Of course we do see when looking at and following the 5 7-pair in row six that this wouldn't work anyway..
But I think my point is that I still don't understand the empty rectangle even with your way of looking at it. Or am I missing something? 😅 Again, I'm not being rude, I appreciate anyone trying to explain it better but I still don't understand it. :/
Next up
Improve at Sudoku: What To Do When You Suck
Easy: Stop sucking, say that you'll be back in a bit, start solving.
What NOT to do when you get stuck: what I did. I um got stuck and left it open for nearly 2 whole days. LOL Now the timer says over 40 hours. rip
Exit out. Start over = 00:00 ☺
I never pay attention to the timer anyhow, not the competitive type
I was stuck until he pointed out the empty rectangle. That was all I needed.
Same here! 😁
I'm late to the party and have just discovered UA-cam sudoku. Strangely soothing, and I think I've learned at least one new trick today.
"Empty rectangle" means a 2x2 area in a box can't contain that digit. (Note: in this puzzle, that 2x2 is split down the middle....that's okay.)
The result is a single row and a single column that covers all possibilities for that digit in the box.
ONE of those points to a known limitation (the 57 pair below).
Now, we can determine if ALL possibilities rule out (or guarantee) something else in the puzzle by ONLY checking two (row or column) instead of all 5 (each cell) possibilities.
How to find it:
Work from what you know: the 57 pairs.
Do they eliminate any 5's or 7's from the row? (Very basic and should be automatic as soon as you find the 57 pair.)
Do they make an x-wing? (That's the next thing I look for.) Scan around for other limited 5's or 7's. Do they line up? (Or partly line up....maybe a skyscraper?)
Y-wing? (Is there a 7 paired with, or a 5 paired with, something else?)
And, finally, empty rectangle...look perpendicular (up/down in this example) to the 57 pair to other boxes partly filled...enough to restrict it to 1 row & 1 column for either digit.
That's how I go about it.
And....I kinda suck at it. So, if you have a better idea, I'd be thrilled to hear it!
P.S. Ya, I'm aware of some more difficult stuff (like swordfish) but haven't even tried looking for them, yet.
Thanks. He didn’t really explain the rectangle with any clarity for those who are unfamilar with it.
What i dont understand is why the 7 cant go in one of those boxes. I see some because theres a 7 in another that crosses but on the right side, above the 8, there isnt any 7 that conflicts.
@@KattLover5412 he had already determined that 1 and 2 were limited to r2c1 and r2c3, so 7 had to be in either row 1 in box 1, or in r3c2. If it was in row 1, it was looking at all of row 1, and if it was in r3c2, it was looking at column 2.
6:20 is exactly where I got to in terms of filled numbers and pencil markings, then was stuck.
By watching your videos I now realize the importance of certain skills, such as knowing instantly when the contents of particular rows, columns or blocks differ largely from one another (i.e. disjoint sets). With practice these skills become automatic and very rapid, a fact that genuinely surprised me.
Definitely need to try and remember that empty rectangle trick. This is the first time I've really followed along with the puzzle myself, and after you showed that, I paused and finished the puzzle. It was marvellous watching the whole thing crumble after using just that one technique! Very satisfying.
The rectangle technique here is pretty amazing, as its using higher order logic, basically a first level recursion exclusion search. This puzzle is quite hard and being able to spot such a complexity so quickly is spectacular.
Like your contributor, I too have been completely stopped with no idea how to proceed and complete a puzzle. I think what might be very interesting is to use the contributors puzzle starting at the point he became stuck, then validating whether his progress was correct, then proceding to show how to move forward. Explain what to look for in order to move on, or in the event his progress was invalid, show how to recognize being at an unsolvable point due to an earlier error.
That's really really clear Greg thanks for sharing
Thank you, this was the exact next step I needed to improve my sudoku logic
Our 95 year old Mom was doing the Sudokus in the News paper, Wednesday through Sunday were insanely difficult, No problem for Her !
I have to say before i found your videos I’ve never done a sudoku puzzle. But now I’m addicted. Thank you. I love your videos.
Took me 31 minutes. Now let's see how he solves it, in half that time while stopping to explain every step lol.
