I love it how we start with esotheric techniques, then we casually mention "8 swordfishes" regarding a previous puzzle, and then we still explain how X-wings work ❤️
He stated that he had trouble seeing his keyboard. Perhaps he thinks he's not a "gamer", and thus cannot be bothered to get a gaming keyboard, which has *tadaa* lights IN the keyboard.
@@Nighthound That's pretty good; I never reached higher than low diamond myself, and that was waaay back in WoL when the game was slower paced than now. Someone needs to make a starcraft based sudoku, Simon would be all over it :D
HOLY SUDOKU! That logic you show for the Tatooine puzzle is amazing. Now I have to start looking for that, just to see if I can find them and figure out how to use them properly. Thanks for teaching us something honestly new.
I solved this without any wings or swordfish - here's a simplified version of my solve path: - fill in all of the 1s. - fill in all of the 9s. - fill in the 37 pair in box 4. - take a look at r4c7. If this is an 8, it forces the 8 in box 9 to go in r7c8, which forces the 8 in box 7 to go in r8c3, which leaves no place for an 8 in box 4. Therefore, r4c7 is not an 8. - since r4c7 can't be an 8, it's effectively a naked single now; it must be a 4. - the rest of the puzzle can be solved with no advanced techniques.
got a simple solve with 1's and 9's. got the hidden pairs. and then i found out that 2 only had 2 options in box 9 by a bit of experimenting with where they could go. and then that forced all the 2's intoplace and the rest came after with no advanced techniques
Had a very similar path (went 1-9 with detours when I spotted easy things). Took me 10 minutes taking it easy, indeed without any advanced techniques. I think it's the first or maybe second time I've beaten Simon's solve time :D
Bingo. I used the 8's too. Force testing the 2 positions for the 8 in the bottom right hand block gives the same result -- RC47 cannot be an 8, so it's a 4. You also end up with a 78 pair in the middle RH block.
I also solved it similarly, 11:28 which is blazing fast for me since I like to take my time on non-very easy puzzles, but I don't count it much since the intention of the solve in the video was to demonstrate the method for teaching purposes, not really to show the simplest path, and I'm also not narrating my steps. I can see myself going on 2 hours with that method and not necessarily being finished....sometimes 45 min will go by and I still might not have spotted one thing needed for an advanced technique, which pretty much never happens with Simon or Mark.
I need to add a shout-out to Trevor Tao, whose video on Tatooine Sunset was the subject of Tom's post. The logic is (I think) equivalent to the MSLS structures as Sam pointed out, but it's a lovely visualization of the solve. (Also need to shout-out forum poster SpAce, who was the first to solve this when I originally posted it, and used one massive beautiful MSLS to do most of the work.) Now to try Macrovius' puzzle. :)
Trevor Tao's video is great! The link is here: th-cam.com/video/blH0aRUERy0/w-d-xo.html I'm glad Simon put a brief explainer of the equivalent MSLS in this video - as he says, it is perfectly gettable once you have a rough idea of what you are looking for, and when you might want to be looking for it. It reminds me of the Times sudoku championship back in 2007, which featured plenty of X-wings and Swordfish. I had realised that the puzzles were going to need those techniques and so was on the lookout for them from the start, whereas my impression was everyone else trying to speed solve them was having to guess. How relevant MSLS will really be under time pressure is yet to be seen - my guess would be only really to get started on a tough puzzle. The various Tatooine puzzles are good candidates here as it's quite easy to see where to look at the start of the puzzle, and I think it might improve on simply guessing (not that Mark was very slow in his video I have to say!)
@@tomcollyer641 I am definitely not a speed solver, so I can't comment on whether it would be used in competition if the opportunity presented itself. I don't know how likely it is for such a puzzle to show up in the first place though, unless it is a deliberate move by the organizers. It's a key tool to solving *some* truly monstrous puzzles for which many computer algorithms can't find a logical path (e.g. Arto Inkala's infamous Escargot has an MSLS which greatly reduces the difficulty, though it is still hard). But otherwise, I don't know how much time it would save outside of the odd "fishy" puzzle designed around an MSLS-type structure. But hey, if there are any competition organizers out there looking for such puzzles, I've got you covered! ;)
I really struggle to see swordfish patterns. I ended up doing this with a colouring technique. Once you have the same digit narrowed down to 2 cells in a lot of boxes you can often create two scenarios for the dispositions of that digit round the grid and then remove that from any cells you had it pencil marked in that aren't coloured one of the colours. Sometimes when you do that the same cell in one box is both colours so you can place it which is nice. I guess that is effectively just the "long way round" of a sword fish when you get right down to it. :). I used that to deduce that no matter where the 7 was in box 4 the 7 in box 8 is ALWAYS in r9c5. After that I spotted that an 8 in r6c3 would create a contradiction forcing 2 8's into row 7. And from there it wasn't too hard. I wish I could spot the swordfish though, it's so much more satisfying I imagine... But I still managed to solve it in about 25 minutes. :)
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@ Simon & Mark: 3 years ago, would you have ever thought that your names would be mentioned in a sentence that contained the phrase "... the world's most popular Sudoku channel"? Well done! A great development and certainly a lot of work! Thanks a lot for this...
Early biplanes had two struts between each wing with torsion cables crossing between them to form an X between the two wings. This is where the term "X-Wing" comes from in Sudoku. The Fairey Swordfish was a biplane that had 3 struts between the wings and thus an X-Wing using 3 digits is called a "Swordfish".
Simon! I just finished one of the 5* puzzles from your app in under 30 mins! (Personal best) Your enthusiasm for Sudoku totally convinced me to subscribe and download.
Great work. Do note though that the number of stars does not necessarily correspond to difficulty. Yesterday it took me about 40 minutes to solve a 5 star puzzle and immediately thereafter I solved a 6 star puzzle within 12 minutes...
OK, I haver made my pledge. Anyone who watches this channel ought to make a pledge likewise. May I suggest an electronic version of the book as a stretch goal, including the on line software to assist in solving the puzzles?
Just pledged too, excited to see that we're already breaching the first stretch goal! The electronic version is a great idea, especially considering we would only get our hands on the physical book sometime in Sept 2021 -- whereas an electronic one could be 'handed' out earlier, and still be edited when/where needed.
I watched the video yesterday, tried to solve it 3 times today. Two times I had errors and restarted... Now I finaly made my first puzzle from this channel. BTW the X-wing and the sordfish are cool and helped me a ton in this one. I like to color my sudoku Thanks Simon, Great channel! Rami from Israel
I used Phistomephel's theorem when I got stuck on the T-Rex. Just color in the corner cells and their corresponding digits in the center frame to see what's left and how many of a particular digit can appear in the cormers/frame.
