In the second puzzle, there's also an 'upside down' skyscraper on 4's in columns 3 and 9. That would allow you to eliminate the 4 in R8C7 and place a 4 in R8C3.
From the starting position of this video, there is an empty rectangle with 3's, and if you use it, you can eliminate the 3 from r3c7, leaving only a possible 4 in that spot. And that move unwinds the entire puzzle!
I found a skyscraper on the 4s, but it was different than the one described in the vid. The one is I used comprises cells R8C7, R8C3, R5C3, R5C9. Using those as the skyscraper easily eliminates the 4 from R6C7 and R7C9. You can also use simple coloring starting on R8C7 to achieve the same result.
At 12:10 you say: "Either C9R5 must be a 4 or C1R6 must be a 4". I don't think this is right due to the 2 in C1R7. The 2 in C1R7 could lead to 4 in both C9R5 and C1R6.The 2 makes the link between C9R5 and C1R7 ambigouos. EDIT: But I just realised the effect is the same if both are 4 i.e that C7R6 cannot be a 4. Without the 2 it is "either or", with the 2 it is "either or both" and I see your conclusion is right in both cases. What a joy to learn these techniques 🙂.
Simple chain solution first puzzle. Testing the odd duck 3 at r8c6 (the only non 1/3 pair on columns 4 and 6) removes all possible 3s in box 9. Therefore r7c4 = 3 ftw
In the first puzzle, there is a simple force test solution with the 34 pair in RC37. If one tries putting a 3 in that position and follows a couple of forced 3's around, you end up with a 3 conflict in C7 -- the 3 in the bottom right block also wants to go in C7. So RC37 has to be a 4. That 4 is enough to crack open the puzzle.
I understand this deduction, but why did you look at the 34 pair? If i'm at this point of a hard puzzle i don't want to arbitrarily put in a digit and 'test' it, at least not without having a reason why i did test this cell.Another comment made the suggestion to test the "only non 1-3 pair in c 4 and 6" which at least sounds like a reason. Also putting the 3 in your mention 34 cell leads with only one step to no possibilites of 3 in block 9 (put in 3 in 3,7 -> only 3 in c6 in 8,6 -> error in block 9). It was confusing for me because you said i had to follow a couple of 3's around? Bear in mind im not a native english speaker so i don't know how to make it sound friendly :D I just wanted to ask: Why do you look at this 34 cell?
That "force test solution" is called a bifurcation, and I think it's a cheap way of solving a puzzle. Not gonna tell people how to solve puzzles, but I personally think following one of multiple paths and turning back around to take another when it's a dead end like you're solving a cereal box maze is not a satisfying way of solving a puzzle, when it's possible to pick the right path straight from the outset. But taking the wrong path *in your head* is fine. The issue I see is placing down digits that you aren't sure belong in their cell. Placing down a digit should be done when the logic has lead you to the absolute certainty that that digit belongs there.
On the second puzzle: I don’t see how you can remove the 4 from R6C7 with the skyscraper. I can see that the skyscraper roofs can both theoretically contain a 4 due to the 4 in R7C7 and I thought that meant the skyscraper doesn’t work? If anyone reads this I’d love to understand
The funny thing is, I found a completely different second Sashimi Finned X-Wing than your second Sashimi Finned X-Wing. I looked in columns 4 and 9, which eliminated the three from column 6 row 8...
Excellent video. Several great concepts and techniques presented. One question. You haven't mentioned removal of candidates in the base row of the two skyscrapers. Since the puzzles collapse, perhaps it is a mute point, but in addition to removal of the candidates due to the sashimi (aka tops of the skyscraper), I assume any extra candidates in the base row could be eliminated just the same as if it was a simple x-wing. Correct?
Both. But in the first place, the x wing should be derived from a lack of candidates either in the rows or in the columns, so just remove candidates from the direction that was not involved at first.
In you example you used the threes in c7 and c9. There is a similar patten using the two threes in c4 and c9. So why use c7 and not c4? Would it produce the same result?
Simply stated, you brute force it. As to uniqueness. What is unique to R8, C6 ? It is the only square in the grid with 1, 2 , and 7, there is another one that is unique R5, C3 with 4 7 3, both have the number 7 and they are 7. Will this work all the time? I don't know.
I don't understand the results of the first assumption with the 3s. There are two different 3s in column 7 that look eligible to me and they are automatically discard and I don't see why - apparently they ar3 so obviously ineligible it's not even worthy of discussion
In the second puzzle, if R6C1 is a 4, then R5C7 has to be a 4, as I understand. You say at 12:05 that either R6C1 or R5C7 must be a 4. I don't understand. Then I lost track.
