That giant explanation for the 6's and 9's and all he had to do was notice that 6 HAD to go into the top-center box of the bottom-center grouping due to the position of the other 6's in the puzzle...
It might be interesting to see a video with an eye tracker, it adds another layer to the explanation because we not only see and hear what you managed to deduce / spot but we can also see which information was considered and rejected at that point in time due to not being able to provide any information and which information was not yet acted upon.
I like how around 10:00 the 6 in the bottom central box was already constrained perfectly by the top and middle central boxes but you proceeded to use uniqueness on the left column... :D great video!
@Fester Blats I used to do sudoku some years ago. Got interested in it through a teacher in highschool, when I got my first smartphone I casually installed it and was solving whenever bored at uni during lectures, or at home, or whenever. There was this one sudoku that I thought defeated me because I didn't know you can do this tecnique. I thought it was guessing, which is illegal. So I though I solved it illegaly. This video gave me so much closure I might get back into sudoku again.
Instead of using the empty rectangle or finned x-wing for the 2's, I actually used the 2 and 8 pairs in rows 3 and 6 to find a double skyscraper, which then eliminated the 2 from r5c5, giving me a 4, which then collapsed the rest of the puzzle as well. Either way, great solve, and again thanks to you guys and this channel for making these types of solves possible for me! I would have never known about any of these wonderful techniques if it weren't for your content.
I've input this into a solver as well, which also gave me the note about not being able to be solved by logic. It does give a finalized solution as if it is solvable, which is the same solution shown here (I layered screenshots to check). But if you prompt the solver to show steps, at some point it states: "Step 37: Brute Force The remainder of this puzzle was not solved by logic. This is because of solver limitations. It does not mean there is not a logical solution to this puzzle." This step has all the same numbers as 12:00 in the video. So it appears these solvers are having difficulty with the X-wing concept.
Brute-force is still logical. If this potential solution satisfies the conditions of a sudoku puzzle, then it's a solution. Otherwise, it's not, so try a different potential solution. It's just not very clever, which is why computers are so much better at brute-forcing these kinds of things. Dumb, but fast.
@@Aeghamedic But an algortihm might stop its logic at some point (finding naked singles, building intersections of row/col/box and so on) and just trying the first of some options and figuring out, whether it is solvable (again with classic tactics) after that decision and I would call that brute forcing, if it comes to the end and confirms "solved", without trying, whether another option might have solved it too.
I was really proud of myself for finding the Skyscraper (at least I think it was one) for the 2's in rows 3 and 6, connected by the columns 4, 5, and 7. This allows us to eliminate the 2 in row 5 column 5. Seriously enjoyed seeing the other strats to break this one open though :)
I decided I'd try this myself and found that once I had the same numbers as you did at 12:53, I could not progress. I ended up assuming an 8 at row 3 column 5 and finished the puzzle from there. But I'm not satisfied with guessing a number... your method of figuring that last part out was very interesting.
I don't understand how he got 4 at 3:24. He said you can see it from comparing the contents of row three and column nine, but I don't see it? (I'm new to Sudoku and this showed up in my recommendations.)
Even though that 6/9 explanation was completely unnecessary to get the 6 in r7c5, I'm still glad, because I feel like not understanding that 2-solution problem has kept me from progressing on so many puzzles before
any tips on how to teach yourself to spot skewed or finned x-wings and skyscrapers etc? so far i can just barely follow along with them, making finding them on my own improbable.
Yes. The obvious tip is to do lots of practice but I have another tip too! When you get stuck on a puzzle, train yourself to look for instances in rows and columns where one number can only go into exactly two positions in that row and column. X-Wings, Finned X-Wings, Skyscrapers, Empty Rectangles ALL require that this condition is met in at least one column/row. By getting better at isolating instances like this, you'll find it easier to start to then scan the other rows/cols for the patterns you need.
you can actually solve up to the point at 14:00 using only "this square can only be x" and "x can only go there" methods, apparently ignoring the 6 and 9 madness. Now the only reason I know this is because I decided to write a sudoku solver for fun, and it got that far only using those 2 methods (it just tries out every possible number past that point, as I have yet to add in other methods)
Question for you. I took the suggester's insinuation that the sudoku was unsolvable as a claim that it didn't have a unique solution. If that's the case, then wouldn't it be improper to use the assumption that it DID have a unique solution to rule out the ambiguity in the bottom left corner?
@@OberonDam If a Sudoku had three solutions, two of which are interchangeable by this simple pair exchange, then you would rule both of them out and find the third solution. You claimed that you would always find a contradiction instead. I am not sure if it is possible to construct a Sudoku, which has three such solutions as I describe, but I at least can't think of an obvious reason, why it should be impossible.