I agree the technique you used was far more elegant than what I did. Filled all candidates and eliminated conflicting cells. But I did finish in 11 mins
Downloaded your app yesterday and have gotten through the first 6 puzzles so far. Really enjoying it. Nicely done. As an aside, whoever ranked puzzle 41 as a 1-star difficulty has been sniffing glue. Cheers from across the pond!!
I only used 1 swordfish and it was the weirdest ever ;) Noticing how the 2-3-7 triple in column 1 interacted with the 2-5-7 triple in column 9 I evaluated what would be the result for both possible options in r5c9 and I found that r9c8 was actually restricted to either 2 or 3. This places the 7 in row 9 in column 5 and this creates a very interesting partial swordfish on 7s in columns 2, 6, 8 and 9 in which r8c9 is a naked 7.
Took me 33 min today, which is a fine time for me. My key observation was that the way that 8s bounced around the grid, made them more restricted than they at first appeared. This let me resolve a pair of 4's and the rest quickly fell into place.
Just when I thought I was going to be reminded that a snake cannot touch itself, we get a classic😆. As always a great job done by Simon on another tricky puzzle!!!
Not sure if the Empty Rectangle on 5's at the end was intended, but it's what I used - alongside a school of Swordfishes - to solve the puzzle. Nice Classic!
Please, if you're reading this, consider making a stretch goal to include an online version (possibly with the same software you use) for the kickstarter book! I would love to make a pledge and receive the puzzles, however, I make way too many marks to work complex puzzles on paper. It gets super messy and overwhelming. Thanks, and keep up the great work!
1:05:50 before watching the video. Despite the time, very proud of myself for having found the logical path to this one! Rather than bifurcating like Tatooine Sunset. Great puzzle, devilishly tricky.
I got a bit lucky on my solve today by considering r4c7. At 11:00, Simon has reduced this cell to 4 or 8. An 8 is impossible since this excludes an 8 from box 4. Using this one gets a solution that doesn't need any x-wing or swordfish.
27:12 Finally in the same ball-park as Simon on a fairly difficult normal Sudoku! Route was a bit different, but not by much. The 2's 5's and 7's seemed to hold the key for me. And once the key is turned, the puzzle unwinds in a flash. Zap! Just like a T.Rex attack! Thanks for a super puzzle. :)
Beautiful puzzle, we should have more of such classics. Though again failed to identify the swordfish and used elimination in box 6 with 25 pair to solve it. Watching simon crack it was again a treat!!
23 minutes but using the technique Mark used to solve Tatooni Sunset; fill in the easy one and nines, then a few more pairs ...then used the 37 pairs in box four to just pick one and see if it breaks the puzzle. Chose 7, marked the starting cell, and did about 20 steps til it broke. Unwound (easy w online game) and tried the 3... solved simply from there. Now, really not elegant and not a fun way to solve...but is a technique I learned last week!
If you fill out the options in first and last column after 1, 9 and 6 and look for 7s round the grid, you see one pattern fits and other clashes. Easy solve.
Nice puzzle. I used a different swordfish on the 7s, but the impact was the same. I had placed some other numbers earlier than Simon, which meant that the end fell apart even quicker. I love some of the variants we've been treated to lately, but I still enjoy the purity of a well-crafted classic. Regarding the kickstarter, I'm glad you seem to have already chosen the original Miracle. I hope the recent two murder puzzles will feature too, particularly CluedoKu with its original artwork. Tatooine Sunset should also feature, if only for swordfish practice. To pick the puzzles solved by Simon, you should probably just count the number of times he says "beautiful" or "lovely". If possible, I'd love it if you could get the setters to write a few lines about their puzzles (possibly in an appendix with the solutions; to avoid spoilers about any special logic they built in).
At 6:35, he mentions another example using 3,4,5,6 in the Tatooine Sunset puzzle but I wasn't able to see how I could use the 4 digits using the same logic. When I tried looking at them in relation to columns 3, 4 and 9, I couldn't really see a use for this since while I found 12 locations (4 digits into 3 columns) there wasn't any extra information to limit the options into finding any triples. Instead, I decided to consider what would happen if I used 4 rows for 4 numbers so I looked at rows 2, 5, 7, and 9. I found 16 valid locations and of note were columns 1 and 6. In column 1, row 9 already has a 3 so the remaining rows contain 4, 5 and 6. In column 6, row 9 already has a 6 so the remaining rows contain 3, 4, and 5. Hopefully this was what Simon was hinting at and this is sound logic.
I can't follow what you're saying. Can you explain further? Rows 2,5,7 don't have a 3,4,5,6 so they have to have those four values somewhere and I don't see any way to exclude all of those values from any empty cell. That's already 18 "valid" locations, and we haven't even considered row 9 yet. Did you maybe do some swordfish eliminations prior to doing this analysis?
Appreciate that Simon doesn't use bifurcation to solve these puzzles, but for all 9x9 sudoku puzzles there is a corollary rule or truism (to the normal sudoku rules) that can be used to solve them all. The rule applies to the 3x9 rectangles (ie the 3 upper, middle and lower 9x3 rows; and the 3 left, middle and right 3x9 columns). It is clear that for each 9x3 or 3x9, there are either (i) 3 pairs of "twin" numbers and 3 singles; or (ii) 3 lots of "triplet" numbers. For any sudoku, of the 9x3s or 3x9s, you may have no "triplets" (most common), one set of triplets (less common), or two sets of triplets (very rare). You can use the above corollary rule (or set of rules) to solve almost any solvable 9x9 sudoku. It means I don't need to use x wings, swordfishes etc. And other advanced techniques to solve even the most difficult of classics. Happy to explain the concept of "twins" and "triplets" further if anyone needs....
