The World’s Hardest Sudoku And The World’s Best Chess Player

Simon responds to a request from a viewer to solve the “World’s Hardest Sudoku”. We also look at what the future of Sudoku solving might look like at competitive level by taking a look, on the eve of the deciding game of the World Chess Championship, at how chess players calculate.

28 Comments

  1. It took me 90 minutes. Only once did i switch numbers when i was 70pct done.

  2. I just solved the sudoku by writing a computer program to do it. My poor laptop spent almost 2 hours going through all the possibilities to prove it's unique. The solution is: (Spoiler)8 1 2 7 5 3 6 4 99 4 3 6 8 2 1 7 56 7 5 4 9 1 2 8 31 5 4 2 3 7 8 9 63 6 9 8 4 5 7 2 12 8 7 1 6 9 5 3 45 2 1 9 7 4 3 6 84 3 8 5 2 6 9 1 77 9 6 3 1 8 4 5 2It took 2.75 minutes to find this solution, but 1.75 hours to show there isn't another one.

  3. When it comes to being able to visualize the board and the moves, I think Sudoku is actually harder than chess. There are 729 possibilities in 81 cells that comprise 27 overlapping sets (or nine arrays, if you're working with each digit separately.) And the variants (espcially jigsaw sudokus) are often pretty unpredictable. Even so, we might get there with classic sudokus, but I think we won't as long as the common notation uses the r#c# format. Using row and column numbers works for chess, because the pieces don't use number names. The older notation "Knight to Queen's Bishop two" used the names of pieces in two different ways. Algebraic notation eliminated that possible source of confusion. In Sudoku notation, when we use r#c#, or even when we assign columns letters instead of numbers but use numbers for rows, the possibility of a mental trip increases. I've played with notation and vocabulary kind of in isolation, but trying to come up with something that can't be misinterpreted. When I write down my last move as TLmr6, I'm saying that when you look at the Top Left Square (box) then go to the middle right cell it is a 6. But if I know it can only be a 5 or a 6, the notation is TLmr(5/6). Or if in the Top Left square I have limited the 6 to one row, I can write TLm?6, and if I know have only two possible columns I can write TLm(c/r)6 and know that I mean the six must fall in the middle row of the Top Left square, but can be in either the center or right cell. How that might translate to mental solving I'm not sure, but on paper you can get surprisingly far without a grid.

  4. super video. arguably the first one which will take Sudoku solving in a complete different dimension. would love to see more debate/ comments on this concept.

  5. I truly believe that the next step in sudoku mastery will not only be ability to keep the whole puzzle in your head, but actually the ability to solve it there, blindfold.
    I remember in one of your past videos Kota solved a hard sudoku from nikoli in 3:30. He were making no pencil marks except for a hidden triple in the very beginning. This makes me think he can keep those marks in his head.

    There is a Russian guy who claims he has taught his kids to actually see with their skin, not with their eyes (Yeah, sounds totally crazy, I know). He conducts classes on that and even runs a private school where kids are being trained in strengthening their visual memory (as a part of seeing-without-eyes training). He says a typical kid in his school can memorize a 10×10 table with 5-digit numbers in every cell – and that I believe.

  6. I'm a chess player, albeit far from the strengths of Magnus and his peers. I understand what you're saying but I'm not sure I agree with the sentiment that sudokus may be solved by chess grand masters. While both chess and Sudoku tick the boxes of logic that we so love, chess also encompasses a certain element of beauty which I find absent in Sudoku. I am however sure that a chess master who found Sudoku solving to be a nice pastime would probably excel. Keeping a Sudoku grid and a lot of xy chains in memory still is very unlike a chessboard position.

  7. Any FIDE 2000+rated player can play blind fold chess..A former word champion played 69 board blind folded at a time.good chess players are also very good sudoku solver .I am a FIDE instructor and also a sudoku player .I can solve rubic cube less than 30 seconds .we have to do mental excise and also physical excise to keep brain active in old age..you have to use your left hand and left leg a day and then use right hand and right leg another day to activate both side of your brain . You have to do lot of meditation for better result. We donot use our brain capacity . Everybody can play blind fold chess if they try sincerely . debasischakrabarty2@ gmail.com

  8. Adding the correct solution to a couple of cells lets Andrew Stuart’s solver finish the puzzle. I filled in A2 and A3 and it still took a great many steps and some of the more arcane routines. Brute solvers all get the same solutions and report that the solution is unique. If you give Andrew’s solver H7 as a 9 (correct) It still can’t figure it out.

  9. Big chess fan here too — been following chess for 30 years. That was an amazing feat by Carson.

    As far as Sudoku, I'm fairly new to the game and have only been playing it a little over a year. After the first few months I started graduating to the harder and harder puzzles. Then tried some "evil" or "fiendish" puzzles and realized I needed some more tools or techniques to solve these. Watched a bunch of tutorials and I think I've watched everyone of your videos at least once. As I was learning all about x-wings, XYZ wings, triples, quads etc., I would still attempt to solve some of the most difficult puzzles.

