The Most Under-Used Sudoku Technique
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Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships. 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
It's funny... I can follow every step you take. I understand the logic. But I'm pretty sure I couldn't find an empty rectangle in the wild to save my life.
What I find is that there is definitely a difference between understanding a technique and internalising it. There is a time gap between the two. I guess the brain needs time to sort out the wiring.
Same here, I have huge trouble doing the empty rectangle spotting. I understood it but I could never have found it if I tried
@@hamzahussain7794 checkout the nonogram or picross puzzle. You will love it
@@deenszxking6818 yeah i love those! I like to do them also! I play hungry cat picross from time to time on my android
@@grenvillephillips6998 so true! i've watched this 3 times and it finally just sunk in. now to actually spot one in the wild.
I'm so ashamed to say that when I clicked on this video and saw that it was a classic sudoku I figured I would give it a go. It then took me over two and a half hours to solve. Watching you breeze through it without any difficulty at any point makes me at once frustrated and in awe. Great job!
Took me 30min filling it all up with pencil marks and my logic... had to come back to the video, then the first 56 logic (which I still don't get it quite well) was enough to crack it, didn't even need the whole "empty rectangle" technique later on. Ended on 40min, but wow, I would've been stuck forever if I didn't check the video, couldn't figure out how to resolve it.
It looks like he jobbed all over your weaker performance
@@sorayaimperial basically the 5 and 6 in column 2 need to go somewhere. They cannot be in box 7 due to the 5 and 6 there. They also cannot go into row 1 of column 2 because of the 5 and 6 in that row. That leaves only 2 squares that a 5 or 6 could go into in that column.
One great technique to use is towards the end of the puzzle and there appears to be no choice. Look for this: All the boxes will have only two choices EXCEPT for one-it will have three choices. One of those choices will appear three times within the box, the column and the row it is part of. That will be the number to select. After that, it all works out in seconds.
@@obcmissions it is called BUG technique.
The lessons on locked pairs and empty rectangle at 5:32 and 14:10 are extremely helpful
Indeed! It's a joy to watch videos like this!
He's driving me crazy when he ignores one empty cell in a square to go off looking for different numbers.
me too could have solved it 10 seconds faster
And shouting doesn't help either.
Yep - UNsubscibe.
I was screaming about the 2-9 pair in the middle block for thirteen minutes before he filled it in 😂
Me too!
I like to think im good at sudokus, but when i hear him discuss how he figured out how there was no six at around 6:50 , that really shows how much more there is to learn!
1: Find a pair of cells (like the 56 pair) in the same row or column, but in different boxes. 2: find a box that has only one row and column left to fill in, where either the row or the column "points" at one of the paired cells. In his example, box 6 points at the 56 in box 4 3: Now see if there is an empty cell that completes a rectangle between the two paired cells, and the intersection of the box you found. In this example, that's R3C8 4: Pretend that one of the paired numbers (in this case the 6) is in the empty cell you found in step 3. 5: "Complete" or "unwind" the numbers... so, put a 5 in R3C2, and a 6 in R5C2. You'll see that because of the two 6's you entered in the grid, you can no longer put a 6 anywhere in Box 6 6: The same is true if you try to put a 5 in (ignoring the existing 5 in Box 3). Try to get in the habit of doing this every time you discover a pair, and soon you'll spot these in the wild.
@@buzzly108 But why he can ignore the opportunity of the 6 not being in a row or column, but diagonally over the 3x3block with the empty rectangle, is what i don't understand.
@@bertbergers9171 I still don't follow the explanation Simon gave in the video, but Michael's explanation makes more sense to me. Read through it again. The goal is to eliminate 6 as a candidate from r3c8. We can do this by considering what would happen if it were a 6. That would force a 6 in r5c2 via the 56 pair. But then every empty cell in box #6 would see a 6, either via r5c2 or r3c8, leaving nowhere to place a 6 in that box. So r3c8 cannot contain a 6. That's all we can conclude at the moment.
