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.
@@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.
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.
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.
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 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.
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!
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
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!
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.
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!
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.
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.
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.
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!
@@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)?
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.
"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.
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.
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!
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!
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.
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.
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.
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), ...' ?
`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
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.
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.
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.
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.
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!
These videos are reassuring to me in one way because they show me I solve puzzles just like an expert. The difference is what takes him 15 minutes takes me FOUR HOURS.
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.
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
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.
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
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.
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
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 :)
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
Regarding the empty rectangle discussed at 5:33, I do not understand why the 6s must be horizontal or vertical, at this point why couldn't they be diagonal, say for example a possible 6 in either r4c8 or r5c9? What rules that out? While I know some advanced techniques I am admittedly unfamiliar with the empty rectangle trick so I'm probably missing some logic here. Could someone help me out and explain the logic, or give a link to a good explanation?
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 do not get why at around the 4:19 mark you say both the 5 and the 6 both have to go in the 2nd column because the 5 can go in the 3rd column and the 6 can go in the 1st column.
at time 8:00, you decide to put 3 on grid 7 bottom row (between 5 and 6). I thought 3 could also be placed next to 2. Why did you choose to place it between 5 and 6 and not next to 2. Can you explain the logic please. This would have changed the way 3 is placed in grid 9. It could have been next to 4 or first one on the last row (3 blank 2).
I struggled with this at first also. But the answer must be: If he put a 3 in R8 C3 he later could not have put a 3 in R 2 or R3 in C.1. He must have seen that but did not explain it.
0:51 I love how Simon refers to 17 minutes and change as a long video when people nowadays complain that the puzzle is too easy if the video is that short! How times have changed...
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.
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
That's a really interesting technique. I'd got to a point where it looked as though there could be two solutions (I know that's impossible), only this technique sorted it out. Thanks for that.
How do you spot the 5&6 at 4:00? I understand the logic, but how do you spot it in the first place? Any pattern or formula to check so that I can spot this kind of logic every time?
I can't speak to exactly how to see those patterns, but I think the speed at which these two find them blows us away, but I personally will see the numbers in a box and then just follow each of the lines and it's offshoots for ones with the same numbers in. It takes me longer than them, but it gets me there. Hope that helps.
Read through the comments -- a reply to a comment -- and there's one (by a Matthew or Michael? sorry!) who lists the steps to use this rectangle technique to eliminate a possibility, how to find it. HTH
At 15:22 how did you decide that it is a definite 2 and not a 9 as at that stage it could be either a 2 or a 9 since the left side grid remained unfilled ?
Hey, someone who has just learned the technique here. I'll try to help you. The thing is that the 2-9 in the center is directly related to the 1-9s at the top. If that center was a 9, that would mean that the one above must be 1 and the one to its left another 9. Both those 9s would block any possible 9 in the 4th square, so it is not a possible solution. He doesn't exactly word it that way but that's the idea. let me know if it helped you. I think I'm getting the hang of it.
At 6.03 why can the 6s be neither horizontal or vertical but a mixture of both as in row 4 square 8 and row 5 square 7?How can you know they are either horizontal or vertical ?
The column required a 3, 7 and 9. The two three's removed the other possibilities for the three to go; therefore it goes in the only legal position. Rewatch 7:50
I struggled with this at first also. But the answer must be: If he put a 3 in R8 C3 he later could not have put a 3 in R 2 or R3 in C.1. He must have seen that but did not explain it.
Trying to do this on my own, I got stuck specifically because I didn't know the empty rectangle for the 6; as soon as it was mentioned, I pressed pause and could finish the puzzle, using the 9 one later on. In other words, this specific puzzle was an excellent lesson on that technique, and would have been very difficult without it.
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.
At around 7:15 seconds, I don’t understand the logic of why the 6 must be either vertical or horizontal. Does it relate to the shape of the empty cells.
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.
@@hwelvaar yes Ian, along that column since the 56 pair eliminated those spots for a 3 to occupy if you looked at rest of that column there already were 3s from other boxes controlling where the 3 could go in that specific column...down to 1 possibility so Simon then filled in the 3. There has to be a 3 somewhere on that column. There only was that 1 spot left.