Andrew Stuart’s solver made only one excursion into “tougher” strategies and readily solved this puzzle. His puzzle uniqueness check returned one result as expected for a “good” puzzle. I suspect the requestor entered digits incorrectly into the solver they used?
I've ran into puzzles like this but kept looking for the logical answer, but in this one there was none either in the boxes, or the vertical or horizontal lines,... However, i did get to the same point where you got when you found your answer to finish,.. I've played around with this idea but felt I should be able to find the answer without doing this,.. this seems to be something akin to fifty fifty guessing to see if you can finish without breaking the two rules. I have had a few that I kept searching for two or three weeks and finally find the answer, and then left them open JUST because the hide was SO elegant,.. like seeing the shadow OF the shadow.
I used the skyscraper techninque with number 2 in rows 3 and 5 to eliminate the number 2 on the r1c8. Finaly I can use this by myself in one puzzle, because I was trying to understand the logic and this techniques are so dificult to me...
I used a Java solver I coded a couple of years ago and it solved this in 0 seconds (so less time than the computer can count before rounding to something greater than 0), this viewer really needs a new solver...
@@forja123 As a matter of fact I did and I know about milliseconds, this doesn't stop the program being fast, I'll give you my github link if you want but all the comments are in French (And before you say something, I'm French but bilingual)
@@TheZeilo You can't solve it is zero seconds. Your timing method is just lacking. But then again, it's Java... Get an average time, solve it one million times and divide the total time taken by a million.
Great solve, and lovely last step. Solution is even simpler since at 9:30 the uniqueness argument is not needed, as the south box already has a 6 forced in the top row, which forces the 6 in the bottom row of the SW box.
Yeah, I dislike the uniqueness argument because it presumes that the creator followed the rule involved - I've definitely found newspaper Sudoku puzzles that did not have a unique solution. At the higher tiers of competence, I'm sure it's probably a safe assumption but I would be extremely hesitant to make it. However, since the 6 was already provable, it didn't alarm me too badly....
From 12:25: If 2 is in R5C5, then 8 must be in R6C4, then 2 in R6C7, forcing 8 into R3C7, putting 2 in R3C5 !!!!, which can't happen. Therefore 4 has to go in R5C5
@@Pingwinho Look at the position at 12:25. R3 has only two positions open: R3C5 and R3C7 & requires a 2 and an 8. If the 8 goes in R3C7, there is no place other than R3C5 for the 2.
Normally I stand... well, sit... in awe. But this one, the first 35 numbers fell to simple rules. Then when you were discussing the finned X-wing in respect of 2s, looking at the pairs of 2s and 8s we get to eliminate the possibility of 2 from r5c5 and that's the /only/ piece of wider logic needed, after the 4 goes in the rest fall to basic rules. HoDoKu evaluates this one as "hard" - well below "Unfair" and "Extreme". :)
I tried this puzzle myself before watching the video and got a slightly different answer, but I thought Sudoku puzzles were supposed to be unique. I didn't notice the 6/9 rectangle until the very end, when they were the last 4 squares left. This is what I got: 685 | 417 | 923 423 | 985 | 617 971 | 623 | 854 ----------------------- 869 | 172 | 345 512 | 349 | 786 734 | 856 | 291 ----------------------- 296 | 714 | 538 347 | 598 | 162 158 | 236 | 479
At the point where you use the empty rectangle / finned x-wing logic, you could also look at both possibilities for R3C5 to rule the 2 out of R5C5, which I believe also cracks the puzzle open. I wonder, based on the computer being unable to solve this, if the uniqueness argument was valid; that is, there might be multiple solutions to the puzzle, which is why it was deemed unsolvable.
Well we at 10:13 we can also use the fact that the only place for a 6 in the middle box in the bottom row is in r7c5 due to the 6:es in rows 4 and 6, so we do not have a uniqueness issue.
Any given starting state should only allow 1 possible solution, so even if you brute forced every unknown possibility there should only be 1 valid solution. From there you could have a computer solve the puzzle as far as it can, then a human can look at what's left and if there's some logic the computer A.I. doesn't know how to deal with. If they can't solve it, share it with others to see if someone else can figure it out. Eventually someone will, or there was a problem with the starting state.
The 6s already preclude the putative invertible pair without resorting to uniqueness. Check the middle three boxes at 11:00, 6 must be top row lower box.