@@bertbergers9171 of course, the overall goal is to spot the pattern by noticing how the 56 pair interacts with the empty cells in box 6, forcing an elimination in r3c8. Wouldn't be very useful if you had to test every possible cell for that elimination logic.
Daniel Hawkins thank you
I had the whole grid filled out with candidates, but without the empty rectangle insight there was no way to unwind the pair/triple/quad cycles. Spent far too long staring before I watched you crack it!
I took a look at a solver, cause I was also not seeing the empty rectangle. Needs X cycles or BUG or XY chain to find it. Things I have even less of a change of noticing.
Exactly the situation I found myself in as well. I believe I understand the logic now ... thx so much for the clear and detailed explanation for the more intermediate solvers like myself!
There was actually. I needed his help for the 56 pairs but solved it from there without either empty rectangle logic or chaining. There was another set of pairs like the 56 somewhere that helped me.
Yep seems like you either have to use the Empty Rectangle or more complicated cycles, chains, etc. Definitely not something you can solve using pairs, simple deduction.
I didn't actually use empty rectangle but I came to a simple forcing chain with 2s, 9s and 1s. [3,4],[3,5],[4,6] were 2-or-9 cells and [3,1],[5,1] were 1-or-9 so if [3,5] was 2, [3,4],[4,6] would be both 9 and [3,1],[5,1] would be both 1 then while being in the same row.
9:44 thought my laptop crashed.
The first example of the anti rectangle didn’t make sense to me. Then the second did make sense. I went back to the first example and now I understand. Thank you!
So, until given a puzzle book 6 weeks ago, i tried Sodoku twice. After watching 5 of these videos today, i realized you cannot do this game without pencil marks; which is how i solve many other puzzles. I tried them in pen over the last 2 weeks, and now i have 4 inked, indecipherable, works of art. Thank you for this channel. It's my new favorite. Cheers
I have been there bud! so much ink haha
The 7 in the bottom right corner could have been found much earlier and would've had other implications for the grid.
I was looking for this comment, when he put the 3 in that square, with the other vertical 7s it made it the top right of that square
Drove me crazy
The whole puzzle could have been solved very easily after that.
Seven!!!
True
4:18 all I was missing to complete the solve. Really wish I had seen that earlier. Thank you!
Empty rectangle! Never knew there was a name for this. I always thought of this as trying out all possibilities and checking if they all lead to the same elimination. Literally the very last trick I ever use as I had no method to spot them. Love the column/row trick! Subscribed
If you think about it, all techniques are essentially forcing a chain in the end, but when a forced chain has a noticeable pattern we give it a name.
He thought that he'd solved all of the 6s at 13:25, but he didn't recognize his oversight until 16:16. Thanks for illustrating the rectangle technique.
Always a pleasure watching your Sudoku solves Simon, I didn't know about empty rectangles so thank you for the explanation.
I paused it at the beginning to try it, messed it up twice, watched until you described the empty rectangle, and that finished it for me. I used it to resolve the exact same two unknowns that you did. Very cool!
The empty rectangle has come up as a hint so many times in the app I use, and I've never understood it. Thank-you for clearing it up for me.
Which app?
@@eggplanthose Sudoku by Brainium on Android. I also found a great Killer Sudoku app, but that one I think has been removed from the Play store.
You are so fast and accurate, impressive! These are the best sudoku videos around. One remark though on the way you explain the empty rectangle: you talk about it as if there can be more 6's in the same 3×3 block, which I found confusing at first. Why not just use the singular, 'The 6 is either in this row, or in that column, (or both), ...' ?
For the first time, I tried this puzzle before watching the video. I think that the "empty rectangle" made the difference between me getting thoroughly stumped and having to guess at a point, and solving it properly. After my first guess led to duplicates after going throughout the grid, I *tried* to find out how two colors could be put in the same box. That would have helped, I think.
The "empty rectangle" method is fantastic! I've seen you use it in other sudoku puzzles and I've been able to use it, though I find it hard to see when the opportunity arises . I never write small numbers in because I prefer to remember what numbers pair up in which boxes, and if I think the puzzle is taking to long a time then I imagine one of the pairs as resolved and then think about how to resolve all the other pairs based on the imagined resolve... it's a great mental exercise. Thank you so much for teaching the 'empty triangle' technique.
