Thank you for featuring another of my puzzles! It's actually exactly a year since the first ThePedallingPianist feature on this channel, so this is a lovely way to celebrate - and Orla has had a lovely nap while her daddy watched this video! Spoilers below... The solution path was pretty much exactly as intended! Once you've worked out that the grid effectively contains four 4x4 Latin Squares (albeit two contain the digits 5-8 and two wrap around the grid), there are a couple of "secrets" I found very interesting that can help speed things up, though they don't really alter the solve path. Firstly, you know that digits exactly 4 orthogonal steps in a straight line away from each other will be opposite polarity (especially helpful in conjunction with the very deliberately placed black dots in rows 4/5). Secondly, within each 4x4 Latin Square (even the ones that wrap around the grid), digits exactly 2 diagonal steps away must be the same. As for that disambiguator near the end - I don't think you're alone in thinking it was horrible! If I'd replaced the row 8 white kropki dot with a black one just to the left, that disambiguation wouldn't have been necessary and the solution would still have been the same... but I decided it was too long since I made the solver consider the theme of the puzzle, and after all, I am horrible!! :D
I thought that the disambiguation near the end was genius! I saw the deadly pattern developing as Simon was solving, and knew that he would apply the rule immediately (especially since he had so thoroughly considered the placement options for the 2x2 Latin square early on) - and was very amused that he did not catch on to it right away! Brilliant in every way, thanks for creating the puzzle (and for your year's worth of contributions!)
@@emilywilliams3237 This was my favourite part of the puzzle too, and I definitely didn't catch it right away - took me a while too. But loved it because as Stuart said, it made you reconsider the theme of the puzzle when you thought that part was done and dusted. Lovely
i don't think I've ever seen as much fear in Simon's eyes than when he thought he had that deadly pattern! The resolve was genius though. This whole puzzle is just brilliantly coherent, the peddling pianist creates art once again! A little outside of my comfort zone so I didn't try it this time, but as always I thoroughly enjoyed watching your solution :)
When I was in college, the pure math professors would call that wrap-around thing Toroidal Boundary Conditions, like Simon does, but the applied math professors would call it Pac-Man Boundary Conditions. Whatever you call it, it's lovely stuff. The lower green 4x4 has all four copies of the same digit on the same positive diagonal (with wrapping), while the upper has the 1s and 4s on the positive diagonal, and the 2s and 3s on negative diagonals. The lower black 4x4 has the even digits repeating along positive diagonals, and the odd digits repeating along negative diagonals. The upper black 4x4 reverses it, with the even digits on negative diagonals and the odds on positive diagonals.
Omg saw that negative constraint step near the bottom left coming and was so happy it did indeed not only show up but was necessary to the solve, so delightfully clever
It's such a conceptual idea, less about unwinding logical "knots" in the grid and more about sitting back and contemplating the nature of the thing. Such a unique idea and as always from ThePedallingPianist so beautifully executed (and with 60% less pulling your hair out! which is the usual case for the mad genius).
These puzzles in puzzles in puzzle They tend to confound and confuzzle. They leave my brain reeling And leaving me just feeling Like I need a hug and a snuzzle. Love the outro music! (Eats all your carrots and leaves a Father Christmas matroishka)
I must say, I would have just plonked the initial 2x2 right in the middle of the grid, assuming that of course that must be it, and then gotten very far away from the actual solution. Thanks for being thorough, Simon, and demonstrating this not only on this puzzle, but in several others. And thanks for this lovely video!
One of the umpteen things I've learned over the past three years or so of watching CtC is to re-read the rules when I get stuck. Sure enough, suddenly the word 'exactly' gave me the the way forward.
Ah yes, just as I was sitting down to do my work. You always post at the perfect time to make me procrastinate the most! In all seriousness though, you guys videos are great to have on in the background while I work, so I thank you for your consistency and amazing solves!
1,000 copies of me in 1,000 rooms with 1,000 pencils could not have solved this in 1,000 hrs, much less been able to set something lke this. You really are very talented, Simon, and the setter is a true genius!
I have no idea how you were able to solve that with the chosen colour scheme. The blue pencil marks on the dark green and black highlighted squares were very difficult on my eyes.
Funny(now) Story: At the very beginning, I got so stuck and confounded that the checker was telling me some digits were wrong. I rechecked my logic twice, before giving up in a huff and coming back to the video to pout in defeat. I assumed the rules were written strangely, and Simon would tell me what grammar technicality I'd missed. And then, watching Simon's elimination of the corners, I got even more confused because he was doing it exactly as I was, and found the location of the 4x4! It was at this moment, after staring at the two squares I had filled in, and clicking the check button a few times in case it would change its mind, that I realized a black dot crossing the edge of the 4x4 could have 4/8, and not just 3/6. I have reached the skill level just past novice, where my confidence flies too close to the sun; it must be a broken solve checker, before it could be my still-developing kropki instincts! Back to the basics for me, while I complete this solve extra carefully. You are the best teachers one could ask for ❤
Even though I couldn't solve it entirely myself - needed to listen Simon's explanations in the beginning to get anywhere - I still loved this puzzle, the way you needed to figure the next steps. I particularly liked how knight's move and the square limit were used to solve the deadly patterns. Took me about an hour.