Regardless of that specific occasion, I'd say it's a bit dangerous to use the uniqueness method when solving a puzzle that's claimed to be unsolvable. Sure it may have to be used eventually.. but in that case it would be a catch 22 problem. ^_^
Here's a sudoku solver written in javascript. It's fast and it never fails. If you're in to code then by all means look at the source using developer options. After entering your grid, you can record what the algorithm does to solve the grid and then play it back. In addition, there are 90 very hard test puzzles to solve. You can try to solve these by yourself or batch solve all of them to see how fast your machine is. www.siliconproductions.com/sudoku/sudoku7.html
@@sebastianschweigert7117 agreed that it's impossible to prove mathematically however I designed it to be fully deterministic. You can watch it work with the record and playback function. Maybe 'has never failed' would be better.
Only Snyder notation required for me; didn't use any uniqueness, the chain on 8s solved it for me. Really wish I had spottedthe empty rectangle on 2s though.
I haven't watched the video yet. I solved it, I got stuck in a situation where 2/8 could be placed (R3, C5), (R3, C7), and (R6, C7). So I drew two more boards and to see which was the right option. I worked the solution where 2 was placed in the (R3, C7) and got a lot more information. I had another place where I had a 50/50 guess based on the information available for the last two 9's. Did the same as before and drew another board to test one solution worked on it and it failed so I went the other one and ended up completing it with little difficulty. I am not an expert at the game and don't understand some of the techniques. Forgotten some I did know.
sudoku9x9.com solves this instantly with logic, the only slightly unusual step (besides hidden and naked singles and a locked candidate) is what they call "coloring" in step 55, which removes the 2 from the possibilities in R5C5 because of R1C8 can either be 1 or 2. It's not even a deep path.
Weird that a computer solver couldn't solve it. If it is using search there must be something wrong with the solver. I used sudoku.unl.edu to solve it and found it requires a GAC+SAC consistency level, which is pretty low.
i think something simple that would really take these videos a step up is background music. it could be something classical or just a little beat. personally, background music really, really helps keep me engaged in videos with not much going on on screen
IMHO - no, no, no! No music please. If the viewer requires music, they can choose it and add it locally ( e.g. radio, CD player) but if the music is in the video it cannot be removed for those who prefer just the speech. As if this stuff isn't hard enough without adding music to make the words harder to hear.
No, no and thrice no. I would stop watching if there was music. I HATE background music on tutorial/instruction videos. Did you have background music at school during lessons? Nope.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
17:00 I'm calling bullshit on the "let's see where this takes us". You've already solved it and you are going back over the scenario that completed the puzzle. That's just trial and error.
I think in this case “unsolvable” means you can’t solve it by making a logical next step. If instead of going “Because of this I should do that.” you just try every possible combination until you find one that works then you’d say it’s “unsolvable”. If the puzzle setup is valid (eg the same number doesn’t show up in the same column) and there’s a unique solution (you can’t swap a pair of numbers at the end and it still works) then it’s technically solvable but maybe not by reasoning about it.
Sage Crane 03:28 Look closely at row 3. Only numbers remaining are 2,4,8. Since there are already 2 and 8 in column 9, this makes 4 the only possible number for cell r3c9.
At the end, you go guessing with trial and error, but only try one branch. Hence, you only know that the sudoku has a solution, but not that it has a unique solution. You also assumed a unique solution earlier. I wonder, whether assuming a unique solution can lead to an unsolvable situation, while an actual solution assists.
There wasn't any trial and error. All the steps were made from logical deduction. Making an assumption then seeing that it leads to a contradiction is a perfectly rigorous way to disprove the assumption (see contrapositive).
@@DaProHobbit At 16:50 he narrows it down to 2 possibilities. The he literally CHOOSES one and comes out with a solution. If it HAD lead to a contradiction, then yes. He would have proven that the choice is false and therefore the other choice must be true (assuming there is a solution to begin with). But since there was no contradiction, we don't know whether the other choice is true or false. So we either assume there is a unique solution, or we don't care whether the solution is unique. Hence, my implied question in the first part, whether a sudoku is still called "solvable" if there are multiple solutions. Would you call an empty 9x9 grid a solvable sudoku? My second part about the contradiction trap when assuming a unique solution refers to 10:00
LordMardur When he says 2 choices, he means 2 logical strategies, not 2 physical choices for numbers. Both strategies lead to the same outcome. I guess his wording was a bit confusing lol
@@DaProHobbit Ok. I think the confusing part is when he says "we either know ... or we know ...", when actually we know both are true. So the number "2" can be eliminated from both positions. I don't quite follow the explanation of the "finned x-wing" though. Sure, the "2" is either in the green block or it is not. But why does it have to be one of the 2 purple blocks (fins) and cannot be the bottom white block? Sure, putting a "2" there leads to a contradiction, but I don't see how that follows from anything he says. There is still the unsatisfying assumption at 11:00 that "good sudokus have one solution". What if this one has multiple solutions with the 6 and 9 in the marked positions? Is that even possible in general? If no sudoku with such arbitrary flips can exist, then this is a valid strategy. But if such flips just should not exist due to esthetics, then the conclusion to eliminate the flip position is invalid.