It is a good question but it is very important to remember that the skyscraper pattern (or indeed the sashimi finned xwing pattern) ONLY results in an effect at the "top" of the skyscraper. ie we are NOT using it to remove the candidate 3 in row 8 column 7. Indeed you are correct in noting that it is perfectly possible for row8col7 to be the 3 in row 8... but consider the implication of this for the skyscraper: if row8col7 is a 3 then both row3col6 AND row2col9 are 3s BUT this doesn't affect the conclusions we were able to draw regarding the skyscraper being able to eliminate 3s from row2col4 and row3col7. ie the skyscraper is saying that either r3c6 or r2c9 is a 3 OR both are 3s - either way we get to eliminate from the squares mentioned. I hope this makes it clearer?
I didn’t get it at first. I was thinking of it still as an X-wing technique. Rewatch it, that’s all I did, sometimes things make a bit more sense 2nd time round.
@C0mmand3r27 Exactly! I have watched more than one explanation of the skyscraper technique, and for some reason they all leave out this crucial point. They tacitly state that there is an either-or relationship there, as is true in the case of an X-wing. But there is NOT an either-or relationship between the two 3s at the top of the skyscraper. There is an either or BOTH relationship. Although this does lead to precisely the same effect as an X-wing, the fact that they do not specifically mention this nuance between the skyscraper and the X-wing IMHO shows a lack of thoroughness in the tutorial approach. It confused me too.
The second position is trivial: Column six has two '7's. The bottom '7' can't be a solution because it would leave the 1s, 2s and 3s in Columns 4 & 6 in a 'closed' 'ladder', there's no unique solution. The first position fails to mention a third column with two '3's in, column 4. So how do we choose? Does it matter? No acknowledgement made. On the subject of these mechanical approaches, how would we know when to apply them? Maybe a puzzle is half resolved, and this may unlock the rest? Or do we fill in the whole thing before starting this process? I use the Easybrain App, on Expert, and have been for a while. It looks like there are three different puzzles being used, they yield in different ways, and my times reflect it. To be clear, any single puzzle has over 2.5 x 10e15 variations that are "topologically similar", meaning you can transform the puzzle in that many ways, and the solution is the same. List below if you want to check. (Sorry for the phrase, it's all I can come up with!) My question is: "Am I doing the same puzzle each time, or are they genuinely different" My check will be to record the number of given numbers in each box, the numbers will stay the same whatever their order. Clearly the total will also be a constant. Does using a mechanical approach give faster times, or just reliability of outcome? Anyway, thanks to the authors, I will be more careful in future to look out for these offsets to the pairings. >>> Substitutions by number: Clearly every number can be switched with another and not change the puzzle; there are 9! ways to arrange nine numbers. Whole puzzle transformations: The whole puzzle can be rotated into four positions and reflected in the diagonal and up/down axes; that's 4x4x4. Box transformations: 2 rotations and 4 reflections can be applied to all the boxes individually, another 8. Row/Column re-ordering: Every row can be shuffled within the box rows 6 ways, and the box rows also shuffle 6 ways, columns similarly, that's 6e8 So that's: 9! x 2e9 x 6e8 = 3.1 x 10e14 (edited)
Surely, you are showing the same example. Don’t you mean the potential 1 and 3 in C4R2 for the other example? If not then I don’t understand the logic... That’s not unusual, though.
I see two other squares under the 6 in column 7 that look eligible to me - why/how can we assume row 9 column 2 is a three? I have worked these puzzles before - am I really just bone crushingly stupid?
I understand all the logic, the hardest bit is spotting when and where they exist
In the second puzzle, there's also an 'upside down' skyscraper on 4's in columns 3 and 9. That would allow you to eliminate the 4 in R8C7 and place a 4 in R8C3.
I saw the same thing.
This is by far your best tutorial! Well done!!!
Been working on a puzzle for hours, finally found a tutorial that really helped!
From the starting position of this video, there is an empty rectangle with 3's, and if you use it, you can eliminate the 3 from r3c7, leaving only a possible 4 in that spot. And that move unwinds the entire puzzle!
Fantastic video, not complicated and straight forward. Love the channel!
I found a skyscraper on the 4s, but it was different than the one described in the vid. The one is I used comprises cells R8C7, R8C3, R5C3, R5C9. Using those as the skyscraper easily eliminates the 4 from R6C7 and R7C9. You can also use simple coloring starting on R8C7 to achieve the same result.
Same here, but didn't notice the R7C9 elimination, but it worked anyway with just the R6C7 elimination.