The technique I learned from this was a number in two columns "squeezed" the number in the bottom row, which I never thought about before, hopefully will use it later on.
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.
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.
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!
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
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
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.
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!
Empty rectangle means a T-shape of four cells empty, or a square of four cells empty, or L-shapes empty wirhin a single block. (Not anti.)
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!
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.
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!
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.
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!
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.
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.
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.
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.
4:18 all I was missing to complete the solve. Really wish I had seen that earlier. Thank you!
That was a wizard level spot
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!
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)?
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.
wow, I FINALLY understand how the empty rectangle works! could never wrap my head around it until this video
"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.
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
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.
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!
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.
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.
9:44 thought my laptop crashed.
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.
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.
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), ...' ?
Always a pleasure watching your Sudoku solves Simon, I didn't know about empty rectangles so thank you for the explanation.
`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
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!
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.
That was hard. Took nearly an hour. Wow. Love it. Now to watch your video. Really like the grid you let us use. Thank you for the share.
Thank you for the tip! I’ve been stuck on a few hard sudokus for a week, hope this helps
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.
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.
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.
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 ones where you demystify some logic i was struggling with seeing are my favorites.
Empty rectangle really screwed me up till late in the game. So well done for spotting it so early.
These videos are reassuring to me in one way because they show me I solve puzzles just like an expert. The difference is what takes him 15 minutes takes me FOUR HOURS.
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.
I love the way you can make markups with both corners and centers! Does anyone know of an iOS app that has this functionality?
they have their own apps on ios and android, they're great!
Alexey Pyzhov thank you, what is it called? I’d love to get it
@@geocline Classic Sudoku! by Cracking the Cryptic. they have other types of sudoku as well
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
14:05 X-wing on 1's in R1C3 & R1C5 & R7C3 & R7C5 eliminates 1's in R8C3 and R8C5.
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.
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
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.
15:22 was what I needed to solve this. Thank you!
I was always so confused about how to spot empty rectangles, but knowing they follow similar patterns as x-wings has really helped!
So this is what Sean Lock does in between episodes of 8 out of 10 cats
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
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 :)
6:05 Please, can anyone explain why 6 can only be in a vertical or horizontal arrangement in this block? Thanks
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
Regarding the empty rectangle discussed at 5:33, I do not understand why the 6s must be horizontal or vertical, at this point why couldn't they be diagonal, say for example a possible 6 in either r4c8 or r5c9? What rules that out? While I know some advanced techniques I am admittedly unfamiliar with the empty rectangle trick so I'm probably missing some logic here. Could someone help me out and explain the logic, or give a link to a good explanation?
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 prefer when you click on a cell and it highlights the corresponding column/row/block. Makes it easier to see.
I do not get why at around the 4:19 mark you say both the 5 and the 6 both have to go in the 2nd column because the 5 can go in the 3rd column and the 6 can go in the 1st column.
at time 8:00, you decide to put 3 on grid 7 bottom row (between 5 and 6). I thought 3 could also be placed next to 2. Why did you choose to place it between 5 and 6 and not next to 2. Can you explain the logic please. This would have changed the way 3 is placed in grid 9. It could have been next to 4 or first one on the last row (3 blank 2).
Because Column 2 needs a 3 and Row 9 was the only available spot.
I struggled with this at first also. But the answer must be: If he put a 3 in R8 C3 he later could not have put a 3 in R 2 or R3 in C.1. He must have seen that but did not explain it.
0:51 I love how Simon refers to 17 minutes and change as a long video when people nowadays complain that the puzzle is too easy if the video is that short! How times have changed...
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.
The way you make us understand is great. Thankyou sir
As a beginner I appreciate this video. I have not seen another video describing it.
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
7 in the bottom right corner . I saw it earlier . I think that would make the puzzle easier further
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.
Hi. Can you explain why the 6’s in block 6 have to be vertical (centre 2) or horizontal (centre 3)? Thanks
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 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
That's a really interesting technique. I'd got to a point where it looked as though there could be two solutions (I know that's impossible), only this technique sorted it out. Thanks for that.