@@JonahHax Ok......to use this vid as an example: if you see the final solution, focusing on rows 1,2 & 3 (the top 9x3 rectangle). In Box 1 (the LHS 3x3 box) you have a 6&8 in row1; a 1&2 in row2 and a 3&9 in row3. But in Box2 (the middle 3x3 box) you have a 3&9 in row1, a 6&8 in row2 and a 1&2 in row3....the same pairings as in Box 1. Finally in box 3 (RHS 3x3 box) you have a 1&2 (row1), a 3&9 (row2) and a 6&8 (row3). Same pairings again. So in this 9x3 rectangle (ie the first three rows) you have 68 as "twins", 12 as "twins" and 39 as "twins". The orphans (ie numbers not twinned with another number) are the remainders (5, 7 and 4) which appear with each of the "twins" only once in one of the three 3x3 boxes. so Rows 1-3 is an example of twins (and orphans). Rows 4-6 is another example of twins/orphans. Similarly for columns. Columns 1-3, 4-6 and 7-9 all have twins/orphans. In the case of Columns 1-3 (the LHS 3x9 rectangle), the twins are 79, 14 and 36...the orphans are 8, 5 & 2. Rows 7-9 (bottom 9x3 rectangle) is an example of TRIPLETS. in Box 7 (bottom LHS 3x3 box), 17&8 are in row 7; 2,5&6 are in row 8; and 3,4&9 are in row 9. But in Box 8 (bottom-middle 3x3 box), 256 is in row7, 349 in row8 and 178 in row9...the same trebles as in box 8. similarly in Box 9 (bottom-RHS 3x3 box) you 349 (row7), 178 (row8) and 256 (row9). Same trebles again. As mentioned before, twins are typical. Of the 6 big rectangles (3x9s or 9x3s) you will usually have 6 (most frequent) or 5 (less frequent) sets of twins. Which means most frequently you have no triplets, but sometimes you have one set of triplets. Very very rarely will you have two sets of triplets (i.e. 4 sets of twins). "Yes but how can you use this to solve a sudoku.....?"
Ans: well in this vid after about 11:00 Simon gets a bit stuck after getting the 1s and the 9s. in rows 7-9 he has 14 out of the 27 squares. His pencil-marks in these rows (especially box 7) make it clear that there can be either (i) triplets (178 being a determinable triplet); (ii) one set of pairs/orphans (49 being a pair and 2 is an orphan); or (iii) another set of pair/orphans (49 being a pair and 3 is an orphan). if you assume triplets apply, you will either solve the whole solution using fairly simple sudoku logic (which will happen in this case) or have a conflict somewhere (in which case, you know the solution must include either (ii) or (iii) - a set of twins/orphans for rows 7-9). Either way, progress is made. Having a certain number of squares out of 27 in a big rectangle is important. if you have 14-18 squares out of 27, you can determine if you have triplets, and if not you can use bifurcation (I think that is the nomenclature used) to eliminate one of the two sets of twins/orphans you can have. More than 9 out of 27, you should only be able to determine if you have triplets or not. More than 18 out of 27, you should be able nail down precisely what the triplets (or as the case may be, the twins/orphans) are. I can't tell you precisely why this works each time, nor can I say this is the most efficient way of doing classic sudoku. - it probably isn't. It certainly isn't elegant like how the cTc guys solve their puzzles. All I know it has something to do with rotational symmetry. And it works for me EVERY time. Hope that explains!
At around 17:59, there's a skyscraper with 8's in r4c2,r6c8,r7c2,r7c8 - which rules out the possibility of an 8 in r4c7 and r6c3 (making both of those cells a 4) :)
I solved tatooine sunset! I did moves that maybe were swordfishes but not sure if it was that...hehe I managed to solve it in about twice his time. What I found to help is if you see a specific number in 1 box of the top row of boxes, 1 in the middle and 1 on the bottom and also not in the same column you then can get all boxes where only 2 potentials of that number...this reduces many of the 3 potentials in a box to only 2. I did that with 3 numbers without able to fill anything in.. the 7s and 9s then that got me a 2 and then later was 5s/6s combo and at that point rest almost was entirely straight up. The colorization in the app really helps here to see it. ok, now tackling this t-rex puzzle. [edit] - solved t-rex in 32 minutes.
21:06 solved for me. I spot some pair and X-wing with 2 but then didn't spot anymore logic so did a little bit bifurcation which solve the puzzle. Gonna enjoy Simon logic solved now.
@13:02 That did something. A 4567 quadruple in row3 (giving the 2 in r3c4 in box2). [[@14:25 he's placing that "2" ]] Cool. [[Earler (@10:02 orso) there was a 237 triple in row9 (that gave that "9 in r9c3" also). Cool again]] That "4567 quadruple" turned into a "457 triple" to place the "6" (@16:01 shortly). Triple "cool." [[@20:03 (after that "swordfish on the 7s"), yes, a 345 triple in row1. [Giving the 6 then 7 in row1. AND, the 7 down in box8] Super cool now , lol. ]]
That's a step towards numerology - if a pattern across three columns ISN'T - then that should rule out the rule itself. What you're describing is that every column and row contains the digits 1-9 only once and each 3x3 contains the numbers 1-9 again only once.
@20:32 Very interesting.. If I'm not mistaken, there's a 45, 345, 345 triple at the top of those columns here (in row one). That places the 6 & 7 from a 67-67 pair. That's the 1st thing I looked at in the these 3 top cells that this swordfish pattern created. (Putting in the candidates in these 3 top cells that was affected by this pattern like Simon instructed). Speaking of columns 2, 5 & 8 that these are in, isn't that the same columns 2, 5 & 8 I was wondering about earlier with the 1,6,9 being in a huge square with rows 2, 5 & 8 though ? That 345 triple may have been there from the start. [[Maybe after the X-Wing pattern on the 2s.. and after placing some 1s and 9s]] Interesting.. Told ya's lol ;) 😂😂 There's definitely a 45, 345, 345 triple in the top three cells here though. I think ? Lol ;) 😂 Good job, Constructor/Setter. Excellent. Yeah, I'm wondering.. I'd swear that makes a 67 remaining pair up there in row one along with that 345 triple. This is huge, (unless I'm mistaken?) Lol ;)) 😂 (Definitely needed that 2 x wing to take out a 2 on one side creating this though ) I think, (again) ? Lol Excellent again though . 😂 [[Oh, not as big as I thought. A swordfish on 5s next (that really broke it open though) I had lost my entire grid by swiping it away by accident (so I thought that 67 was bigger). I hate when that happens though. I had to start over, lol. ;) 😮😂
There was a very nice logic on 8's after the free 1''s and 9's as well as the pairs in box 4, 6 and 7 were pencil marked. You do not need any more but the pencilmarking of 8's in box 9. Now in row 7 the 8's were locked in 2 positions as well as in column 2. So if r2c4 and r7c8 were true (consist 8's) r4c7 cannot be an 8 and if it is not it also cannot be an 8 because there were only 2 position's of 8 in box 9. This gives a naked 4 in r4c7 and a second 78 pair in box 6. The nice thing is with the same 8-combination and the new 78 pair you can remove another 8 in position r6c3, which again gives you a naked 4 and a second 28 pair in box 4. By nice easy Sudoku rules this gives another 4 at r2c5. And that forces all 8's in the right positions, unwinding all existing pairs and unfolding incredibly quick the whole puzzle.