At 12:10 you say: "Either C9R5 must be a 4 or C1R6 must be a 4". I don't think this is right due to the 2 in C1R7. The 2 in C1R7 could lead to 4 in both C9R5 and C1R6.The 2 makes the link between C9R5 and C1R7 ambigouos.
EDIT: But I just realised the effect is the same if both are 4 i.e that C7R6 cannot be a 4. Without the 2 it is "either or", with the 2 it is "either or both" and I see your conclusion is right in both cases. What a joy to learn these techniques 🙂.
Simple chain solution first puzzle. Testing the odd duck 3 at r8c6 (the only non 1/3 pair on columns 4 and 6) removes all possible 3s in box 9.
Therefore r7c4 = 3 ftw
Complicated as hell for me, but I can follow the logic...but spotting them is really hard.
This was the most eye-opening lesson!
absolutely great, it's fantastic
Still don't get it. I can see it's either a 4 or 7 but still don't know which?
In the first puzzle, there is a simple force test solution with the 34 pair in RC37.
If one tries putting a 3 in that position and follows a couple of forced 3's around, you end up with a 3 conflict in C7 -- the 3 in the bottom right block also wants to go in C7. So RC37 has to be a 4.
That 4 is enough to crack open the puzzle.
I understand this deduction, but why did you look at the 34 pair? If i'm at this point of a hard puzzle i don't want to arbitrarily put in a digit and 'test' it, at least not without having a reason why i did test this cell.Another comment made the suggestion to test the "only non 1-3 pair in c 4 and 6" which at least sounds like a reason.
Also putting the 3 in your mention 34 cell leads with only one step to no possibilites of 3 in block 9 (put in 3 in 3,7 -> only 3 in c6 in 8,6 -> error in block 9). It was confusing for me because you said i had to follow a couple of 3's around?
Bear in mind im not a native english speaker so i don't know how to make it sound friendly :D I just wanted to ask: Why do you look at this 34 cell?
That "force test solution" is called a bifurcation, and I think it's a cheap way of solving a puzzle.
Not gonna tell people how to solve puzzles, but I personally think following one of multiple paths and turning back around to take another when it's a dead end like you're solving a cereal box maze is not a satisfying way of solving a puzzle, when it's possible to pick the right path straight from the outset.
But taking the wrong path *in your head* is fine. The issue I see is placing down digits that you aren't sure belong in their cell. Placing down a digit should be done when the logic has lead you to the absolute certainty that that digit belongs there.
On the second puzzle: I don’t see how you can remove the 4 from R6C7 with the skyscraper. I can see that the skyscraper roofs can both theoretically contain a 4 due to the 4 in R7C7 and I thought that meant the skyscraper doesn’t work?
If anyone reads this I’d love to understand
Great explanation
I absolutely love your videos.
surely in the skyscaper at 12:10 row 6 column is a 4 and row 5 column 9 is also a 4, it is not an either or as you state.
He means it must be in one, the other, or both. It can't be neither. Although you're right, it could be both.
Really nice! Thank you for this video.
Excellent!
Thanks for this great lesson Simon. You have the ability to explain things very clearly!
The funny thing is, I found a completely different second Sashimi Finned X-Wing than your second Sashimi Finned X-Wing. I looked in columns 4 and 9, which eliminated the three from column 6 row 8...
Excellent video. Several great concepts and techniques presented. One question. You haven't mentioned removal of candidates in the base row of the two skyscrapers. Since the puzzles collapse, perhaps it is a mute point, but in addition to removal of the candidates due to the sashimi (aka tops of the skyscraper), I assume any extra candidates in the base row could be eliminated just the same as if it was a simple x-wing. Correct?
Why do you never consider 1/3 in Col4 Row2 ?
How do you know for X wings whether to eliminate candidates from the rows or columns?
Both. But in the first place, the x wing should be derived from a lack of candidates either in the rows or in the columns, so just remove candidates from the direction that was not involved at first.
Could you please put the link to the puzzle for us to try? Thanks!
In you example you used the threes in c7 and c9. There is a similar patten using the two threes in c4 and c9. So why use c7 and not c4? Would it produce the same result?
Simply stated, you brute force it. As to uniqueness. What is unique to R8, C6 ? It is the only square in the grid with 1, 2 , and 7, there is another one that is unique R5, C3 with 4 7 3, both have the number 7 and they are 7. Will this work all the time? I don't know.
What does 'mark 1' mean?
So why the 3s?