LordMardur The premise of a sudoku is usually that there is a unique solution, so we can always assume that. Badly designed ones might have multiple solutions like the 6/9 thing, but in that case they're not really proper sudokus. The purple fins come from needing to have a 2 in the top row- they work as part of the X-wing in the same way that the middle square works, so in any case, a 2 can't go in the bottom of the top box.
As vocalnerd pointed out, the uniqueness trick was actually unnecessary: "I like how around 10:00 the 6 in the bottom central box was already constrained perfectly by the top and middle central boxes but you proceeded to use uniqueness on the left column... :D great video!"
Guy, I do think that's a fair point. And as someone who likes logic, mea culpa. Thankfully, in this instance, it seems that there is only one solution anyway but, given the challenge, I probably shouldn't have used uniqueness in the solve. Good spot!
@@CrackingTheCryptic As it happens I think Sarsoar is correct (although I don't think I'm being quite as 'stupid' as they seem to think). You assume from the outset that the puzzle's solvable then look for a contradiction (which in this case never arose). Made me think though!
We can not "see" where your eyes are looking. Please invest in kit that allows this. This is in addition to your new mike that stops echo and bloody kids.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
That giant explanation for the 6's and 9's and all he had to do was notice that 6 HAD to go into the top-center box of the bottom-center grouping due to the position of the other 6's in the puzzle...
That was hilarious.
At least we now know :D It might serve useful in another sudoku
7:05 nice bluff :)
It might be interesting to see a video with an eye tracker, it adds another layer to the explanation because we not only see and hear what you managed to deduce / spot but we can also see which information was considered and rejected at that point in time due to not being able to provide any information and which information was not yet acted upon.
@@AnonimityAssured That sounds like you don't want to see the eye movements
@@AnonimityAssured That sounds like fun to me
I like how around 10:00 the 6 in the bottom central box was already constrained perfectly by the top and middle central boxes but you proceeded to use uniqueness on the left column... :D great video!
I agree with you, it's very nice that he did that... intentional or not, it certainly added a mini-lesson about sudokus in the process. :D
@Fester Blats I used to do sudoku some years ago. Got interested in it through a teacher in highschool, when I got my first smartphone I casually installed it and was solving whenever bored at uni during lectures, or at home, or whenever. There was this one sudoku that I thought defeated me because I didn't know you can do this tecnique. I thought it was guessing, which is illegal. So I though I solved it illegaly. This video gave me so much closure I might get back into sudoku again.
That is called avoidable rectangle
Instead of using the empty rectangle or finned x-wing for the 2's, I actually used the 2 and 8 pairs in rows 3 and 6 to find a double skyscraper, which then eliminated the 2 from r5c5, giving me a 4, which then collapsed the rest of the puzzle as well. Either way, great solve, and again thanks to you guys and this channel for making these types of solves possible for me! I would have never known about any of these wonderful techniques if it weren't for your content.
When I did the puzzle I ended up using the same method. With so many naked pairs it seemed obvious I would be able to use them to my advantage.
10:30 OR.... you can find that there has to be a 6 in r7c5 and that also solves it
I've input this into a solver as well, which also gave me the note about not being able to be solved by logic. It does give a finalized solution as if it is solvable, which is the same solution shown here (I layered screenshots to check). But if you prompt the solver to show steps, at some point it states:
"Step 37: Brute Force
The remainder of this puzzle was not solved by logic. This is because of solver limitations. It does not mean there is not a logical solution to this puzzle."
This step has all the same numbers as 12:00 in the video. So it appears these solvers are having difficulty with the X-wing concept.
Brute-force is still logical. If this potential solution satisfies the conditions of a sudoku puzzle, then it's a solution. Otherwise, it's not, so try a different potential solution.
It's just not very clever, which is why computers are so much better at brute-forcing these kinds of things. Dumb, but fast.