@7:27 You solve a 2 in r5c9 and say "and that might be important... he says and then nothing happens as a result". What you missed is that it creates a bi-value cell of 39 where your cursor is pointing (r5c4), which creates a locked-pair in box 5. As a result, 1 is the only candidate for r5c5 in box 5, but in your actual solve you didn't get it until 6 minutes later (13:25).
Thanks
I had a slightly different approach at the empty rectangle portion. Spotting the possible positions of 7 in row 1 and in row 6 led to an X-wing with a fin leading to elimination of 7 in the third row of the first box. This led me to conclude 7s are exclusively in the first row of box 1, and in row 2 of box 3. The rest followed as per Simon's.
This video shows how much work Simon has made to make this channel succeed. I really really like this channel glad it made it.
Things like not changing the box 1s 1 and 2 corner marks to centre marks was weird though, but that’s only cause I’m used to what he uses now.
sudoku guy has a real good tutorial on these puzzles and goes at a pace you can follow ,
Ânytime i get stuck, i just find the next number.
Thank you so much for this advice! It made me win the world championship
Oh crap! Why didn't I think of that?!
I did it, getting help from you when I got stuck. Thank you! Without you I never would have figured out the next steps. I don't know any of the "tricks" but was still able to muddle along.
I solved the 7 without knowing about the empty rectangle logic. It was mostly: if thats a 7, thats a 7 and that's a 7 and that's a 7....but thats illogic because thats two 7s in the same row. I guess it's bifurcation
That's the only thing I can understand at that point; through trial and error, you'd end up with two 7s in column 5 if you put the 7 in R3C2.
Inversely, I see no conflicts with other 7s if you put a 7 in either R1C2 or R1C3.
But, I watched the empty rectangle explanation about ten times and I still have no idea what it means.
This is the level of strident confidence I exhibit in the moments leading up to my discovery that I've been working based on some error committed, possibly early in the going.
I copied out this puzzle onto paper and tried to solve it myself. I got very stuck after the 5,7 part and watching your rectangle logic helped me so that I was able to switch off the video and complete it myself! Thank you SO much for explaining that extremely interesting logic which I desperately needed after so much frustration and finally admitting that I needed your help!
It's quite beautiful watching you work. And enlightening.
First time I understood the use of the "empty rectangle" (even though this "rectangle" was divided into two parts instead of a single block). Nicely taught.
Love to hear the thought process verbalised it really helps most enjoyable thank you. I'm slowly getting better🇬🇧☺️
A lovely puzzle Simon.
Tky for not racing through it.
I learnt a lot today!
The "pointy 7" thing was mind blowing. I would have never got that :-/
Thank you Simon, really appreciate the slow progressive walk through. It highlights my analytical short comings!!!
I solved it differently. Again, your way is more elegant than mine.
Lost you at around 10:40 when you started talking about numbers having a _direction_ . I thought numbers were scalars. And I don't understand how you were able to eliminate 7 from the top right corner. I went back and watch several times but to no avail. Anyway, I do appreciate your efforts to improve our puzzle solving abilities.
The direction he is talking in this particular case is:
Horizontal - row 1 positions 1 and 3, if there is a 7 in one of those two positions it will eliminate the possibility of being a 7 on the position 9 of the same row.
Vertical - rows 1 and 3, position 2 on both, if there is a 7 in either of those two positions, that will unravel the 5/7 pair that he found on row 6. If he assumes that the 7 is vertical, on row 6 position 2 it will be a 5 and on row 6 position 9 will be a 7.
These are assumptions, not certainties.
But it can only be on of these two hypotheses, and that gives him certainty that there can not be a 7 on row 1 position 9, so there must be a seven on row 2 positions 8 or 9.
And from there he can eliminate some other pairs he annotated before.
Better way to phrase the logic he uses is that there CANNOT be 7 in R1C9 no matter where a 7 is placed in the first block. If R1C1/2/3 are 7 then R1C9 CANNOT BE 7. If R3C2 is 7 then R6C2 is 5. If R6C2 is 5 then R6C9 is 7. If R6C9 is 7 then R1C9 CANNOT BE 7. Whew!
CB GB why isn’t the 7 considered in R2C3? I am lost in this technique because of this single doubt?