I like the Tatooine Sunset trick. I mean, I'd use it to place the 2 in row 2 right off, but that's me. The T-Rex took me 23 minutes and a few odd seconds. Now to see how Simon solves it. ETA: Simon and I do not think alike at all. Columns 1 and 9 were calling long before he considered them.
You had the solution far sooner! Notice that at 20:56 when you filled in the 7 in the bottom row it was on a cell which was one of two options for a 3. So you could have immediately filled in that 3 in the other cell. (It is a rule I have, whenever you find something complex and fill in a number, always check what were the pencil marks you already had in that cell) No need for swordfishes in this case :-)
A couple of comments about the 48 pair in R4C7. I used this, too in a sort of "broken swordfish" pattern. (Kinda like a broken x-wing.) Not sure I'd ever spot it again, though, since the logic is kinda fuzzy in my head.
10:43 "So we've done one pass through the numbers.. with just a couple of pairs to show for it. " (or whatever you said). You missed the 6 in r4c1 though. The 6sixes were thrown down into row 6 of box 5 from the start (taking out that bottom 6 in box 4 in one of it's only two diagonal cells there). That's only gonna give ya something insignificant I have a feeling though because I see something happening down columns 2, 5 & 8 along with rows 2,5 & 8 with the numbers 169 all three ways in a square that Simon's going to do something with next I have a feeling. That's gonna do something. I have no idea what though. (Think I've gotten too used to Simon spotting stuff, lol) (And, Mark) 😂 Ps: it does add another "169 Column" though. (I have no idea if that's useful from that huge 169 square in the other rows/columns though). 11:49 Oh, he just found it right after (the 6) lol. Good job. Something's still up with them 169s though. ;) (Unless it's just an oddity) All in the same rows and columns forming a huge square though ? That would have to be an EXTREME oddity or coincidence then lol 😂 I'm not kidding, lol. It's: 1 9 9 1 6 6 6 9 1 , forming a huge square though, lol. ;) 😂
8:01... but I still can't see these advanced techniques! Maybe a few puzzles that are impossible to do without the swordfishes, skyscrapers, empty rectangles, etc? I think I need to be forced to use them... boxed into a corner, so to speak! After a decade, I can rarely even spot a y-wing! Pairs, box-line pointing, x-wing is about all my mind can register. I can't name the other situations, but I seem to pick them up intuitively. But I'm not really learning anything in terms of logic (which never has been my forte). Although I love to watch your pattern recognition skills at work!
I assume that swordfish are a solitary creature but, should they ever congregate in numbers, I propose that the collective noun be a "Simon of swordfish" following his Tatooine Sunset exhaustive efforts
I understand the need to explain x-wings or swordfishes to new viewers every time, but I really don't think explaining it by considering cases or thinking what would happen if we placed the digit somewhere else is the intuitive way to explain it. Isn't it simpler to say: hey, we know the numbers in these 3 rows need to go in the positions I highlighted. We need to put 3 of them in the highlighted squares, because there needs to be one in each row. But the highlighted squares are arranged in 3 columns, so obviously each of the 3 numbers must go in one of these columns. I think that's more straightforward and convincing to just see that rather than think... Hang on... What happens if I put a number somewhere else? I personally see that as an unnecessary confusion.
Hi reporting a possible glitch in the software of the puzzle below. If you click the checker it says it doesn't look right no matter what you enter? Also I was focused on the 916 pattern in each corner so plotted the 6's very early.
I come here for the naked singles in my area.
sometimes they are hidden though
I love it how we start with esotheric techniques, then we casually mention "8 swordfishes" regarding a previous puzzle, and then we still explain how X-wings work ❤️
Man, I wish I had a pound for every time Simon said a square was one number then immediately typed a consecutive number into it.
He stated that he had trouble seeing his keyboard. Perhaps he thinks he's not a "gamer", and thus cannot be bothered to get a gaming keyboard, which has *tadaa* lights IN the keyboard.
Oh, and sudoku is a game, let there be no doubt about it.
@@breinnarn Simon is definitely a gamer though, he used to be in the top 5 Masters on EU server for Starcraft 2
@@Nighthound That's pretty good; I never reached higher than low diamond myself, and that was waaay back in WoL when the game was slower paced than now. Someone needs to make a starcraft based sudoku, Simon would be all over it :D
@@breinnarn he's already done SC sudokus on this channel
HOLY SUDOKU!
That logic you show for the Tatooine puzzle is amazing.
Now I have to start looking for that, just to see if I can find them and figure out how to use them properly.
Thanks for teaching us something honestly new.
I solved this without any wings or swordfish - here's a simplified version of my solve path:
- fill in all of the 1s.
- fill in all of the 9s.
- fill in the 37 pair in box 4.
- take a look at r4c7. If this is an 8, it forces the 8 in box 9 to go in r7c8, which forces the 8 in box 7 to go in r8c3, which leaves no place for an 8 in box 4. Therefore, r4c7 is not an 8.
- since r4c7 can't be an 8, it's effectively a naked single now; it must be a 4.
- the rest of the puzzle can be solved with no advanced techniques.
got a simple solve with 1's and 9's. got the hidden pairs. and then i found out that 2 only had 2 options in box 9 by a bit of experimenting with where they could go. and then that forced all the 2's intoplace and the rest came after with no advanced techniques
Had a very similar path (went 1-9 with detours when I spotted easy things). Took me 10 minutes taking it easy, indeed without any advanced techniques. I think it's the first or maybe second time I've beaten Simon's solve time :D
Bingo. I used the 8's too.
Force testing the 2 positions for the 8 in the bottom right hand block gives the same result -- RC47 cannot be an 8, so it's a 4. You also end up with a 78 pair in the middle RH block.
Agreed. Solved in 10m03s without any "techniques". I also solved the Tatooine Sunset in the same manner, in under 20m.
I also solved it similarly, 11:28 which is blazing fast for me since I like to take my time on non-very easy puzzles, but I don't count it much since the intention of the solve in the video was to demonstrate the method for teaching purposes, not really to show the simplest path, and I'm also not narrating my steps. I can see myself going on 2 hours with that method and not necessarily being finished....sometimes 45 min will go by and I still might not have spotted one thing needed for an advanced technique, which pretty much never happens with Simon or Mark.
I need to add a shout-out to Trevor Tao, whose video on Tatooine Sunset was the subject of Tom's post. The logic is (I think) equivalent to the MSLS structures as Sam pointed out, but it's a lovely visualization of the solve.