@@Aeghamedic But an algortihm might stop its logic at some point (finding naked singles, building intersections of row/col/box and so on) and just trying the first of some options and figuring out, whether it is solvable (again with classic tactics) after that decision and I would call that brute forcing, if it comes to the end and confirms "solved", without trying, whether another option might have solved it too.
3:00 I too am looking for naked singles, mate!
I was really proud of myself for finding the Skyscraper (at least I think it was one) for the 2's in rows 3 and 6, connected by the columns 4, 5, and 7. This allows us to eliminate the 2 in row 5 column 5. Seriously enjoyed seeing the other strats to break this one open though :)
I decided I'd try this myself and found that once I had the same numbers as you did at 12:53, I could not progress. I ended up assuming an 8 at row 3 column 5 and finished the puzzle from there. But I'm not satisfied with guessing a number... your method of figuring that last part out was very interesting.
I don't understand how he got 4 at 3:24. He said you can see it from comparing the contents of row three and column nine, but I don't see it? (I'm new to Sudoku and this showed up in my recommendations.)
Paweł Kęcerski ah I understand now. Thank you.
Also took me a minute to get it.
Even though that 6/9 explanation was completely unnecessary to get the 6 in r7c5, I'm still glad, because I feel like not understanding that 2-solution problem has kept me from progressing on so many puzzles before
any tips on how to teach yourself to spot skewed or finned x-wings and skyscrapers etc? so far i can just barely follow along with them, making finding them on my own improbable.
Yes. The obvious tip is to do lots of practice but I have another tip too! When you get stuck on a puzzle, train yourself to look for instances in rows and columns where one number can only go into exactly two positions in that row and column. X-Wings, Finned X-Wings, Skyscrapers, Empty Rectangles ALL require that this condition is met in at least one column/row. By getting better at isolating instances like this, you'll find it easier to start to then scan the other rows/cols for the patterns you need.
you can actually solve up to the point at 14:00 using only "this square can only be x" and "x can only go there" methods, apparently ignoring the 6 and 9 madness. Now the only reason I know this is because I decided to write a sudoku solver for fun, and it got that far only using those 2 methods (it just tries out every possible number past that point, as I have yet to add in other methods)
Question for you. I took the suggester's insinuation that the sudoku was unsolvable as a claim that it didn't have a unique solution. If that's the case, then wouldn't it be improper to use the assumption that it DID have a unique solution to rule out the ambiguity in the bottom left corner?
I thought so too but if you look at it when he was doing that you'll notice the 6 was solvable anyway.
If the non-unique solution was the correct 'solution'. Then by assuming uniqueness holds true would also end in an unsolvable solution.
@@OberonDam If it had more than two solutions, I'm not so sure about your statement. Otherwise I think you are right.
@@clumsyjester459 the point is that a non-unique solution isn't a solution. No matter what.
@@OberonDam If a Sudoku had three solutions, two of which are interchangeable by this simple pair exchange, then you would rule both of them out and find the third solution. You claimed that you would always find a contradiction instead. I am not sure if it is possible to construct a Sudoku, which has three such solutions as I describe, but I at least can't think of an obvious reason, why it should be impossible.
5:48 niceeee
In the case of uniqueness, how do you know which numbers need to be eliminated in order to ensure it's a unique solve??
Andrew Stuart’s solver made only one excursion into “tougher” strategies and readily solved this puzzle. His puzzle uniqueness check returned one result as expected for a “good” puzzle. I suspect the requestor entered digits incorrectly into the solver they used?
Now that Nikoli website is down where do you get some insane sudoku puzzles?
We hope, in the not too distant future, you'll be able to come to us...
I've ran into puzzles like this but kept looking for the logical answer, but in this one there was none either in the boxes, or the vertical or horizontal lines,... However, i did get to the same point where you got when you found your answer to finish,.. I've played around with this idea but felt I should be able to find the answer without doing this,.. this seems to be something akin to fifty fifty guessing to see if you can finish without breaking the two rules. I have had a few that I kept searching for two or three weeks and finally find the answer, and then left them open JUST because the hide was SO elegant,.. like seeing the shadow OF the shadow.
I used the skyscraper techninque with number 2 in rows 3 and 5 to eliminate the number 2 on the r1c8. Finaly I can use this by myself in one puzzle, because I was trying to understand the logic and this techniques are so dificult to me...
I used a Java solver I coded a couple of years ago and it solved this in 0 seconds (so less time than the computer can count before rounding to something greater than 0), this viewer really needs a new solver...
i bet you didn't code it yourself as you apparently don't know about milliseconds
@@forja123 As a matter of fact I did and I know about milliseconds, this doesn't stop the program being fast, I'll give you my github link if you want but all the comments are in French (And before you say something, I'm French but bilingual)
@@TheZeilo You can't solve it is zero seconds. Your timing method is just lacking.