Thanks you,,, finally I understand the logic of the Empty Rectangle, And I did spot the 2nd one :) :) (after you pointed out there is one) Making some progress :)
5:00-6:25 When he mentions the empty rectangle, by deducing that 6 is not possible on the cell he marked '2' in the corner, if you fill in some of the more obvious numbers, you can quickly deduce the number in that cell is actually 8. Using that 8, you can then solve the upper square to be 2, then most of the 3x3 square in the top right hand corner can be solved. Great piece of logic there
I'm glad you did that too. I also got there without knowing the trick and wondered if it had just been a fluke. I would have been stuck on the second one though.
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.
Amazing to see how much more comfortable and polished your videos have gotten over the past year or so. This is fine but definitely not as easy to watch as the newer stuff.
Came here from your "The Witness"-series and this was my first finished sudoku and first sudoku video... it took me 3 solid hours making an effort not to guess anything, very eye opening to see an efficient method afterwards.
I did the sudoku first, then when I couldn't continue, I went back to the video and you helped me with the 5/6 pair. I went on with the sudoku, when I needed help again I continued the video and you taught me the empty rectangle trick with the 5/6 pair. I continued, nearly solved the whole thing, had a bunch of 1/2/9 situations that I could not fill in. I remembered the empty rectangle with the horizontal and vertical perspectives, identified a field that in any case could only be a 1, solved the puzzle! Thank you!
15:22 was what I needed to solve this. Thank you!
The ones where you demystify some logic i was struggling with seeing are my favorites.
44:22. Made a leap of faith based on rules I learnt off here - I wasn't quite sure if I was doing the right thing, but it worked! Perhaps it does go in when I drift off to sleep! Keep it up!
"Today might be kind of a long video." Hearing this comment during a 17-minute video, just a couple of days after watching the 1 hour 40 minute video, is very funny. It's amazing to me how far sudoku, and this channel, and - I imagine - a whole lot of viewers like me have come in the past year and a half. One tiny silver lining to the pandemic cloud.
wow, I FINALLY understand how the empty rectangle works! could never wrap my head around it until this video
Another quick and easy one from last year. I did this one in only 22 minutes, so only 5 minutes more than your solve (but I wasn't explaining anything either). Thanks for the videos! Also I like your explanation of the empty rectangle a lot better than some of the descriptions online. Even though your explanation didn't define why it is called an empty rectangle (the number you are looking at can't be in the other four (or more) cells in the box, those being the empty rectangle as I understand it) your description does identify the more salient point that the row and column lines formed next to the empty rectangle combined with an interlocking pair does let you eliminate the digit from the square seen by the other cell on the pair in the matching column (or row if the pair is in a row). See, even I have trouble explaining it, but at least I do understand it well, now.
`I spotted the empty rectangle for 5s and 6s but proceeded with the 5s....your explanation that the 5 in R9C1 and so we must go for the 6s is the eye opener!!! I dint go for the empty rectangle and got lot more numbers in various squares but there were so many 6s in the unfinished puzzle, that I went for the solution done by you!! Good show
5:00 - Empty Rectangle Pattern
The only time I saw him actually explain a "technique".
Istill dont get it
@@LisaLaMagna me either. I don't understand why the 6 can only go vertical or horizontal.
@@Homerenoideas Because you can only place the 6 in the tetris-like pattern in that 3x3 box. In the beginning it's still unknown where to place the 6 but it has to be either in the lower three boxes in row 5 (horizontal) or in the two boxes in column 8 (Vertical). (Row 5 column 8 would be both, horizontal and vertical) No matter where you place the 6 in the box it can never be in row 3 column 8 for the following reasons: If the 6 is in the three boxes in row 6 it has to be in row 3 column 2 because of the 56 pair in column 2 and then the 6 couldn't be placed in row 3 column 8. The same applies of course if the 6 was placed in one of the two boxes in column 8.
