📕Get my FREE Solving Guide that will help you solve over 80% of all Sudoku puzzles🧩to include NYT Hard👉👉www.buymeacoffee.com/timberlakeB/e/125822 Timestamps 0:00 Intro 00:22 It’s Solving Time 01:05 World’s Hardest Sudoku List 02:16 Trick #1 05:49 Symmetrical Version of Tridragon 06:30 Trick #2 10:24 Continuing Solving Original Puzzle 13:24 Advanced Strategy #1 15:50 Advanced Strategy #2 17:10 Advanced Strategy #3
@6:10 Like in math, commutative property doesnt change the result. So that I can write A*B=B*A or rearrange the sudoku puzzle to look a bit differently, as long as this is the same puzzle, then it doesnt matter if you move rows or columns around to make it easier to see. What you did to this puzzle, it is the same puzzle as you were given. Solving B*A faster than solving A*B is perfectly fine.
18:27 Also, we now know that the lower row of the middle right box contains the numbers 2, 8, and 9. Therefore, counting across the row, that leaves one number which is un-accounted for, which must be in the 1st column of the lower row of the center box - which is 3.
Excellent video - your explanation of the scyscrapers now makes sense to me where it didn't before. 2 rows with only two options, 2 in same column, 2 elsewhere (pink) wherever pink see each other can not be the value.
they say you must be a egg head or a bit dum if you do sudikos but its funny when you get a number in the right square the thing is there is only so many options so you can easily work it out
You don't really need to re-factor the puzzle at all though. You can just make the rule that the 3 589s need to be on different rows and different columns. Wouldn't that yield the same result?
I was certain that this featured the same feature that an earlier puzzle featured a while ago: three digits 589 arranged so that they couldn't fill all their cells without colliding. Like the earlier puzzle, one cell contained a fourth option that saved the puzzle. I had to test carefully that all 589 combinations broke the puzzle, and I'm terrible at three colors. Once I placed that 4, I placed several other digits as well. I got sort-of stuck then. I centermarked the rest of the grid, and found two skyscrapers (in 5 and 9). I also found something that began as a 239 Y-wing, but required a chain to find a second 3, to eliminate a 3 from column 8 and give me 29 pair. I was still stuck. Finally, I bifurcated on the 58 cell R5C7. 8 caused collisions; 5 was the correct digit. 6:20 Yes, I recognize that switching rows doesn't change anything about the puzzle. I suspect that one who notices that doesn't really need to swap things in the first place. 15:50 I missed that second skyscraper in 5s. Had I found it, I might have avoided the bifurcation. The bifurcation cell was one of the base cells of the skyscraper. 17:40 Better still: the cell I bifurcated on was the cell you solved using remote pairs. (The first skyscraper removed the 9.) I tried remote pairs earlier, but got nowhere.
Love the swapping of rows, columns and block rows or block columns. I'd say go for it, but since I don't think this is easy to do with current tools of on-line puzzles, then it is too much trouble. I personally don't like "chains", too much trouble to decide when one must look for a chain - same with coloring.
The 589 pattern looked similar to what I’ve seen in Loki and other tridagon puzzles, except for the columns being reversed. I knew I could solve if I made them look like the same pattern as Loki. Does that help?
1) The basic strategy 2) Locked pairs or locked triplets, etc. 3) Counting to account for all possible numbers across a row, column or box 4) Counting all possible numbers in each cell to account for all possibilities/Accounting for what numbers are NOT possibly - therefore, there is only ONE place where a number IS possible 5) X-Wings 6) Bi-Furcation
I solved this with a tri-oddagon, skyscraper, a finned x-wing and found an XYZ wing too. Can’t remember exact order. I didn’t find any useful remote pairs, but I think I eliminated a 5 in some other way. Took a while, but got there in the end! Intrigued to watch your video now as it looks like we had different solves, and keen to learn still!
thank you for your video! answering the question: of course it is ok to use symetry, btw I find it easier to look for the tridagon first and then (I often mix them up )do the row or block exchange to verify that they really occupy a "diagnoal` I guess that will help me a lot
@ If you cannot make any sort of break in then it’s worth looking if symmetry can help. One thing I look for are similarities in the placement of the givens in rows and columns, plans even blocks. If swapping then seems to make certain patterns easier to see, then you can consider it. Hope that helps.