But then again, it's Java...
Get an average time, solve it one million times and divide the total time taken by a million.
PleAse someone help how does he know that a 4 has to go in the 9th column at 3:30 I don’t understand
It's the only number unique to that row and column. Any other number would make a duplicate in either the column or the row.
Which software are you using in these videos?
The software is listed in the description:
▶SOFTWARE◀
We mainly use Duncan's Sudoku Solver, which is available at www.littlegogs.com/index.shtml
Great solve, and lovely last step. Solution is even simpler since at 9:30 the uniqueness argument is not needed, as the south box already has a 6 forced in the top row, which forces the 6 in the bottom row of the SW box.
Yeah, I dislike the uniqueness argument because it presumes that the creator followed the rule involved - I've definitely found newspaper Sudoku puzzles that did not have a unique solution. At the higher tiers of competence, I'm sure it's probably a safe assumption but I would be extremely hesitant to make it. However, since the 6 was already provable, it didn't alarm me too badly....
uniqueness is such a reddit strategy
real solvers don't use it
When's the first time that Simon says "Now we're cooking with gas" ? This is not that time :-D
here you are: :) ua-cam.com/video/Puk4HqLxOdg/v-deo.html
That logic at 10:57 👌
I mean, the 6 in box 2 and 5 pretty much tell you where the 6 in block 8 is. Which immediately tells you the 6 in block 7.
From 12:25: If 2 is in R5C5, then 8 must be in R6C4, then 2 in R6C7, forcing 8 into R3C7, putting 2 in R3C5 !!!!, which can't happen. Therefore 4 has to go in R5C5
@@Pingwinho Look at the position at 12:25. R3 has only two positions open: R3C5 and R3C7 & requires a 2 and an 8. If the 8 goes in R3C7, there is no place other than R3C5 for the 2.
Maybe she just said it's unsolvable so you would solve it :)
Very helpful video. Thanks!
I really enjoy every single one of your totally awesome sudoku puzzle videos
Thank you so much, nice Exapanitation, great teacher.
Normally I stand... well, sit... in awe. But this one, the first 35 numbers fell to simple rules. Then when you were discussing the finned X-wing in respect of 2s, looking at the pairs of 2s and 8s we get to eliminate the possibility of 2 from r5c5 and that's the /only/ piece of wider logic needed, after the 4 goes in the rest fall to basic rules.
HoDoKu evaluates this one as "hard" - well below "Unfair" and "Extreme". :)
I tried this puzzle myself before watching the video and got a slightly different answer, but I thought Sudoku puzzles were supposed to be unique. I didn't notice the 6/9 rectangle until the very end, when they were the last 4 squares left. This is what I got:
685 | 417 | 923
423 | 985 | 617
971 | 623 | 854
-----------------------
869 | 172 | 345
512 | 349 | 786
734 | 856 | 291
-----------------------
296 | 714 | 538
347 | 598 | 162
158 | 236 | 479
@Sarsoar Thanks, I looked it over several times and didn't see that.
At the point where you use the empty rectangle / finned x-wing logic, you could also look at both possibilities for R3C5 to rule the 2 out of R5C5, which I believe also cracks the puzzle open.
I wonder, based on the computer being unable to solve this, if the uniqueness argument was valid; that is, there might be multiple solutions to the puzzle, which is why it was deemed unsolvable.
Well we at 10:13 we can also use the fact that the only place for a 6 in the middle box in the bottom row is in r7c5 due to the 6:es in rows 4 and 6, so we do not have a uniqueness issue.
I believe it was just a bad solver. I stuck it in hodoku and it identified a solution immediately.
This one was relatively easy for me, took me about 11 minutes. I always try to do them myself before I start to watch.
I don't get how you found the first 4?
Interesting. Hodoku reads this puzzle as invalid. I imagine it's because there are multiple solutions, which in Sudoku should not be the case.
tiotito31 Do you have a way to tell what those multiple solutions might be?
I managed to do it in 21 minutes by plain Sudoku rules, and no special tricks.
This was a challenge. By marking what it couldn't be it fell.
How would you test whether a sudoku is completely unsolvable?
Any given starting state should only allow 1 possible solution, so even if you brute forced every unknown possibility there should only be 1 valid solution. From there you could have a computer solve the puzzle as far as it can, then a human can look at what's left and if there's some logic the computer A.I. doesn't know how to deal with. If they can't solve it, share it with others to see if someone else can figure it out. Eventually someone will, or there was a problem with the starting state.