@@madamid100 I see how this always precludes putting the six in column 8 row 3. I don't see why we then argue that the six "must be either vertical or horizontal" in the right side middle box. Why would it be illogical to place placeholders for 6 in all four empty squares in that tetris configuration (in the puzzle state at about 6:00 where he hasn't marked placeholders for 5 or 6 in that box, yet)?
Just getting into your videos - never heard of empty rectangle before this one. Wicked.
I started solving it myself then got stuck ! then I watched you use the magic technique ! wow
Lol, so I was just stuck on a puzzle for several hours. After not making any progress for an hour, I give up and decide to watch some cracking the cryptic to get some inspiration. This is the first video I watch, and I realize I might have an empty rectangle that I missed. Go back to my puzzle, find an empty rectangle in a couple minutes. Three minutes later the entire puzzle is solved! Thanks!
Thank you for the tip! I’ve been stuck on a few hard sudokus for a week, hope this helps
42 MIn on my second go but I did not use the empty rectangle technique. it's always a pleasure to see you cracking! hope to see you again!
So this is what Sean Lock does in between episodes of 8 out of 10 cats
I was always so confused about how to spot empty rectangles, but knowing they follow similar patterns as x-wings has really helped!
No clue about that empty rectangle when solving it by myself...took me several X-Wings and Skyscrapers (also made progress there due to your videos) to finally crack it after endless time by excluding several numbers...such a complicated pathway compared to the shown solution...Big thanks for showing that route!
yea i think all his empty rectangles could be spotted with skyscrapers and kites in this puzzle, not 100% sure though.
The amount of progress in this channel has been phenomenal.
I had no idea other people used this technique! I have been playing sudoku for 4 years now and have only known this method and taught myself everything I know. My record time on easy is 1:09 and 8:47 for Expert. As I finally look at stuff online I realize I know pretty much everything and love watching this youtuber now to see the crazy puzzles he gets to do- ill pause it and try to beat his time! I beat him for this puzzle and most because he stops to explain things as I go on.
Empty rectangle really screwed me up till late in the game. So well done for spotting it so early.
I sort of learned a new trick, the empty rectangle... but I doubt if I can recognize when to use it and when it can't work. But I imagine it's something I'll be able to learn now that I've seen it. I guess I'll have to keep watching! great show, thanks
Great explanation of the empty rectangle. I think I've got it now. Thanks.
I'll need to remember the empty rectangles technique, thank you for showing this!
Around 4:39 I think the correct move should be focusing on column 2 and realizing that 3 has to be in r9c2, and this will certainly avoid using the rectangle technique for box 6, which could be a bit unclear
Very neat at before the 4:50 mark seeing that quickly on the boxes to the far left that the center column had 2 squares in need of a 5 and 6. He'd be a good chess player at tracking loose and hanging pieces.
I tried it on my own took twice as long as you, but i found the key was triplets - there were so many and cracked the puzzle for me!
Good! The empty rectangles trick was new to me, and even after 2 hours I couldn't spot any other way to solve this one. Wonder how often it's the key move.
quite often with harder puzzles...as harder puzzles you often find pairs along a row or column but in different boxes.
He is much better at explaining for the masses! I just do it all in my head, without leaving the little numbers behind, which are so important for teaching people how to improve their skills.
I prefer when you click on a cell and it highlights the corresponding column/row/block. Makes it easier to see.
Thanks, always learning. Just a note that the check button says it doesn’t look right even when all is correct. This was the 1st time I’d tried it out. Thanks again.
7 in the bottom right corner . I saw it earlier . I think that would make the puzzle easier further
This video did the trick. I tried the puzzle before watching, and I got stuck. I saw your description of the empty rectangle and I paused the video and was able to finish the puzzle by spotting the second empty rectangle on my own. So, I picked up a skill. I really think the second empty rectangle technique was necessary.
Awesome technique! Thanks for showing it
The way you make us understand is great. Thankyou sir
I'm pretty sure this will revolutionise my Sudoku game. Thank you!