Sudoku Joy calls the skyscrapers Fish patterns. But Their uniqueness test where you have a rectangle with say 36, 36, 36 and 346 where the first two 36s are in one block and the 36 and 346 are in another block making a rectangle - one can eliminate these when they pop up in sudoku joy, but if you look at the puzzle when it is solved, many times, there will be violations of the uniqueness test. So I'm not sure how they don't have errors. Any thoughts there? What I mean when I say they pop up is that as one works on filling in pencil possibilities, one sees a potential uniqueness violation. But if you just look for a potential violation where 3 of the 4 corners are filled in, and you fill it in with a non violating number, you'll break the puzzle.
First fill in the 578s, then the column switching comes naturally for those who has watched Loki. Switching is a nice technique, only that one needs to switch back after solving the puzzle.
To solve a puzzle every "trick" can be use. The chain stuff that you are very good at. But this is not something that would use, because if hard for me to visualize. And yes!!! I knew it has something to do with the 589 triple! 🎉 To me: if 5 is in R9C1 we can't place 9 in box 4 or box 8. Then after 2 fives. I can see that, if 5 is in R8C4 we can't place 5 in box 9 or box 5. I know what a skyscraper is but sometimes is hard for me...😅 Thank you! 😎
If it helps, the way I visualize chains is by thinking of a pair as an input/output, so if I want to chain a 45, 57, 79, 49, i think of the 45 as a 4 input/5 output. So when I look at the next pair, I see it merging with the 57, so 4 inputs to output 7, which merges with the next in the chain of 79 making 49, which merges with the next in the chain of 49 to make 44. That means that any cell seen by the first cell of 45 and the last cell of 49 cannot contain a 4.
Maybe you shouldve started with triplets before swapping the columns, so ppl who have issues visualising it would understand step by step connection between different methods (3D and CS in this case)
there's a faster way to solve. at 15:45, there's another skyscraper at the sixth and seventh columns. if you look at that, you'll realise that 5 can't be in r4c6, because that would mean that there's a 5 at r9c7, meaning there's a 5 at r4c8. but that can't be, since there's already a 5 in row 4. therefore, the 5's are in r5c7 and r9c6, and from here on it's smooth sailing
Centermarking the heavy houses, I spotted the trivalue collection immediately without isomorphism, probably because you did Loki so recently. Then, I'm ashamed of myself. No amount of staring revealed the skyscrapers, and I got your help on the first one. The second one was obvious once I saw the first one. Then I didn't spot the remote pair, but used an XY chain on the 89's to put a 3 in R6C4.
I think we are somewhat used to a puzzle collapsing after you get through the hardest strategy, but this one still had some fight in it. Thank you so much for watching.
What I did to get 4 is just that all of the 589s are staring at each other so I kind of did something similar to that of unique rectangle to get 4. I didn't finish solving yet but I thought I'd share my own evaluation.
Isn't there an easy 3 in row 2, column 4? Then there are lots of 589s, and row 1 column 1 is one of {1,5}. Then you get the 4 in the middle block, and the rest of the puzzle basically solves itself.In short: I'm confused as to how this puzzle gets such a difficulty rating - even without the column swaps you did!
I can tell you that a trivalue oddagon pattern will cause a computer solver to rate the puzzle as extremely difficult, but a human can notice the pattern quite easily by using the tips I showed in this video. I am not sure if I follow your first question, though. There already is a 3 in the block you indicated. Can you explain further?
@@SmartHobbies Before making any other moves, there is a 3 in both rows one and three, as well as a 3 in both columns 5 and 6. The only possible placement of 3 in the second block that is row 2, column 4. Certainly to start there is no 3 there?
@@marknandor784 The second block already has a 3 in it (row 3, column 6). The 3 in the second row has to be in the 3rd block, and the 3 in column 4 has to be in the 5th block.