I have a Sudoku book where in a lot of the puzzles it was possible to have 2 correct solutions.
How do you spot the 5&6 at 4:00?
I understand the logic, but how do you spot it in the first place?
Any pattern or formula to check so that I can spot this kind of logic every time?
I can't speak to exactly how to see those patterns, but I think the speed at which these two find them blows us away, but I personally will see the numbers in a box and then just follow each of the lines and it's offshoots for ones with the same numbers in. It takes me longer than them, but it gets me there. Hope that helps.
Read through the comments -- a reply to a comment -- and there's one (by a Matthew or Michael? sorry!) who lists the steps to use this rectangle technique to eliminate a possibility, how to find it. HTH
Just getting into your videos - never heard of empty rectangle before this one. Wicked.
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.
At 15:22 how did you decide that it is a definite 2 and not a 9 as at that stage it could be either a 2 or a 9 since the left side grid remained unfilled
?
Hey, someone who has just learned the technique here. I'll try to help you.
The thing is that the 2-9 in the center is directly related to the 1-9s at the top. If that center was a 9, that would mean that the one above must be 1 and the one to its left another 9. Both those 9s would block any possible 9 in the 4th square, so it is not a possible solution. He doesn't exactly word it that way but that's the idea. let me know if it helped you. I think I'm getting the hang of it.
At 6.03 why can the 6s be neither horizontal or vertical but a mixture of both as in row 4 square 8 and row 5 square 7?How can you know they are either horizontal or vertical ?
at 8:45 you have the 7 and 9 combined in 2 boxes. but there can only be a 7 in the top box because in the other horizontal boxes can't be a 7.
Love the trill in Mozart’s Sonata in C major! (Love your videos too...)
So THAT'S what it's called!! Thanks!
How did you get a 3 at 8:02?
The column required a 3, 7 and 9. The two three's removed the other possibilities for the three to go; therefore it goes in the only legal position. Rewatch 7:50
56 HAD to be in the 2 blocks marked off, so the 3 remaining empty squares needed to be 3,7,9, of which 2 of them were being blocked by 3s.
I struggled with this at first also. But the answer must be: If he put a 3 in R8 C3 he later could not have put a 3 in R 2 or R3 in C.1. He must have seen that but did not explain it.
Trying to do this on my own, I got stuck specifically because I didn't know the empty rectangle for the 6; as soon as it was mentioned, I pressed pause and could finish the puzzle, using the 9 one later on. In other words, this specific puzzle was an excellent lesson on that technique, and would have been very difficult without it.
How did you pause? That's been something I've wanted in their webapp.
@@beamer908
I pressed pause on the video. Sorry for the false hope.
Empty rectanges are a beautiful technique. I hope I am able to spot one in on my own sometime.
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.
At around 7:15 seconds, I don’t understand the logic of why the 6 must be either vertical or horizontal. Does it relate to the shape of the empty cells.
I'll need to remember the empty rectangles technique, thank you for showing this!
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.
When you put the 56 in second column it leaves only one space for the 3?
Indeed, and from there more 3’s can be filled.
@@hwelvaar yes Ian, along that column since the 56 pair eliminated those spots for a 3 to occupy if you looked at rest of that column there already were 3s from other boxes controlling where the 3 could go in that specific column...down to 1 possibility so Simon then filled in the 3. There has to be a 3 somewhere on that column. There only was that 1 spot left.
I'm pretty sure this will revolutionise my Sudoku game. Thank you!
Where can i sen you a sudoku? I got one what is the first I cant solve after years...
Before watching your channel and sudoku guy I hardly ever finished expert sudoku, now my best time is 8 minutes.
Empty rectangle. I think that's all I'm missing in my life. Thank you!
How can I obtain the grid generator tool you utilize to solve other sudoku puzzles
5:03 empty rectangle. 14:43 eliminates the 1, then the 9. I had to use simple coloring to finish, and that obviously required several more steps.
Can you recommend any books with similar strategies in them?
Question please, how to double check suduko answers once finished? Thanks!
The technique I learned from this was a number in two columns "squeezed" the number in the bottom row, which I never thought about before, hopefully will use it later on.
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!