Thanks, I think this tactic will help me in future solving!
By George I've got it! No more 'what if' guesswork? Well perhaps....... Cheers, Stewart
15:20 that literally solved it for me, i was stuck for so long and couldn't figure out why. but the simple fact that the center square isnt a 9 just made everything domino effect into place for me. those empty rectangles are so powerful wow
exactly same thing happened with me lol
That's a new one for me. I think I understand it. I'll put it in the tool box and give it a go. Thanks for the tip.
I finished in 46'18" , guessing the 6 on the way. Thanks for letting us try the puzzles out as it lets us backtrack without rubbing out a pencil mark.
This randomly showed up in my youtube recommendations, so a bit of a necro. The most advanced techniques needed to solve the puzzle are a Sashimi X-Wing and a BUG+1 (or short chain) Singles: r6c6=5, r6c4=6, r6c2=8, r6c3=4, r6c9=1, r3c7=4, r7c1=4, r9c5=4, r1c4=4 c2 has a naked pair, 7 & 9, in r1c2 & r7c2. r3c279, r5c279, & r9c279 Singles: r9c2=3, r8c9=3, r5c8=3, r9c8=1, r2c7=1, r1c8=2 r23c6 form locked candidates for digit 2. r23c452 r1c23 form locked candidates for digit 7. r3c137 Singles: r9c6=7, r3c4=7, r7c9=7, r1c2=7, r7c2=9, r9c7=9 X-wing for digit 1, r3c1, r3c6, r8c1, r8c6. r38c351 Singles: r3c3=3, r2c4=3 r23c5 are locked candidates for digit 5. r78c55 r2c1, r2c9, r4c1, r4c8 together form a Sashimi X-wing for digit 6. r3c86 Singles: r3c8=8, r2c5=8, r5c9=8, r3c5=5, r2c3=5, r5c2=5, r3c8=5, r3c2=6, r5c7=6, r7c8=6, r2c9=6, r4c1=6, r8c5=6, r3c9=9 r23c1 form locked candidates on digit 2. r1c52 There's an obvious BUG+1. But I like chains, so r5c5=9 => r4c49 & r1c59 => r1c3=9 & r4c3=9, which is a contradiction, so r5c59, r1c39, & r4c39. Singles: r1c3=1, r3c6=1, r7c5=1, r1c8=1, r3c1=2, r2c6=2, r4c3=2, r5c5=2, r6c6=2, r7c7=5, r8c4=5, r5c1=7, r8c3=7, r7c3=8, r8c7=8, r1c5=9, r2c1=9, r4c4=9, r5c3=9, r8c6=9
Well done. This was an awesome video
This puzzle took a little under 2 hours!! For me, I had to look where things couldn't be by a little guess and check. Going to watch video now and see if there was an easier strategy!! Thanks!
The way I internalized empty rectangles is when I have a pair and a 3x3 with only a row and a column, together they point at a location. If a number from the pair is in that location, it messes up where it can go in the 3x3 (Its similar to proof by contradiction: If its here, then it leads to a problem, so it cant be there)
59:05, while listening to a podcast. did plenty of staring blankly at it waiting for my brain to notice any kind of pattern. embarrassingly resorted to entering all the possibilities for every cell, and it was only then that i noticed a triad in column 3 that ultimately unwound the rest of it for me.
14:05 X-wing on 1's in R1C3 & R1C5 & R7C3 & R7C5 eliminates 1's in R8C3 and R8C5.
Thanks for the technique. I'd like to comment that although this video is about the "empty rectangles" technique, you've missed several immediate numbers, ('4' in the middle-left block at the beginning, then '7' in the bottom-right one, and I think there was also a '3' somewhere... and then you ignored a single empty cell in a block), which would have made the solution faster and easier.
I didn't know about this trick. Thank you.
To me, a novice, it appears that initial “empty rectangle” of his with the 6 unlocked most everything... and that the puzzle was meant to be much, much more difficult if you didn’t know the technique. Gosh I adore this channel.