I did take a shot at this puzzle, and found what looked like an oddagon, so I plugged in a 4. That gave me some progress, but now stuck with a puzzle that appears unsolvable. The video asks for our opinion on this type of puzzle, and I would vote that it should not be legal to have to restructure a puzzle in order to solve it.
You made the right call with the 4, Brad. The puzzle is still not easy from there but is manageable if you know some advanced strategies like skyscrapers and remote pairs. Thank you for sharing your thoughts on rearranging the puzzle.
Restructuring the puzzle isn't required to solve it. The same logic that determines that the oddagon formation cannot be solved with just 3 numbers can still be applied without swapping columns around. The rearrangement just helps to make it more recognizable.
Just re-watched that part of the video… Now I understand it! It is similar to X-Wings, but not as symmetrical - one side/base is on different rows… Thanks.
I don't see the point in swapping the rows and columns, if you don't already know the pattern is there you're just randomly refactoring. I can see scanning for a sort of L of boxes with triples in different rows and columns per box to know that they look into another box and restrict the triple from falling entirely in different rows and columns in that box.
I agree that swapping is not entirely necessary for this solve. Some solvers only recognize the trivalue oddagon pattern when it is arranged a certain. I was attempting to show how you could use symmetry to make the pattern look more familiar and emphasize that many other extreme sudokus can be solved with symmetry. Are there any strategies in particular that you would like to learn more about?
This took me about half an hour, while eating dinner, so I don't think it's that hard. Swapping columns and rows, etc., is cool. I'd move the blank nine square at bottom right to the middle in two swaps.
@@SmartHobbies I don't have the software to move row, columns, etc,. about, but I some of the toughest puzzles can be cracked by going after the hardest block, like that empty one. I solved the puzzle using the other strategies, before I played the part of the video that explained the trick of exploiting two pairs or three triplets of missing numbers, so those I knew.
@SmartHobbies I understand that there's an urge to explain every little thing about your approach, I have a similar tendency, but one must realize that explaining to someone is always a trade off between several things. One would have to balance someone's interest in the explanation with how much detail they know. So one can avoid repetition, redundancy and dwelling on indirectly related facets of the topic at hand. Those would be my suggestions.
📕Get my FREE Solving Guide that will help you solve over 80% of all Sudoku puzzles🧩to include NYT Hard👉👉www.buymeacoffee.com/timberlakeB/e/125822
Timestamps
0:00 Intro
00:22 It’s Solving Time
01:05 World’s Hardest Sudoku List
02:16 Trick #1
05:49 Symmetrical Version of Tridragon
06:30 Trick #2
10:24 Continuing Solving Original Puzzle
13:24 Advanced Strategy #1
15:50 Advanced Strategy #2
17:10 Advanced Strategy #3
@6:10 Like in math, commutative property doesnt change the result. So that I can write A*B=B*A or rearrange the sudoku puzzle to look a bit differently, as long as this is the same puzzle, then it doesnt matter if you move rows or columns around to make it easier to see.
What you did to this puzzle, it is the same puzzle as you were given. Solving B*A faster than solving A*B is perfectly fine.
Commutative Property. I love the math analogy. Thank you so much for sharing. 😊
18:27 Also, we now know that the lower row of the middle right box contains the numbers 2, 8, and 9. Therefore, counting across the row, that leaves one number which is un-accounted for, which must be in the 1st column of the lower row of the center box - which is 3.
Excellent video - your explanation of the scyscrapers now makes sense to me where it didn't before. 2 rows with only two options, 2 in same column, 2 elsewhere (pink) wherever pink see each other can not be the value.
I am glad you found that helpful. Are there any other strategies that you are looking to learn?
and if I may add: Termes are such lifesavers (tips of course how could I have missed that)
they say you must be a egg head or a bit dum if you do sudikos but its funny when you get a number in the right square
the thing is there is only so many options so you can easily work it out
@ 😄
You don't really need to re-factor the puzzle at all though. You can just make the rule that the 3 589s need to be on different rows and different columns. Wouldn't that yield the same result?