At the end there is also a skyscraper on 28 in row 3 and 6, eliminating the 2 in r5c5 as a third possibility.
Maybe the solver couldn't solve it because you assumed there was a unique solution.
The 6s already preclude the putative invertible pair without resorting to uniqueness. Check the middle three boxes at 11:00, 6 must be top row lower box.
@@kevinjamesmartin7127 Ah yeah, (5,7) is a 6 because of (4,3) and (6,6). So (3,9) must be a 6.
Regardless of that specific occasion, I'd say it's a bit dangerous to use the uniqueness method when solving a puzzle that's claimed to be unsolvable. Sure it may have to be used eventually.. but in that case it would be a catch 22 problem. ^_^
Here's a sudoku solver written in javascript. It's fast and it never fails. If you're in to code then by all means look at the source using developer options.
After entering your grid, you can record what the algorithm does to solve the grid and then play it back.
In addition, there are 90 very hard test puzzles to solve. You can try to solve these by yourself or batch solve all of them to see how fast your machine is.
www.siliconproductions.com/sudoku/sudoku7.html
"It's fast and it never fails"
Impossible to prove
@@sebastianschweigert7117 agreed that it's impossible to prove mathematically however I designed it to be fully deterministic. You can watch it work with the record and playback function. Maybe 'has never failed' would be better.
I feel dumb after watching this.
You probably are.
5:49
Nice
Brilliant!
Nicely solved.
I thought solving it was very easy, I had you do it for me. (haha) Very good lesson, I hope to be a learned someday.
Actually didn't have any trouble with this solve, oddly enough.
Only Snyder notation required for me; didn't use any uniqueness, the chain on 8s solved it for me. Really wish I had spottedthe empty rectangle on 2s though.
I stroked out for about 10 minutes
I haven't watched the video yet. I solved it, I got stuck in a situation where 2/8 could be placed (R3, C5), (R3, C7), and (R6, C7). So I drew two more boards and to see which was the right option. I worked the solution where 2 was placed in the (R3, C7) and got a lot more information. I had another place where I had a 50/50 guess based on the information available for the last two 9's. Did the same as before and drew another board to test one solution worked on it and it failed so I went the other one and ended up completing it with little difficulty. I am not an expert at the game and don't understand some of the techniques. Forgotten some I did know.
sudoku9x9.com solves this instantly with logic, the only slightly unusual step (besides hidden and naked singles and a locked candidate) is what they call "coloring" in step 55, which removes the 2 from the possibilities in R5C5 because of R1C8 can either be 1 or 2. It's not even a deep path.
Maybe the requester needs to get a better sudoku program? Duncan's did this one almost as fast I did...
It's more probable that the requester just missed a number or made a mistake while imputing it to the sudoku solver
@@Jokseej oh yeah I hate when I'm halfway through before I notice I did that
The solver I wrote solves it in 0.3 seconds on my pc using integer linear programming.
Im sure an asian did it 100 times faster
13:34 that was the hard part
Weird that a computer solver couldn't solve it. If it is using search there must be something wrong with the solver. I used sudoku.unl.edu to solve it and found it requires a GAC+SAC consistency level, which is pretty low.
mind.... blown!
i think something simple that would really take these videos a step up is background music. it could be something classical or just a little beat. personally, background music really, really helps keep me engaged in videos with not much going on on screen
IMHO - no, no, no! No music please. If the viewer requires music, they can choose it and add it locally ( e.g. radio, CD player) but if the music is in the video it cannot be removed for those who prefer just the speech. As if this stuff isn't hard enough without adding music to make the words harder to hear.
@@ridefast0 oh i see you, all of those are good points and valid
No, no and thrice no. I would stop watching if there was music. I HATE background music on tutorial/instruction videos. Did you have background music at school during lessons? Nope.
Why am I here and why did I watch the whole video?
This is what happens when binge watching videos after midnight.
For me it was very easy. A skyscraper solved the final nut. ;)
You're supposed to prove it has an unique solution and use uniqueness as an argument for it. Isn't that circular logic?
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
17:00 I'm calling bullshit on the "let's see where this takes us". You've already solved it and you are going back over the scenario that completed the puzzle. That's just trial and error.
Is there an unsolvable sudoku?
I think in this case “unsolvable” means you can’t solve it by making a logical next step. If instead of going “Because of this I should do that.” you just try every possible combination until you find one that works then you’d say it’s “unsolvable”. If the puzzle setup is valid (eg the same number doesn’t show up in the same column) and there’s a unique solution (you can’t swap a pair of numbers at the end and it still works) then it’s technically solvable but maybe not by reasoning about it.