(Also need to shout-out forum poster SpAce, who was the first to solve this when I originally posted it, and used one massive beautiful MSLS to do most of the work.)
Now to try Macrovius' puzzle. :)
Trevor Tao's video is great! The link is here: th-cam.com/video/blH0aRUERy0/w-d-xo.html
I'm glad Simon put a brief explainer of the equivalent MSLS in this video - as he says, it is perfectly gettable once you have a rough idea of what you are looking for, and when you might want to be looking for it. It reminds me of the Times sudoku championship back in 2007, which featured plenty of X-wings and Swordfish. I had realised that the puzzles were going to need those techniques and so was on the lookout for them from the start, whereas my impression was everyone else trying to speed solve them was having to guess.
How relevant MSLS will really be under time pressure is yet to be seen - my guess would be only really to get started on a tough puzzle. The various Tatooine puzzles are good candidates here as it's quite easy to see where to look at the start of the puzzle, and I think it might improve on simply guessing (not that Mark was very slow in his video I have to say!)
@@tomcollyer641 I am definitely not a speed solver, so I can't comment on whether it would be used in competition if the opportunity presented itself. I don't know how likely it is for such a puzzle to show up in the first place though, unless it is a deliberate move by the organizers. It's a key tool to solving *some* truly monstrous puzzles for which many computer algorithms can't find a logical path (e.g. Arto Inkala's infamous Escargot has an MSLS which greatly reduces the difficulty, though it is still hard). But otherwise, I don't know how much time it would save outside of the odd "fishy" puzzle designed around an MSLS-type structure.
But hey, if there are any competition organizers out there looking for such puzzles, I've got you covered! ;)
I never really knew how to use x-wings until this video. Thanks Simon!
I really struggle to see swordfish patterns. I ended up doing this with a colouring technique. Once you have the same digit narrowed down to 2 cells in a lot of boxes you can often create two scenarios for the dispositions of that digit round the grid and then remove that from any cells you had it pencil marked in that aren't coloured one of the colours. Sometimes when you do that the same cell in one box is both colours so you can place it which is nice. I guess that is effectively just the "long way round" of a sword fish when you get right down to it. :). I used that to deduce that no matter where the 7 was in box 4 the 7 in box 8 is ALWAYS in r9c5. After that I spotted that an 8 in r6c3 would create a contradiction forcing 2 8's into row 7. And from there it wasn't too hard. I wish I could spot the swordfish though, it's so much more satisfying I imagine... But I still managed to solve it in about 25 minutes. :)
@ Simon & Mark: 3 years ago, would you have ever thought that your names would be mentioned in a sentence that contained the phrase "... the world's most popular Sudoku channel"? Well done! A great development and certainly a lot of work! Thanks a lot for this...
I think I finally understand the swordfish...except for why it's called a swordfish.
A swordfish is a type of plane from WW2
Early biplanes had two struts between each wing with torsion cables crossing between them to form an X between the two wings. This is where the term "X-Wing" comes from in Sudoku.
The Fairey Swordfish was a biplane that had 3 struts between the wings and thus an X-Wing using 3 digits is called a "Swordfish".
@@desyncer this is less fun than thinking it's from "Star Wars" and that movie that shows Halle Berry's boobs.
@@qfmarsh64 Hey, but you at least tried.
to make it more of an in depth thing
a berry close up
all curvey and close
juicy and forever curving
Sooo much of my lack in understanding is about the naming of these 'tricks'
Soooooo muuuuch!
Simon! I just finished one of the 5* puzzles from your app in under 30 mins! (Personal best) Your enthusiasm for Sudoku totally convinced me to subscribe and download.
Great work. Do note though that the number of stars does not necessarily correspond to difficulty. Yesterday it took me about 40 minutes to solve a 5 star puzzle and immediately thereafter I solved a 6 star puzzle within 12 minutes...
you have the same pseudonym as me @Anon Ymous
I have just found your channel this last week, it has given me a wonderful way to jumpstart my brain for my Grad school
The 9/1/6s make a kind of checkerboard pattern using the trick you showed with the first puzzle
Let's get cracking: 7:03
OK, I haver made my pledge. Anyone who watches this channel ought to make a pledge likewise. May I suggest an electronic version of the book as a stretch goal, including the on line software to assist in solving the puzzles?
Just pledged too, excited to see that we're already breaching the first stretch goal! The electronic version is a great idea, especially considering we would only get our hands on the physical book sometime in Sept 2021 -- whereas an electronic one could be 'handed' out earlier, and still be edited when/where needed.
“No one puts 9s in the corner of the grid”. You looked so pleased making that reference lol.
21:53 for me for the T-Rex puzzle. Took a LOT of coloring, but no guesswork. I'm happy with how I did on this.
Nice puzzle!
OMG this is the very first time that my solve was faster than the length of the video. So proud at 23:58
A soda and watching a genius solve sudoku with relative ease is a perfect way to end the evening off. Thanks for the work Simon!
Great! I used the 'pincers and pivots' on 8's in row 8 and column 2 from box 7. It resolved the 48 pair in r4 c6. Loving the videos.
I watched the video yesterday, tried to solve it 3 times today. Two times I had errors and restarted... Now I finaly made my first puzzle from this channel.
BTW the X-wing and the sordfish are cool and helped me a ton in this one. I like to color my sudoku
Thanks Simon, Great channel!
Rami from Israel
I need to have my ears cleaned because sometimes I understand 'No more sudoku rules apply!' :-)
Easiest puzzle ever!
I used Phistomephel's theorem when I got stuck on the T-Rex. Just color in the corner cells and their corresponding digits in the center frame to see what's left and how many of a particular digit can appear in the cormers/frame.
I agree the technique you used was far more elegant than what I did. Filled all candidates and eliminated conflicting cells. But I did finish in 11 mins
Downloaded your app yesterday and have gotten through the first 6 puzzles so far. Really enjoying it. Nicely done. As an aside, whoever ranked puzzle 41 as a 1-star difficulty has been sniffing glue. Cheers from across the pond!!
I only used 1 swordfish and it was the weirdest ever ;)
Noticing how the 2-3-7 triple in column 1 interacted with the 2-5-7 triple in column 9 I evaluated what would be the result for both possible options in r5c9 and I found that r9c8 was actually restricted to either 2 or 3. This places the 7 in row 9 in column 5 and this creates a very interesting partial swordfish on 7s in columns 2, 6, 8 and 9 in which r8c9 is a naked 7.