It would Simon. Thanks for pointing that out. 👍🏻
@@SmartHobbies If you really wanted to thank me, you could pin my post. 😁
I was certain that this featured the same feature that an earlier puzzle featured a while ago: three digits 589 arranged so that they couldn't fill all their cells without colliding. Like the earlier puzzle, one cell contained a fourth option that saved the puzzle. I had to test carefully that all 589 combinations broke the puzzle, and I'm terrible at three colors. Once I placed that 4, I placed several other digits as well.
I got sort-of stuck then. I centermarked the rest of the grid, and found two skyscrapers (in 5 and 9). I also found something that began as a 239 Y-wing, but required a chain to find a second 3, to eliminate a 3 from column 8 and give me 29 pair. I was still stuck. Finally, I bifurcated on the 58 cell R5C7. 8 caused collisions; 5 was the correct digit.
6:20 Yes, I recognize that switching rows doesn't change anything about the puzzle. I suspect that one who notices that doesn't really need to swap things in the first place.
15:50 I missed that second skyscraper in 5s. Had I found it, I might have avoided the bifurcation. The bifurcation cell was one of the base cells of the skyscraper.
17:40 Better still: the cell I bifurcated on was the cell you solved using remote pairs. (The first skyscraper removed the 9.) I tried remote pairs earlier, but got nowhere.
Sounds like you were on the right path for most of it, John. Congrats on solving it all the way.
Love the swapping of rows, columns and block rows or block columns. I'd say go for it, but since I don't think this is easy to do with current tools of on-line puzzles, then it is too much trouble. I personally don't like "chains", too much trouble to decide when one must look for a chain - same with coloring.
Thanks for the feedback! I agree about swapping being hard to do with paper and pencil and certain apps.
06:19 Since I always does sudoku in magazines, swapping columns/rows aren't feasible.
Thank you for your feedback. That's a great time for this puzzle. Have you seen these strategies before?
@@SmartHobbies Not really, since the time periods I do Sudoku puzzles does coincidence with the time periods I'm also not connected to the internet.
How did you decide which columns to swap? Trial and error or was there something that triggered you to know those were the ones to swap?
The 589 triples helped to locate the columns
The 589 pattern looked similar to what I’ve seen in Loki and other tridagon puzzles, except for the columns being reversed. I knew I could solve if I made them look like the same pattern as Loki. Does that help?
You can't use symmetry on paper. This feels a little bit like cheating
It does feel like something beyond the rules of Sudoku.
What techniques do you like to use to solve Sudoku?
@@SmartHobbies well, skyscraper or matching pairs for example. But I have to say that was a very difficult puzzle. Though I do like a good challenge !
Graph paper and a lot of patience. Maybe multiple colors.
@@histrion2some people can swap in their head.
1) The basic strategy
2) Locked pairs or locked triplets, etc.
3) Counting to account for all possible numbers across a row, column or box
4) Counting all possible numbers in each cell to account for all possibilities/Accounting for what numbers are NOT possibly - therefore, there is only ONE place where a number IS possible
5) X-Wings
6) Bi-Furcation
I solved this with a tri-oddagon, skyscraper, a finned x-wing and found an XYZ wing too. Can’t remember exact order. I didn’t find any useful remote pairs, but I think I eliminated a 5 in some other way. Took a while, but got there in the end! Intrigued to watch your video now as it looks like we had different solves, and keen to learn still!
Very nice Paula. Glad to hear you were able to solve this one with all those strategies you’ve learned. 😎
thank you for your video! answering the question: of course it is ok to use symetry, btw I find it easier to look for the tridagon first and then (I often mix them up )do the row or block exchange to verify that they really occupy a "diagnoal` I guess that will help me a lot
Thank you for your feedback and tip. That is helpful. Have you solved many puzzles before with symmetry?
But how do you recognize that symmetry may help? Thanks.
@ If you cannot make any sort of break in then it’s worth looking if symmetry can help. One thing I look for are similarities in the placement of the givens in rows and columns, plans even blocks. If swapping then seems to make certain patterns easier to see, then you can consider it. Hope that helps.