    I do the puzzles with pen and paper and pencil in the pairs, which I believe you call the Snyder notation. With only the pair notation, I find it’s sometimes quite difficult to spot the naked triples, and it sometimes requires a lot of grinding through each row and cell to spot these, especially when there are few numbers in that row or column. Not knowing all the various subtle techniques of Sudoku, I found myself using force-testing (FT) to test the implications of choosing one number of a twin pair or position, and trying to note the implications in my head in an attempt to make progress that way. I think it's a learned skill and after a while one gets better at this and you can keep quite a few number positions in your head that are implied by the choices you are testing.

    In my experience the results of FT vary considerably from … I'm getting nowhere here — I better get back to the traditional techniques, to quite simple and quick number resolves on very difficult puzzles that can make these very challenging puzzles seem easy.

    One of the problems with FT is that if you choose the correct number or position of the pair you are going to test, one can put half the puzzle in one's head and you won't find a contradiction or conflict. One begins to think hmmmm … maybe that's the right number. But unless your really talented like Carlsen, most people will run into a limit fairly quickly.

    Other problems include …

    — following a FT several numbers deep, you may resolve a number, but resolving that number still doesn't help crack the puzzle open … … back to the XYZ grind. 🙂

    — the forcing implication of the chain quickly runs out, and nothing is resolved as there are still 2 or more numbers that can be put in any open square at the end of the chain.

    If no number conflict is found, sometimes the best one can hope for is that some number of a pair that you have marked in pencil gets punted to the same position no matter which candidate you test with the FT. I find that this is quite frequently the result of a successful FT. Other times, there may still be simply too many open spots and possibilities on the grid to make progress this way, or, one simply ends up trying to hold too many number positions in your head and you reach your limit without any numbers resolved.

    In choosing numbers to FT, I'm always looking to see if there are any immediate numbers forced into positions, as many implication chains run out quickly. I suppose one could try and remember all the squares with 2 or more numbers, in then but this becomes increasingly difficult, as you would have to start choosing one of 2 secondary numbers in a chain and test each one of these in your head, and so on. This would become increasingly difficult.

    FT has become one of my goto Sudoku tools, but I think FT is just another tool in the Sudoku toolbox in addition to all the various techniques you have discussed in your videos. I think it is more useful on the most difficult level of puzzles, as even most of the hard puzzles can be solved with fairly straightforward techniques. Running a bunch of number positions in your head on simply a hard puzzle with no results can end up being a waste of time with no results, whereas straightforward techniques are a surefire way to get results and make progress. FT also makes for a good fallback strategy to try and make progress on a particular puzzle if you can't spot some other tactics like a naked triple, XYZ-wing, or hidden pair that help the solution of the puzzle along.

  10. I have come across some nice fiendish puzzles over at …

    https://www.fiendishsudoku.com/sudoku.html

    where simple force-testing (FT) works beautifully to crack open a difficult puzzle.

    You might want to look at the Aug. 24, 2017 Fiendish puzzle at that link. Be sure to click on the Fiendish tab.

    My FT solution for that puzzle follows. So, if you want to try and take a crack at this puzzle first, read no further. I think it is a good example of how useful sometimes even a simple FT strategy can be on a hard puzzle.

    ** solution

    Once you have filled in all the preliminaries of this puzzle, there should be a 2, 4, 8 pair penciled in the top right hand block. The isolated 6 in RC41 should also be filled in.

    In column 7, there will be only 2 positions left for the 6, R3 or R8. If you put the 6 in the R3 position, the 2,4,8 all get punted and resolved into their positions. If you place the 6 in R8, a 5 pair gets penciled in that bottom right hand block and forces a 58 pair in the top right block. Either way, the 2 and 4 get resolved in the top right block. This gets the puzzle going nicely.

    There is then a 69 pair in column 9 and follow up.

    Once you have followed through that, there will be another simple FT to get the puzzle going again.

    There should be a 25 pair in the bottom middle block and a 39 pair in row 7.

    At this point, in R7 there should be only 2 positions for the 2, C1 or C8. If the C8 position is chosen for the 2, it will punt the 7 in the right hand bottom block to row 9, but following the 2 chain will also try and force a 5 into that spot — so the 2 has to go in column 1 for row 7. After follow up there should be a 69 pair in row 9, and rest of the puzzle is routine.

    Hopefully your progression followed mine closely and my notes make sense.

  11. I've been aware of this video from an immensely talented friend of mine (Sun Cheran) for a while without quite fully understanding what was going on – I think the task is to fill, from memory, a nearly blank grid with a valid sudoku solution, subject to colour constraints as well.

    http://www.youtube.com/watch?v=DQq9wfJ_6aw&t=40m1s

    Incidentally I gave Cheran a copy of the 2018 Times grand final set of 4 whilst in Prague earlier this month. A little bit slow by her standards, but 17 minutes flat blew everyone else out the water!