I LOVE CLASSIC SUDOKU
TY SIMON AND MARK
😍😍😍
ok i have to learn about swordfish. i see them when he is showing it, but i don't know enough to see them on my own.
Watch his video about the tattooine sunset sudoku. After that you'll be able to see them very easily :) (It's labeled "how NOT to cheat in Sudoku")
@@Luxalpa
Thank you, I missed that one. I will watch it now!
@w yes, i believe this is correct... it's the same logic, but with triplets
Took me 33 min today, which is a fine time for me. My key observation was that the way that 8s bounced around the grid, made them more restricted than they at first appeared. This let me resolve a pair of 4's and the rest quickly fell into place.
Just when I thought I was going to be reminded that a snake cannot touch itself, we get a classic😆. As always a great job done by Simon on another tricky puzzle!!!
18:21 my best ever time for a hard classic sudoku. found the 2 swordfish fairly quickly and that did it
Not sure if the Empty Rectangle on 5's at the end was intended, but it's what I used - alongside a school of Swordfishes - to solve the puzzle. Nice Classic!
Please, if you're reading this, consider making a stretch goal to include an online version (possibly with the same software you use) for the kickstarter book! I would love to make a pledge and receive the puzzles, however, I make way too many marks to work complex puzzles on paper. It gets super messy and overwhelming. Thanks, and keep up the great work!
43:37 and I'm proud as punch that I spotted the swordfishes! Great puzzle.
1:05:50 before watching the video. Despite the time, very proud of myself for having found the logical path to this one! Rather than bifurcating like Tatooine Sunset. Great puzzle, devilishly tricky.
I got a bit lucky on my solve today by considering r4c7. At 11:00, Simon has reduced this cell to 4 or 8. An 8 is impossible since this excludes an 8 from box 4. Using this one gets a solution that doesn't need any x-wing or swordfish.
27:12 Finally in the same ball-park as Simon on a fairly difficult normal Sudoku! Route was a bit different, but not by much. The 2's 5's and 7's seemed to hold the key for me. And once the key is turned, the puzzle unwinds in a flash. Zap! Just like a T.Rex attack! Thanks for a super puzzle. :)
Proud of myself for getting the x wing on 2s and the sword fish on 7s. Couldn’t see that sword fish on the 5s though. Getting better everyday :)
@7:42 You could have said there is something "fishy" going on with the placements
i love how the swordfish slowly turns into a x-wing pattern at around 21:00
now i'm realising that a x-wing that was a swordfish doesn't give any more information. (should be pretty obvious)
Beautiful puzzle, we should have more of such classics. Though again failed to identify the swordfish and used elimination in box 6 with 25 pair to solve it. Watching simon crack it was again a treat!!
15:20 "We didn't do _two_ badly there"
... I'll see myself out.
Swordfishes, and x-wings sudoku 👌🏽👊🏽
23 minutes but using the technique Mark used to solve Tatooni Sunset; fill in the easy one and nines, then a few more pairs ...then used the 37 pairs in box four to just pick one and see if it breaks the puzzle. Chose 7, marked the starting cell, and did about 20 steps til it broke. Unwound (easy w online game) and tried the 3... solved simply from there.
Now, really not elegant and not a fun way to solve...but is a technique I learned last week!
really enjoyed this puzzle
Hope everyone is having a great day!
If you fill out the options in first and last column after 1, 9 and 6 and look for 7s round the grid, you see one pattern fits and other clashes. Easy solve.
Nice puzzle. I used a different swordfish on the 7s, but the impact was the same. I had placed some other numbers earlier than Simon, which meant that the end fell apart even quicker.
I love some of the variants we've been treated to lately, but I still enjoy the purity of a well-crafted classic.
Regarding the kickstarter, I'm glad you seem to have already chosen the original Miracle. I hope the recent two murder puzzles will feature too, particularly CluedoKu with its original artwork. Tatooine Sunset should also feature, if only for swordfish practice. To pick the puzzles solved by Simon, you should probably just count the number of times he says "beautiful" or "lovely".
If possible, I'd love it if you could get the setters to write a few lines about their puzzles (possibly in an appendix with the solutions; to avoid spoilers about any special logic they built in).
Brutal! Nice to get some practice with swordfish!
Yay, 19:55 for me. :D Looking for swordfish/ coloring diversing paths especially the 8s gave me almost everything I needed
The astonishment in his voice when realising it's a relatively quick one :D
At 6:35, he mentions another example using 3,4,5,6 in the Tatooine Sunset puzzle but I wasn't able to see how I could use the 4 digits using the same logic.
When I tried looking at them in relation to columns 3, 4 and 9, I couldn't really see a use for this since while I found 12 locations (4 digits into 3 columns) there wasn't any extra information to limit the options into finding any triples.
Instead, I decided to consider what would happen if I used 4 rows for 4 numbers so I looked at rows 2, 5, 7, and 9. I found 16 valid locations and of note were columns 1 and 6.
In column 1, row 9 already has a 3 so the remaining rows contain 4, 5 and 6.
In column 6, row 9 already has a 6 so the remaining rows contain 3, 4, and 5.
Hopefully this was what Simon was hinting at and this is sound logic.
I can't follow what you're saying. Can you explain further? Rows 2,5,7 don't have a 3,4,5,6 so they have to have those four values somewhere and I don't see any way to exclude all of those values from any empty cell. That's already 18 "valid" locations, and we haven't even considered row 9 yet. Did you maybe do some swordfish eliminations prior to doing this analysis?
@@JerryTheK i honestly don't know what i was talking about, i couldnt figure out how to actually progress through this puzzle
classic sudokus are the best! and this one was really difficult imho
15:09 "So we actually didn't do *two* badly there"
24:43 for me. I didn't use any swordfish. I just used some highlighting to eliminate some candidates.
Appreciate that Simon doesn't use bifurcation to solve these puzzles, but for all 9x9 sudoku puzzles there is a corollary rule or truism (to the normal sudoku rules) that can be used to solve them all. The rule applies to the 3x9 rectangles (ie the 3 upper, middle and lower 9x3 rows; and the 3 left, middle and right 3x9 columns). It is clear that for each 9x3 or 3x9, there are either (i) 3 pairs of "twin" numbers and 3 singles; or (ii) 3 lots of "triplet" numbers. For any sudoku, of the 9x3s or 3x9s, you may have no "triplets" (most common), one set of triplets (less common), or two sets of triplets (very rare).
You can use the above corollary rule (or set of rules) to solve almost any solvable 9x9 sudoku. It means I don't need to use x wings, swordfishes etc. And other advanced techniques to solve even the most difficult of classics.