Thanks for the lesson :)
I got to a point on this grid where all the empty squares each had 2 possibilities and I couldn't see where I could crack through it. I tried a trick where I used the colors to represent the numbers to make a guess on one of my squares and followed that until I got to the end, or got a conflict. I got lucky as that first guess didn't conflict anywhere. So just replaced the colors with the corresponding numbers, and the check button called it good. Using the colors allows me to keep my marks in the grid so I don't lose track of what point I would need to use the back button up to.
Empty rectangle. I think that's all I'm missing in my life. Thank you!
Oh I was already doing this! I didn't know how to fully explain it wasnt until recently that it stopped physically hurting to keep all the numbers in my head to accomplish it properly. Even with notation it's a lot to keep track of to make eliminations.
Thank you. I learned something today :D
Nice teaching moment, keep it up. I might be able to get through one of these without your help.
I was stuck on puzzle #23 in your app. Even with hint #2 about this technique for the 7s and 9s, I just couldn't wrap my head around this. This video is very helpful - I wanted to understand it before using the hint and continuing.
this is the first ctc puzzle I solved in under an hour! Though I didn't encounter any ER while doing so, interestingly enough.
Hi Simon thanks a lot I learn so many technique from you . Now I can solve many hard sudoku problem. Btw i am from the Philippines.
I was waiting for you to put the 7 in the bottom right box at 8:55. I think that would’ve unlocked things much earlier, especially in column 2
Empty rectanges are a beautiful technique. I hope I am able to spot one in on my own sometime.
I was banging my head saying 7 in the bottom right after he filled the one under it for like 4 mins I think but the technique you showed off I never new about so that was helpful
After listening to your empty-box analysis I wondered why the 6s couldn't be on a diagonal from one another rather than just vertical or horizontal. This is similar to the 29 diagonal pair in the middle box.
“This it’s gonna be a long video” four years later we have over two-hour videos and these ones look like a breeze Kudos CTC!
is there a good ie quick way of spotting hidden triples, when other numbers are also present in those cells? Often takes me ages to see them?
I learned something, thank you! Was able to put it into practice for once. haha
Love the trill in Mozart’s Sonata in C major! (Love your videos too...)
So THAT'S what it's called!! Thanks!
As a beginner I appreciate this video. I have not seen another video describing it.
How do I import a puzzle in to your app that I purchased? (Nit puzzle specific but didn’t know where else to ask). Thanks!
at 4:19 ... couldn't you mark at that point when you put the 5-6 par in r5c2, you could put in the same 56 pair using logic into r4c8. So that square couldn't be anything else.
How can I obtain the grid generator tool you utilize to solve other sudoku puzzles
Every time I got stuck on this one it was an obvious pencil mark I was overlooking for a naked single or the second empty square. I learned the empty square working through this video. Maybe now I can get through the first puzzle on Sven's Sudoku Pad... I've only been going at it for 2-3 days lol
6:05 Please, can anyone explain why 6 can only be in a vertical or horizontal arrangement in this block? Thanks
Thanks for explaining how to work it out.Where do I get a blank Sudoku so I can copy given numbers into the array and solve it using your controls.Many Thanks
I didn't understand the empty rectangle thing at first but an easy way to get it is to put the 6 in the square where it's not supposed to be. that will resolve the 56 pair and then there will be nowhere to put a 6 in that box with 3 empty squares. this would actually work even if there was an empty cross in that box, because the two 6s would still see all the squares
G'day, I watch you do these so easily. You seem to ignore sets (row, column or box) that only need one digit put into them. Then go looking for more complicated solutions. Even sets that only need 2 numbers seem to be ignored. I look for a set with the fewest options and work up from them.
Your verbal shorthand differs from my own so I struggled to follow your game solution on the webpage indicated. What you call "the empty rectangle" is something I resort to only when I'm stuck and need to resort to next-level compound logic to move forward. Perhaps I need to do harder puzzles more often for practice. None of the game pages where I normally play allow for distinct Center and Corner pencil notation so it's not been part of my repertoire. Thanks.