Can someone walk me through how he knew row 3 column 9 was a 4?
Sage Crane
03:28 Look closely at row 3. Only numbers remaining are 2,4,8. Since there are already 2 and 8 in column 9, this makes 4 the only possible number for cell r3c9.
@@KLS13143344 Thanks!
He must have mistyped the puzzle into the solver.
At the end, you go guessing with trial and error, but only try one branch. Hence, you only know that the sudoku has a solution, but not that it has a unique solution. You also assumed a unique solution earlier.
I wonder, whether assuming a unique solution can lead to an unsolvable situation, while an actual solution assists.
There wasn't any trial and error. All the steps were made from logical deduction. Making an assumption then seeing that it leads to a contradiction is a perfectly rigorous way to disprove the assumption (see contrapositive).
@@DaProHobbit At 16:50 he narrows it down to 2 possibilities. The he literally CHOOSES one and comes out with a solution. If it HAD lead to a contradiction, then yes. He would have proven that the choice is false and therefore the other choice must be true (assuming there is a solution to begin with). But since there was no contradiction, we don't know whether the other choice is true or false. So we either assume there is a unique solution, or we don't care whether the solution is unique.
Hence, my implied question in the first part, whether a sudoku is still called "solvable" if there are multiple solutions. Would you call an empty 9x9 grid a solvable sudoku?
My second part about the contradiction trap when assuming a unique solution refers to 10:00
LordMardur When he says 2 choices, he means 2 logical strategies, not 2 physical choices for numbers. Both strategies lead to the same outcome. I guess his wording was a bit confusing lol
@@DaProHobbit Ok. I think the confusing part is when he says "we either know ... or we know ...", when actually we know both are true. So the number "2" can be eliminated from both positions.
I don't quite follow the explanation of the "finned x-wing" though. Sure, the "2" is either in the green block or it is not. But why does it have to be one of the 2 purple blocks (fins) and cannot be the bottom white block? Sure, putting a "2" there leads to a contradiction, but I don't see how that follows from anything he says.
There is still the unsatisfying assumption at 11:00 that "good sudokus have one solution". What if this one has multiple solutions with the 6 and 9 in the marked positions? Is that even possible in general? If no sudoku with such arbitrary flips can exist, then this is a valid strategy. But if such flips just should not exist due to esthetics, then the conclusion to eliminate the flip position is invalid.
LordMardur The premise of a sudoku is usually that there is a unique solution, so we can always assume that. Badly designed ones might have multiple solutions like the 6/9 thing, but in that case they're not really proper sudokus.
The purple fins come from needing to have a 2 in the top row- they work as part of the X-wing in the same way that the middle square works, so in any case, a 2 can't go in the bottom of the top box.
I think because it came down to the uniqueness part and there was 2 solutions
As vocalnerd pointed out, the uniqueness trick was actually unnecessary: "I like how around 10:00 the 6 in the bottom central box was already constrained perfectly by the top and middle central boxes but you proceeded to use uniqueness on the left column... :D great video!"
Isn't the uniqueness argument slightly flawed here? You set out to show that it's solvable but then use the fact that it's solvable to solve it...
I agree, though I suspect that the rest of the logic might still have worked to solve it without the uniqueness argument.
Well, if you use arguments that assume it's solvable and they don't work, then you know it's not solvable :)
@@kacpers6975 Sure, but conversely if they do work you haven't proved it's solvable
Guy, I do think that's a fair point. And as someone who likes logic, mea culpa. Thankfully, in this instance, it seems that there is only one solution anyway but, given the challenge, I probably shouldn't have used uniqueness in the solve. Good spot!
@@CrackingTheCryptic As it happens I think Sarsoar is correct (although I don't think I'm being quite as 'stupid' as they seem to think). You assume from the outset that the puzzle's solvable then look for a contradiction (which in this case never arose). Made me think though!
sum wholesome sudoku
At 5:51 he says 69 lololololololololol
9 minutes
Not that bad really. Solved in 22 min b4 watching vid. Can't believe a solver couldn't get this.
We can not "see" where your eyes are looking.
Please invest in kit that allows this.
This is in addition to your new mike that stops echo and bloody kids.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.
I solved it a completely different way... I found that the r5c5 square couldn't be a two because of the sckewed x-wing (singles chain) between the 2/8 pairs in row 3 and 6. Also, getting the two's first automatically resolves the 6/9 uniqueness issue.