I don't understand the results of the first assumption with the 3s. There are two different 3s in column 7 that look eligible to me and they are automatically discard and I don't see why - apparently they ar3 so obviously ineligible it's not even worthy of discussion
In the second puzzle, if R6C1 is a 4, then R5C7 has to be a 4, as I understand. You say at 12:05 that either R6C1 or R5C7 must be a 4. I don't understand. Then I lost track.
I think the app I use requires skyscrapers to solve some of the puzzles.
This might be the lesson I needed. Now it's time to practice 😜
5.10 onward, you discuss sky scrapper on digit 3's in columns 6 and 9. Should you not consider the possibility of 3 in row 8 column being true?
It is a good question but it is very important to remember that the skyscraper pattern (or indeed the sashimi finned xwing pattern) ONLY results in an effect at the "top" of the skyscraper. ie we are NOT using it to remove the candidate 3 in row 8 column 7. Indeed you are correct in noting that it is perfectly possible for row8col7 to be the 3 in row 8... but consider the implication of this for the skyscraper: if row8col7 is a 3 then both row3col6 AND row2col9 are 3s BUT this doesn't affect the conclusions we were able to draw regarding the skyscraper being able to eliminate 3s from row2col4 and row3col7. ie the skyscraper is saying that either r3c6 or r2c9 is a 3 OR both are 3s - either way we get to eliminate from the squares mentioned. I hope this makes it clearer?
@@CrackingTheCryptic thankyou for the explanation.
I'm still confused on how it's an either-or relationship with those threes in rows 2 and 3. Why can't they both be 3's?
Because those are the only two boxes in column 6 and 9 that can contain a 3 - pause at ua-cam.com/video/EI714JZ0cqg/v-deo.html and look
I didn’t get it at first. I was thinking of it still as an X-wing technique. Rewatch it, that’s all I did, sometimes things make a bit more sense 2nd time round.
@C0mmand3r27 Exactly! I have watched more than one explanation of the skyscraper technique, and for some reason they all leave out this crucial point. They tacitly state that there is an either-or relationship there, as is true in the case of an X-wing. But there is NOT an either-or relationship between the two 3s at the top of the skyscraper. There is an either or BOTH relationship. Although this does lead to precisely the same effect as an X-wing, the fact that they do not specifically mention this nuance between the skyscraper and the X-wing IMHO shows a lack of thoroughness in the tutorial approach. It confused me too.
The second position is trivial: Column six has two '7's. The bottom '7' can't be a solution because it would leave the 1s, 2s and 3s in Columns 4 & 6 in a 'closed' 'ladder', there's no unique solution.
The first position fails to mention a third column with two '3's in, column 4. So how do we choose? Does it matter? No acknowledgement made.
On the subject of these mechanical approaches, how would we know when to apply them? Maybe a puzzle is half resolved, and this may unlock the rest? Or do we fill in the whole thing before starting this process?
I use the Easybrain App, on Expert, and have been for a while. It looks like there are three different puzzles being used, they yield in different ways, and my times reflect it.
To be clear, any single puzzle has over 2.5 x 10e15 variations that are "topologically similar", meaning you can transform the puzzle in that many ways, and the solution is the same. List below if you want to check. (Sorry for the phrase, it's all I can come up with!)
My question is: "Am I doing the same puzzle each time, or are they genuinely different"
My check will be to record the number of given numbers in each box, the numbers will stay the same whatever their order. Clearly the total will also be a constant.
Does using a mechanical approach give faster times, or just reliability of outcome?
Anyway, thanks to the authors, I will be more careful in future to look out for these offsets to the pairings.
>>>
Substitutions by number: Clearly every number can be switched with another and not change the puzzle; there are 9! ways to arrange nine numbers.
Whole puzzle transformations: The whole puzzle can be rotated into four positions and reflected in the diagonal and up/down axes; that's 4x4x4.
Box transformations: 2 rotations and 4 reflections can be applied to all the boxes individually, another 8.
Row/Column re-ordering: Every row can be shuffled within the box rows 6 ways, and the box rows also shuffle 6 ways, columns similarly, that's 6e8
So that's: 9! x 2e9 x 6e8 = 3.1 x 10e14
(edited)
Which sudoku software is this?
Surely, you are showing the same example. Don’t you mean the potential 1 and 3 in C4R2 for the other example? If not then I don’t understand the logic... That’s not unusual, though.
nice......
What App are you using?
I don't see the very first bit of logic with the 3s
I see two other squares under the 6 in column 7 that look eligible to me - why/how can we assume row 9 column 2 is a three? I have worked these puzzles before - am I really just bone crushingly stupid?
But can’t neither be true