Happy to explain the concept of "twins" and "triplets" further if anyone needs....
yes please explain.
@@JonahHax Ok......to use this vid as an example: if you see the final solution, focusing on rows 1,2 & 3 (the top 9x3 rectangle). In Box 1 (the LHS 3x3 box) you have a 6&8 in row1; a 1&2 in row2 and a 3&9 in row3.
But in Box2 (the middle 3x3 box) you have a 3&9 in row1, a 6&8 in row2 and a 1&2 in row3....the same pairings as in Box 1. Finally in box 3 (RHS 3x3 box) you have a 1&2 (row1), a 3&9 (row2) and a 6&8 (row3). Same pairings again.
So in this 9x3 rectangle (ie the first three rows) you have 68 as "twins", 12 as "twins" and 39 as "twins".
The orphans (ie numbers not twinned with another number) are the remainders (5, 7 and 4) which appear with each of the "twins" only once in one of the three 3x3 boxes.
so Rows 1-3 is an example of twins (and orphans). Rows 4-6 is another example of twins/orphans.
Similarly for columns. Columns 1-3, 4-6 and 7-9 all have twins/orphans. In the case of Columns 1-3 (the LHS 3x9 rectangle), the twins are 79, 14 and 36...the orphans are 8, 5 & 2.
Rows 7-9 (bottom 9x3 rectangle) is an example of TRIPLETS. in Box 7 (bottom LHS 3x3 box), 17&8 are in row 7; 2,5&6 are in row 8; and 3,4&9 are in row 9. But in Box 8 (bottom-middle 3x3 box), 256 is in row7, 349 in row8 and 178 in row9...the same trebles as in box 8. similarly in Box 9 (bottom-RHS 3x3 box) you 349 (row7), 178 (row8) and 256 (row9). Same trebles again.
As mentioned before, twins are typical. Of the 6 big rectangles (3x9s or 9x3s) you will usually have 6 (most frequent) or 5 (less frequent) sets of twins. Which means most frequently you have no triplets, but sometimes you have one set of triplets. Very very rarely will you have two sets of triplets (i.e. 4 sets of twins).
"Yes but how can you use this to solve a sudoku.....?"
Ans: well in this vid after about 11:00 Simon gets a bit stuck after getting the 1s and the 9s. in rows 7-9 he has 14 out of the 27 squares. His pencil-marks in these rows (especially box 7) make it clear that there can be either (i) triplets (178 being a determinable triplet); (ii) one set of pairs/orphans (49 being a pair and 2 is an orphan); or (iii) another set of pair/orphans (49 being a pair and 3 is an orphan). if you assume triplets apply, you will either solve the whole solution using fairly simple sudoku logic (which will happen in this case) or have a conflict somewhere (in which case, you know the solution must include either (ii) or (iii) - a set of twins/orphans for rows 7-9). Either way, progress is made.
Having a certain number of squares out of 27 in a big rectangle is important. if you have 14-18 squares out of 27, you can determine if you have triplets, and if not you can use bifurcation (I think that is the nomenclature used) to eliminate one of the two sets of twins/orphans you can have. More than 9 out of 27, you should only be able to determine if you have triplets or not. More than 18 out of 27, you should be able nail down precisely what the triplets (or as the case may be, the twins/orphans) are.
I can't tell you precisely why this works each time, nor can I say this is the most efficient way of doing classic sudoku. - it probably isn't. It certainly isn't elegant like how the cTc guys solve their puzzles. All I know it has something to do with rotational symmetry. And it works for me EVERY time.
Hope that explains!
Went without using any advanced techniques and took me ~36 minutes. Great puzzle.
At around 17:59, there's a skyscraper with 8's in r4c2,r6c8,r7c2,r7c8 - which rules out the possibility of an 8 in r4c7 and r6c3 (making both of those cells a 4) :)
I solved tatooine sunset! I did moves that maybe were swordfishes but not sure if it was that...hehe I managed to solve it in about twice his time. What I found to help is if you see a specific number in 1 box of the top row of boxes, 1 in the middle and 1 on the bottom and also not in the same column you then can get all boxes where only 2 potentials of that number...this reduces many of the 3 potentials in a box to only 2. I did that with 3 numbers without able to fill anything in.. the 7s and 9s then that got me a 2 and then later was 5s/6s combo and at that point rest almost was entirely straight up. The colorization in the app really helps here to see it. ok, now tackling this t-rex puzzle. [edit] - solved t-rex in 32 minutes.
21:06 solved for me. I spot some pair and X-wing with 2 but then didn't spot anymore logic so did a little bit bifurcation which solve the puzzle. Gonna enjoy Simon logic solved now.
@13:02
That did something.
A 4567 quadruple in row3 (giving the 2 in r3c4 in box2).
[[@14:25 he's placing that "2" ]]
Cool.
[[Earler (@10:02 orso) there was a 237 triple in row9 (that gave that "9 in r9c3" also).
Cool again]]
That "4567 quadruple" turned into a "457 triple" to place the "6" (@16:01 shortly).
Triple "cool."
[[@20:03 (after that "swordfish on the 7s"), yes, a 345 triple in row1. [Giving the 6 then 7 in row1. AND, the 7 down in box8]
Super cool now , lol. ]]
I see a T-Rex in the grid.
I agree, Simon.
Thanks for the classic.
Did it in 19:07, pretty happy with that!
That's a step towards numerology - if a pattern across three columns ISN'T - then that should rule out the rule itself. What you're describing is that every column and row contains the digits 1-9 only once and each 3x3 contains the numbers 1-9 again only once.
@20:32
Very interesting..
If I'm not mistaken, there's a 45, 345, 345 triple at the top of those columns here (in row one).
That places the 6 & 7 from a 67-67 pair.
That's the 1st thing I looked at in the these 3 top cells that this swordfish pattern created. (Putting in the candidates in these 3 top cells that was affected by this pattern like Simon instructed).
Speaking of columns 2, 5 & 8 that these are in, isn't that the same columns 2, 5 & 8 I was wondering about earlier with the 1,6,9 being in a huge square with rows 2, 5 & 8 though ?
That 345 triple may have been there from the start.
[[Maybe after the X-Wing pattern on the 2s.. and after placing some 1s and 9s]]
Interesting..
Told ya's lol ;) 😂😂
There's definitely a 45, 345, 345 triple in the top three cells here though.
I think ? Lol ;) 😂
Good job, Constructor/Setter.
Excellent.
Yeah, I'm wondering..
I'd swear that makes a 67 remaining pair up there in row one along with that 345 triple.