TheNav360 That’s because of the 1,2 pair shared between R2 C1 and R2 C3. If he puts a 7 in R2 C3 then the regular Sudoku logic is broken because both a 1 and 2 can’t fit in the box
He's just meaning that every cell affects both its row (up and down)and column (left right). I don't understand the term "empty rectangle" as it applies to one block, but the whole exercise definitely formed a rectangle, with an empty cell in the same row above each matched pair. So both of the pairs could affect row 1.
2:05 cat meows, I get up and go feed my cats thinking it was them calling from downstairs
I tried this one before I started watching and got up to the 57 pair. I couldn't get past that point until he explained it. Initially, I couldn't understand what he was talking about until I tried it myself and walked through it. It finally hit me and I want then able to complete the sudoku...in the past, I would have given up on it.
Thank you, Simon! I came to this one just today, looking for more lessons in basic sudoku techniques. I didn't see the "empty rectangle" when I tried the puzzle, and it turns out that it's fairly key -- without it, I got stuck at a point where I couldn't place the 7 in box 2 (and lots of other places tied to it), and had to guess between two locations and find a contradiction. Now that I see the empty rectangle, I see that effectively what I was doing was working out the same logic by brute force!
This helped me a lot. Thanks Simon.
wow the t-shape technique was so helpful! i was really stuck with only using the snyder notation. thanks so much!
I've watched a few of your videos now and i'm extremely impressed by the logic you apply. I'm still trying to get/ understand some of the techniques you employ. It's mostly far too advanced for my brain i'm afraid.
There's one thing I do, which I don't see you doing quite as much, which is, once i've figured out where a number goes on the grid, I then try to "chase that number around" all over the grid. In other words, I assume that each number I put down is a clue to where that same number goes in another cell, row or column. I then use the Sneider (?) notation at as many places as I can before moving to the next one.
So at 2:52 I would have penciled in my 8s in column 1 in the bottom square, row 6 in the middle square, before moving to the 2s. I work on the assumption that whichever number is on the grid the most is the easiest to solve (yeah, i'm at basic sudoku techniques!)
Anyway, thanks for sharing. I hope to learn more as i continue to watch and observe.
I didn't quite get the empty rectangle logic, but it did get me to evaluate the possible 7's in box 1, and I was able to eliminate the 7 I had penciled into the bottom room as unworkable, and that broke the puzzle for me. I had the 57 pairs in the center row, but I hadn't eliminated the other possibilities, after penciling in all possibles.
Very clear and helpful solve.
I really dont understand the empty rectangle logic at all.. can you do a deep dive on that please?
Try it yourself. Try to put a five or a seven in one of the 57-pairs. Watch what happens to the top right square. No matter what you do, it cannot be a seven. Pause after he highligts the blue T-shape and try it. Remember to only fiddle with the 57 pairs.
@@pierrenilsson6189 I am confused because if you look at his empty rectangle he hasn't eliminated 7 as a candidate from the top right square (marked with a 1-2, It's column Column 3, Row 2). If you follow empty rectangle logic one way it gives everything one position. If you follow the logic the other way it leaves 4 options between Box 1 and Box 3.
I recreated the puzzle from that point and made an imgur album with 3 pictures(scroll down to see them).
The first is all 7 candidates remaining on the board in white, everything else blocked out in purple. Then the two options for 7s filled in. Both still seem viable, it doesn't seem like it was an empty rectangle.
imgur.com/a/F8er9JB
@@Jackleber I was confused at first as well. He didn't say it explicitly because maybe it was obvious to him, but on the two cells marked with 1 and 2 in the top left box there can not be any other number, otherwise there would be no room left for both 1 and 2 in that box. In particular there can be no 7.
@@Jackleber What you missed is that in the top left block, the 12 is a 12 pair. You cannot put a 7 in the 2nd row of the top left block (because those squares can only have a 1 or a 2), only the top row, hence eliminating the 7 from the top row of the top right square.
@@pierrenilsson6189 Thank you. I couldn't understand what he was saying until you pointed out a 7 could never be at the topmost rightmost square either way, therefore enabling the puzzle solver to use Snyder notation.
it's so cool when i learn a new sudoku trick and i see the puzzle click into place! this channel is awesome
I FINALLY understand empty rectangle. Thank you!