Sudoku Joy calls the skyscrapers Fish patterns. But Their uniqueness test where you have a rectangle with say 36, 36, 36 and 346 where the first two 36s are in one block and the 36 and 346 are in another block making a rectangle - one can eliminate these when they pop up in sudoku joy, but if you look at the puzzle when it is solved, many times, there will be violations of the uniqueness test. So I'm not sure how they don't have errors. Any thoughts there? What I mean when I say they pop up is that as one works on filling in pencil possibilities, one sees a potential uniqueness violation. But if you just look for a potential violation where 3 of the 4 corners are filled in, and you fill it in with a non violating number, you'll break the puzzle.
TriDRAGon, that you dragged the columns around. Very clever.
😀
First fill in the 578s, then the column switching comes naturally for those who has watched Loki. Switching is a nice technique, only that one needs to switch back after solving the puzzle.
I agree. Have you done much solving with symmetry before?
To solve a puzzle every "trick" can be use. The chain stuff that you are very good at. But this is not something that would use, because if hard for me to visualize.
And yes!!! I knew it has something to do with the 589 triple! 🎉
To me: if 5 is in R9C1 we can't place 9 in box 4 or box 8. Then after 2 fives. I can see that, if 5 is in R8C4 we can't place 5 in box 9 or box 5. I know what a skyscraper is but sometimes is hard for me...😅
Thank you! 😎
Awesome. Glad you saw it. 😎
If it helps, the way I visualize chains is by thinking of a pair as an input/output, so if I want to chain a 45, 57, 79, 49, i think of the 45 as a 4 input/5 output. So when I look at the next pair, I see it merging with the 57, so 4 inputs to output 7, which merges with the next in the chain of 79 making 49, which merges with the next in the chain of 49 to make 44. That means that any cell seen by the first cell of 45 and the last cell of 49 cannot contain a 4.
@@GeldarionTFS Whoaaa! This is how a smart brain works! Haha
You explained very well! Thanks for that! =)
When setting I often swap columns to put 3 in the corner
Love it!!!😊
Maybe you shouldve started with triplets before swapping the columns, so ppl who have issues visualising it would understand step by step connection between different methods (3D and CS in this case)
Good point. Thanks for the feedback.
there's a faster way to solve. at 15:45, there's another skyscraper at the sixth and seventh columns. if you look at that, you'll realise that 5 can't be in r4c6, because that would mean that there's a 5 at r9c7, meaning there's a 5 at r4c8. but that can't be, since there's already a 5 in row 4. therefore, the 5's are in r5c7 and r9c6, and from here on it's smooth sailing
Nice job finding that Skyscraper! Thank you so much for sharing a quicker way to solve this.
Have you ever been on the Sudoku Player’s Forum before?
@@SmartHobbies thanks. and no, i haven't
@@ihaetschool3361 There are some smart people on there. I learned quite a bit about Sudoku theory from reading it.
Centermarking the heavy houses, I spotted the trivalue collection immediately without isomorphism, probably because you did Loki so recently. Then, I'm ashamed of myself. No amount of staring revealed the skyscrapers, and I got your help on the first one. The second one was obvious once I saw the first one. Then I didn't spot the remote pair, but used an XY chain on the 89's to put a 3 in R6C4.
I think we are somewhat used to a puzzle collapsing after you get through the hardest strategy, but this one still had some fight in it. Thank you so much for watching.
The goal of the puzzle is to solve it?, right... So it is OK by me... Stay safe Have a Happy Thanksgiving...J
What I did to get 4 is just that all of the 589s are staring at each other so I kind of did something similar to that of unique rectangle to get 4. I didn't finish solving yet but I thought I'd share my own evaluation.
Great observation. Did you try the rest of it?
@@SmartHobbies I failed. 😔maybe the next sudoku I'll win
@ I am sure you will. 💪🏻
Isn't there an easy 3 in row 2, column 4? Then there are lots of 589s, and row 1 column 1 is one of {1,5}. Then you get the 4 in the middle block, and the rest of the puzzle basically solves itself.In short: I'm confused as to how this puzzle gets such a difficulty rating - even without the column swaps you did!