This is huge, (unless I'm mistaken?) Lol ;)) 😂
(Definitely needed that 2 x wing to take out a 2 on one side creating this though )
I think, (again) ? Lol
Excellent again though . 😂
[[Oh, not as big as I thought.
A swordfish on 5s next (that really broke it open though)
I had lost my entire grid by swiping it away by accident (so I thought that 67 was bigger).
I hate when that happens though.
I had to start over, lol. ;) 😮😂
For the first time in world history I was faster than Simon! Free hugs to everyone 😂😂😂
There was a very nice logic on 8's after the free 1''s and 9's as well as the pairs in box 4, 6 and 7 were pencil marked. You do not need any more but the pencilmarking of 8's in box 9. Now in row 7 the 8's were locked in 2 positions as well as in column 2. So if r2c4 and r7c8 were true (consist 8's) r4c7 cannot be an 8 and if it is not it also cannot be an 8 because there were only 2 position's of 8 in box 9. This gives a naked 4 in r4c7 and a second 78 pair in box 6. The nice thing is with the same 8-combination and the new 78 pair you can remove another 8 in position r6c3, which again gives you a naked 4 and a second 28 pair in box 4. By nice easy Sudoku rules this gives another 4 at r2c5. And that forces all 8's in the right positions, unwinding all existing pairs and unfolding incredibly quick the whole puzzle.
26:55 -- feels a bit slower than usual but I absolutely loved the puzzle
Finished in 21:38. Didn't need any swordfishes; only the x-wing on 2s
I read Macrovirus. Rather contaminating puzzle.
I like the Tatooine Sunset trick. I mean, I'd use it to place the 2 in row 2 right off, but that's me. The T-Rex took me 23 minutes and a few odd seconds. Now to see how Simon solves it. ETA: Simon and I do not think alike at all. Columns 1 and 9 were calling long before he considered them.
The top of the grid is the T-Rex's neck. The right side is the top of the head and at the bottom are the jaws
One of the fastest solves I've had, 13:02
Fantastic
You had the solution far sooner! Notice that at 20:56 when you filled in the 7 in the bottom row it was on a cell which was one of two options for a 3. So you could have immediately filled in that 3 in the other cell. (It is a rule I have, whenever you find something complex and fill in a number, always check what were the pencil marks you already had in that cell) No need for swordfishes in this case :-)
Yeah it was cracked @ 20:56 simple sudoku techniques solve the rest.
At 82 YOA I am three weeks behind your thinking but I think I was always one week behind anyway. Best regards.
A couple of comments about the 48 pair in R4C7. I used this, too in a sort of "broken swordfish" pattern. (Kinda like a broken x-wing.)
Not sure I'd ever spot it again, though, since the logic is kinda fuzzy in my head.
10:43
"So we've done one pass through the numbers.. with just a couple of pairs to show for it. " (or whatever you said).
You missed the 6 in r4c1 though.
The 6sixes were thrown down into row 6 of box 5 from the start (taking out that bottom 6 in box 4 in one of it's only two diagonal cells there).
That's only gonna give ya something insignificant I have a feeling though because I see something happening down columns 2, 5 & 8 along with rows 2,5 & 8 with the numbers 169 all three ways in a square that Simon's going to do something with next I have a feeling.
That's gonna do something.
I have no idea what though.
(Think I've gotten too used to Simon spotting stuff, lol)
(And, Mark)
😂
Ps: it does add another "169 Column" though. (I have no idea if that's useful from that huge 169 square in the other rows/columns though).
11:49
Oh, he just found it right after (the 6) lol.
Good job.
Something's still up with them 169s though. ;)
(Unless it's just an oddity)
All in the same rows and columns forming a huge square though ?
That would have to be an EXTREME oddity or coincidence then lol 😂
I'm not kidding, lol. It's:
1 9
9 1 6
6
6 9 1
, forming a huge square though, lol. ;) 😂
8:01... but I still can't see these advanced techniques!
Maybe a few puzzles that are impossible to do without the swordfishes, skyscrapers, empty rectangles, etc?
I think I need to be forced to use them... boxed into a corner, so to speak!
After a decade, I can rarely even spot a y-wing! Pairs, box-line pointing, x-wing is about all my mind can register.
I can't name the other situations, but I seem to pick them up intuitively.
But I'm not really learning anything in terms of logic (which never has been my forte).
Although I love to watch your pattern recognition skills at work!
Empty rectangle on 7 in box 1 eliminates 7 from R2C9; that cell is a 5; then it is a breeze from there no X-wing needed.
I need to practice my swordfish and x swings
One day I will spot a swordfish pattern without a prompt from Simon. One day!
When the 8s were near a Swordfish, I slot-machined it, which spat out two 4s and made the puzzle fall apart for me.
10:20 Simon trying not to laugh at his "Dirty Dancing" reference.
I assume that swordfish are a solitary creature but, should they ever congregate in numbers, I propose that the collective noun be a "Simon of swordfish" following his Tatooine Sunset exhaustive efforts
Apparently it's a flotilla of swordfish. I much prefer a Simon of swordfish...
Is there a sudoku app where i can put my notes on the side/corner and in the centre?
Today I learned what ‘ab initio’ means.
The name of the brand-new trick has been coined "SET Theory". Three columns for (9,7,2) and three rows for (3,4,5,6).
I understand the need to explain x-wings or swordfishes to new viewers every time, but I really don't think explaining it by considering cases or thinking what would happen if we placed the digit somewhere else is the intuitive way to explain it. Isn't it simpler to say: hey, we know the numbers in these 3 rows need to go in the positions I highlighted. We need to put 3 of them in the highlighted squares, because there needs to be one in each row. But the highlighted squares are arranged in 3 columns, so obviously each of the 3 numbers must go in one of these columns. I think that's more straightforward and convincing to just see that rather than think... Hang on... What happens if I put a number somewhere else? I personally see that as an unnecessary confusion.
I've thought this for a long time
Hi reporting a possible glitch in the software of the puzzle below. If you click the checker it says it doesn't look right no matter what you enter? Also I was focused on the 916 pattern in each corner so plotted the 6's very early.
I got stuck and had to guess at one point... Felt bad, but I got my guess right
Couldn't solve it on my own. With the swordfish clue, I got 44:25.
For the T-Rex 18:21
Tatooine Sunset 20:32
Swordfish rocks!
I couldn't figure out why the Puzzles kept resetting. My mouse had a button mapped to F5. Arg. That has been bothering me for a while.
great
24:58 - it feels a little slow but it is what it is...
Finally I can take my nap today..
Is the book gonna feature sudoku only? More puzzle variety, please! :(