Tried the puzzle myself and was really happy to try the key technique for solving this one. Will remember to try for the empty rectangle whenever I get stuck again
10:44 the final piece I needed to crack it! It's been a long time since I did sudoku.
I always struggled on hard sudokus. After watching this video this morning I finally solved the hard daily sudoku! Thanks for the video and making it easy to follow
the empty rectangle was new to me. thank you!
So pissed that I missed that 57 double in row 6..
would you please explain how to find it. thanks
@@lxramirez9788 It's explained in the video
The way we're learning... Is just *chef kisses*
Well I finally understand what an empty rectangle is and how to use it. Thank you!
I was able to find the 57 on row 6, but I didn't know about that empty box with a T shape, so I went without it and it took me almost 1h33min to solve it... and you did it in less than 17min... that's the power of an advanced technique. Thank you for sharing that.
Another on my tour of older videos on the channel. As I watched this, I was struck by a few things. One is how far the technical production values have come and the heightened affect (and probably comfortableness - is that a word?) of Simon (in this video) and Mark (in other videos from this era) on the channel have come since August 11, 2019. That's very nice. Second is the great difference there is between an "ordinary" classic sudoku from that era, probably machine-generated, and a hand-crafted puzzle, even a classic. Third, I decided I'd skim through the comments ... and quickly gave that up - there are hundreds of comments, and nearly a million views (surely some are more recent than when the video was first released, I would imagine). Current videos get scores of comments and scores of thousands of views. Fourth, the comments that I did get around to are so appreciative and say things like, "I learn so much, I am beginning to spot things like empty rectangles, etc." - i.e., mentioning what are now, by today's video standards, much more basic or fundamental patterns. My conclusion from all of this is that SUDOKU itself has come so very far in the past nearly 3 years, and I credit the visionary work of CTC in featuring and encouraging hand-crafted puzzles, teaching techniques for solving puzzles in such a lovely and helpful way, and consistently putting the novice solver or new-to-the-channel solver at the forefront of the type of information that is featured. (And I have learned something from this video, as well, about the empty rectangle pattern.) I am so enjoying my exploration of the earlier days of CTC - thanks to Simon and Mark for the riches to be discovered!
Thank you. Very helpful.
wow i was stuck and that empty rectangle instantly helped me crack the puzzle!
Took me 39 minutes to solve it, because I was not familiar with the empty rectangle logic. Finally argued my way into the same logic after about 30 minutes and got it, but I'm glad to see that that was precisely what Simon did to solve this as well! I was pretty sure I had missed something far more elementary, so I'm happy to see I hadn't! :D
great! i usually mark all positions but this helps me find smarter ways to do it using the logic of the outcome!
this helped me a lot, thank you!
Wow, that "empty rectangle" just opened the whole puzzle; incredible.
I'm new on this channel, I dont know these techniques. It took me 1 hour and 35 minutes to finish it without this method. I am gonna look for more videos to learn more! Thanks!!
8:51 here you explain about the rectangle shape. I could follow everything up to that point. So now I have to figure out how to recognize the rectangle shape method. Because it didnt made sense how the 7 could point in two directions, either down or to the side.
Me too
In that example, if the 7 ”points” to the side, then the 7 can’t go in any other boxes in row 1. So the 7 has to go in the middle two boxes of that 3x3 square. If the 7 “points” down, then there are no other 7’s in column 2. That means that the 57 pair in row 6 column 2 is 5, making the number on the far right highlighted in pink a 7. So the only number in the top right 3x3 square that can be a 7 is the very middle. So in both examples, that empty box in row 1, column 9 can’t be a 7. So the 7 is either in row 2 column 8 or 9. That’s why he puts the pencil marks in those two boxes.
Thank you Mark!! My wife and I bought the Sven's Sudoku pad App, and got stuck on some of the default puzzles!