  12. hi Sudoku Guys Please give a look and visit my channel regarding Sudoku Puzzle

  13. I'd like to see Magnus face Meruem from hunter x hunter at chess

  14. i solved this in 53 minutes. I was pretty suprised

  15. I'm am avid chess player, and I can understand the correlation between the two games. Prior to watching sudoku solving videos, I would solve the most impossible puzzles by doing the puzzle in my head (I would find two singles, and figure, for example, if this is a 5, this is a 4, and eliminates all other 4s in this row, leaving a 1 and 3, and 1 and 3 in this row, creating a naked pair or locked sets, etc, and then do the same for the other number) until I find an illogical entry. I've tried doing the pairings as the gentleman Cryptic does when he solves his puzzles, and have found it more difficult that way.

  16. One thing that came to mind, is: elite chess players can briefly look at a board from a past game and replicate it from memory with relative ease, but if they were presented with a board where the pieces have just been placed randomly, they faired no better at remembering the board than your average muggle. This suggests that it's something in the repeated pattern of real-game positions that they come across time and again, and the many restrictions of where the pieces can realistically end up, that helps them to remember the position, and not that they're memorising the contents of 64 squares, or even specifically the position of up to 32 pieces. They're able to chunk the position of the pieces into batches of established patterns.

    Maybe I'm wrong, but that doesn't seem like something you can really do with a sudoku grid. There aren't any established patterns that dictate the shape of the grid or positions of any of the numbers. You would just have to memorise the content of 81 squares…. which seems tricky…

    I vaguely remember there was a girl who 'solved' a sudoku blindfold on the Chinese tv show 'The Brain' (最强大脑), but if I remember rightly, she actually rather formulaically created a solution from a virtually empty grid with just a couple of numbers in it (so countless possible solutions). Mind you, they do have all sorts of freaks on that show that could probably actually solve blindfolded… I don't know how they do any of the crap they do…

  17. Hey,
    I saw a video somewhere that claimed that you need 17 digits, to solve a sudoku.
    This one has 21… So how can this be the hardest sudoku ever?

  18. I am not sure if it will go that way, though you cannot exclude pure brilliance. But a chessboard is not in a random condition like a Sudoku grid is. So I think that is one reason, you won't see anybody just remembering the grid/number layout of a Sudoku.
    I don't remember where I saw it, there was some tv-show about chess players trying to remember the position of the pieces on a chess board, and if the pieces where in a naturally played position, the players had no problems remembering how it was, but if it was random, they were as lost at the rest of us (yes I mean me).

  19. I just solved this a few hours ago. Took about 2 months since I started trying (with a very long break because I got overwhelmed). Had been waiting to watch this video because I wanted to solve it on my own. I'm planning on making a video on my approach, maybe in a week or 2 (I speak Spanish and plan to make a video in both languages) it would be awesome if you watch it and give me your professional opinion on my approach

  20. Sudoku should remain a game for average people like us. The exceptionally smart people need something exceptionally hard to interest them. That exceptionally hard wud frustrate us average people to death. There are more of us than them. Can we have a game moderately hard but not extremely hard PLEASE? It is nice to know that as we continue to play Sudoku, the game injects a nice feeling of achievement. That is motivational to go on and solve more Sudoku. I think playing chess is the same. Not too many people can play chess in their head. Is it necessary? In my opinion NO. Just being an average guy, is enough.

  21. Hello, good day. Well, I solved it. It was no fun. Most of all it was guessing and luck, I did not have to do all the series, I only developed half of the initial 32 candidates. There were 22 pages of notebook. I spent about two hours a day for two weeks. Well thank you and excuse my english.

  22. i thought magnus carlsen himself is gonna solve the worlds hardest sudoku

  23. These puzzles are frequently solved by elimination or contradiction. If you can prove that one of a pair of some sort can't be then it must be the other.

  24. maybe a stupid question…. but what makes a classic sudoku hard to solve? is it only the way how the given digits are placed in the grid?

  25. I wonder if this has ever been re-looked at with the new understandings of various set theories etc.

  26. I am quite familiar with the blindfold chess feats. Any grandmaster can play blindfold chess, even against comparable opponents, without any loss of skill, and even under timed conditions. Any of the world's strongest players can play several blindfold games at the same time, but typically they do this against weaker opponents. Under timed conditions, they can only handle a few opponents, but that is due to limitations of the interface (the system handling the information flow between the board and the player).

    I have seen a video where Magnus demonstrated that he is able to recall in some detail not only every game he has ever played, but also any important game he has ever seen.

    I have been trying to correlate these facts with what I see Simon and Mark do. It's not as obvious as it is with chess, but it's clear that Simon and Mark do hold the entire grid in their active memory. Simon solves more slowly, and rarely makes mistakes, but we know that he does see into the future. Mark also sees into the future, but he makes (and corrects) enough mistakes that we have enough data to be able to say that he also retains the past (the history of the solution) in his active memory.

  27. Watching this older video and I'm appalled at seeing so many digits

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