I can tell you that a trivalue oddagon pattern will cause a computer solver to rate the puzzle as extremely difficult, but a human can notice the pattern quite easily by using the tips I showed in this video.
I am not sure if I follow your first question, though. There already is a 3 in the block you indicated. Can you explain further?
@@SmartHobbies Before making any other moves, there is a 3 in both rows one and three, as well as a 3 in both columns 5 and 6. The only possible placement of 3 in the second block that is row 2, column 4. Certainly to start there is no 3 there?
@@marknandor784 The second block already has a 3 in it (row 3, column 6). The 3 in the second row has to be in the 3rd block, and the 3 in column 4 has to be in the 5th block.
There's nothing wrong with switching numbers, rows, columns and blocks around. You could in principle just undo your switches when finished.
I did take a shot at this puzzle, and found what looked like an oddagon, so I plugged in a 4. That gave me some progress, but now stuck with a puzzle that appears unsolvable. The video asks for our opinion on this type of puzzle, and I would vote that it should not be legal to have to restructure a puzzle in order to solve it.
You made the right call with the 4, Brad. The puzzle is still not easy from there but is manageable if you know some advanced strategies like skyscrapers and remote pairs.
Thank you for sharing your thoughts on rearranging the puzzle.
Restructuring the puzzle isn't required to solve it. The same logic that determines that the oddagon formation cannot be solved with just 3 numbers can still be applied without swapping columns around. The rearrangement just helps to make it more recognizable.
14:56 I don’t get it… Why can you solve and say that that cell must be a 5? Thanks.
Just re-watched that part of the video… Now I understand it! It is similar to X-Wings, but not as symmetrical - one side/base is on different rows… Thanks.
Just re-watched the video - now I follow the logic. Thanks!
You are welcome. Keep the questions and observations coming, JJ. I can tell you are on the path to becoming an excellent solver. 👍🏻
I don't see the point in swapping the rows and columns, if you don't already know the pattern is there you're just randomly refactoring. I can see scanning for a sort of L of boxes with triples in different rows and columns per box to know that they look into another box and restrict the triple from falling entirely in different rows and columns in that box.
I agree that swapping is not entirely necessary for this solve. Some solvers only recognize the trivalue oddagon pattern when it is arranged a certain. I was attempting to show how you could use symmetry to make the pattern look more familiar and emphasize that many other extreme sudokus can be solved with symmetry.
Are there any strategies in particular that you would like to learn more about?
A “three-column [or row] band” is called a “chute”.
Thank you for the tip. 👍🏻
automorphic transformat are pk for me. But don't work on paper.
You make a great point. Thank you for sharing.
Swapping is fine.
This took me about half an hour, while eating dinner, so I don't think it's that hard.
Swapping columns and rows, etc., is cool. I'd move the blank nine square at bottom right to the middle in two swaps.
Nice David. Thanks for sharing and pointing that out. Have you seen this strategy before?
@@SmartHobbies I don't have the software to move row, columns, etc,. about, but I some of the toughest puzzles can be cracked by going after the hardest block, like that empty one. I solved the puzzle using the other strategies, before I played the part of the video that explained the trick of exploiting two pairs or three triplets of missing numbers, so those I knew.
the funamenal trick it to have fun
😀
589 triples blocks 4 and 8 columns 3 and 4....
Great hint, Roger.
Lots of 589s through the left hand side of puzzle.
Solving by experience and not by logic is not fun
You make an interesting point. How do you approach your solving?
This is the slowest video I have ever watched
Some people have said that they listen to my videos to help them fall asleep. Is there something I could do to make this more interesting for you?
@SmartHobbies I understand that there's an urge to explain every little thing about your approach, I have a similar tendency, but one must realize that explaining to someone is always a trade off between several things. One would have to balance someone's interest in the explanation with how much detail they know. So one can avoid repetition, redundancy and dwelling on indirectly related facets of the topic at hand. Those would be my suggestions.
@@museruse1 Great point. I will consider that. Thank you.