After 11:38 I solved the puzzle solo and actually got to complete it, I am very impressed! Thanks for your help.
i used to play ny times sudoku on the way to school on the subway, trying to beat it before i got to school but i guess this puzzle would've made me miss my stop haha. that box logic was genius. i guess i still learn something new everyday. glad i found your channel thru the chinese coin puzzle which was also genius and fun. definitely subbed for more puzzles and techniques
i understand the empty rectangle logic but spotting it THAT fast is crazy. simon is a beast fr
Thank you for the illuminating video. I particularly liked the explanation of the 7 in the 3 x 3 square top left corner pointing either across in a particular row or pointing down in a particular column and this forcing a 7 in one of two positions for the 3 x 3 square top right position. We see that the vertical column pointed to by the 7 when the 7 points vertically intersects a row containing a 5/7 pair at one of the paired positions forcing a 7 at the paired opposite position in the 5/7 paired row and the vertical column from this paired opposite position (being column 9 in this case) eliminates a 7 at the top row of the 3 x 3 top right square. Also a 7 pointing horizontally in the original 3 x3 square top left also eliminates the top right 3 x3 square containing a 7 in the top row. We get that the original horizontal row pointed to by the 7 (when the 7 points horizontally) intersecting the vertical column pointed to by the paired opposite cannot contain a 7. It is quite an ingenious argument and I amended the argument to help me understand it better.
Brilliant thank you!
8:41 this is really mind blowing to me ... Thanks sir, i learn something new today.
Just seen this one. Very pleased to have been able to solve it without using any markings.
I got stuck on the puzzle up to the rectangle method for the 7 in the top-right 3x3 grid. Once that was explained, I was able to complete the rest very easily. Thanks for teaching the method.
very useful insight into your process
That was really helpful! I felt I would get "stuck" trying only to use Snyder notation, however moving beyong that and using cell logic will help a lot! Thanks!
Thanks
This was really helpful!
Took me 1h 17m to complete, never played sudoku before, thx youtube for this recomendation and thx Simon and Mark for making this channel
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.
Wow - it is amazing how fast your mind works. I can’t keep up!
Today, I watched this video for the second time and then started the NYT hard sudoku and there that triple was. It only about 50 minutes to finish the puzzle whereas it usually takes a little over a hour. Before I started watching your videos, it would ha d taken a couple of hours if I just didnt give up. I'd like to thank the two of you for all your videos.
Empty rectangle technique was really helpful
Never heard of an empty rectangle before but luckily I tested the 57 pair in a chain and eliminated the 7s from the top3 rows, same end result
I had two 7s in Block 4 and I did the "What If each was 7" game and determined that either way the 7 was placed in the lower corner in Block 2. That finished off the 6s and I was off and running. Took me an hour and 4 minutes, however. Mark's Empty Rectangle method is much faster, but I have to learn to see it.
This T-logic in the first rectangle is your knowledge of how Sudoku is constructed. I couldn't get it from your explanation. I had to go through a "simulation" until I was forced to rule out the 7 being where the 3 is. Anyway, thanks for the link so that I could do the Sudoku!
The 1 can be placed immediately in the lower left corner of the indicated box because of the top middle and bottom right boxes.
When you get stuck, it just means you missed an empty rectangle.
This is frustrating for me because I taught myself how to solve Sudokus and I developed my own notation, but it isn't as sophisticated as what the experts use and it does not make it easy to spot empty rectangles. I also prefer pencil and paper but that obviously makes things harder.
I just did this in your software in 37 minutes and I feel good about that :)
Great puzzle solving skills but you don’t have to say I think all the time you’re so good you can say I know in almost every situation. Keep it going though and love watching you solve puzzles
Every expert sudoko has its own mind blowing logic
Aaaahh..The empty rectangle got it going...Still took me another 10 Minutes or so, but eventually it blew wide open. Thank you for sharing this.
It took me 34:28 and I had to peak at your video twice: first for the 57 in row 6, then for the results of that with the empty rectangle. I would never have found that... I understand the technic, but I'm not quite sure I can reproduce it later. Very educating
Took me absolutely ages - spent 1:23:39 on this one. Great puzzle
this is a brilliant puzzle
Awesome!
When I tried this puzzle, I got to 6:56 and immediately tried an inference the two 7's R5C3 and R6C2 -- because they are not parallel. If there is a 7 at R5C3, then there is a 7 at R6C9. It is very similar logic to the empty rectangle, but you start with numbers that are "off kilter". I find it easier to spot than the empty rectangles.
The empty rectangle logic was absolutely awesome
I love the thumbnail. No spoilers :+)