I have to say that I absolutely love your videos. I've been watching for a while and have been pausing the video right after you start the puzzle and give it a shot myself. I managed to get this one on my own today. Watching it afterwards and seeing you be like "wait something is wrong" in regards to the 1/3 in the bottom was the exact same thought process I had. Appreciate everything you and the team do with this channel!
For the double clicking to work, you’d have to remove the black. When you double click a square that is both blue and black, the software will highlight any squares that contain blue or black.
Yes. You can get away with temporarily removing the black from just one black/blue cell, so that it's just blue, then double-clicking it to select just the cells that contain any blue. But there wasn't really any need to keep any black at all, and it would have made reading pencil marks and digits a lot easier had it been removed earlier (or even better, never used at all - it's too dark!).
That was another goos solve Simon, but yout persistent use of dark colours made it practically impossible to visually follow the solve, even on a 22" inch screen. Totally impossible on an iPhone. Please try to delete unneeded colours, thank you.
One of those problems where every word of the instructions is crucial. I went around in circles with a 3 and 4 "2x2" square until I realised it wasn't breaking the rules. Nice solve
I did this puzzle late the other night and was sure it would make its way here. There is one deduction that just eluded me for way too long (it was so obvious in hindsight), and i fully expect Simon to just get it within the first few minutes.
Yup, I got the deduction that you can't fit an N square in an N+1 square, but I missed that the minimum nesting size was 2N. I also concluded that a 2×2 couldn't live in the corner of a 4×4, but I forgot to explore putting a 2×2 anywhere else in the 4×4. Simon is, as expected, shooting well ahead of my 11pm brain
You literally had the solution for the N*N grid being limited to exactly 3, but somehow forgot it immediately. Maybe it was way under your radar. Love your videos.
19:58 for me. That puzzle was a lot of fun to solve, even if I did take way too long to recognize that no Latin square could be embedded in the corner of another. My solve path ended with that nearly deadly pattern of 1s and 3s in the lower left, and I found the way that that disambiguated to be an absolutely beautiful ending to the puzzle.
Brilliant. I worked backwords from 8X8, because to go down from there you need to go to 4x4. And there are no 1:2 ratios in the 5-8 sets, so the 4X4 needs to incorporate as many black dots as possible and land any others on a line between regions.
This was so clever. Just when I thought I'd get stuck with just one xwing remaining, I realized that one possible solution would drop a second 2 by 2 Latin square in the grid, and that was the final disambiguation. Just when you thought you were done with thinking about those boxes. 00:24:39, now I've got to see Simon solve it just to see if he runs into the exact same situation.
The way I determined the 4X4 is this: (suppose we use the same color scheme as Simon) - On each black dot, there is at least one green square. - Since each row must have 4 consecutive (potentially wrapping) greens, r1c5, r1c6, and r1c7 must be green. - This implies the blackness of r5c5, r5c6, and r5c7. - We then need a green at r4c5. - This fixes a rectangular region of greenness at r1-r4 X c5-c7. - If the last column of the 4X4 is at c8, then there would be two 4X4 in the puzzle. Thus, the 4X4 must be r1-r4 X c4-c7.
I spent twenty or so minutes just playing around in the grid, and thought I had one of seemingly multiple solutions. Then I realised the importance of there being *exactly* three Latin squares, and no more! I had a 4x4 in one corner, so naturally had an extra Latin square in the opposite corner. But it took me a few minutes of head scratching to work out why I hadn't stumbled on a valid solution. So then I restarted the puzzle and did it a lot more methodically, finding the right spot for the 4x4 the same as Simon. I completed that 4x4, then all the 5678s, and finished with the seemingly deadly 13 pattern. I also couldn't see immediately how it could possibly be resolved, yet I was so close! Felt great when it dawned I couldn't create a second 2x2 Latin square.
Another point, having sussed there must be an 8x8 Latin square surrounding the whole lot - you could choose a purple frame, so if there's no three in the corner at least you get a sing-song.
What a mesmerizing puzzle! I remained baffled for a long time, more or less tracing out all the same exploratory dead ends Simon did (but more slowly). Even when I finally found the right track, I was prepared to learn I'd gone horribly wrong. I've never been so happy to reach the end of a puzzle (after overcoming the beautifully-baked-in deadly pattern panic at the end; for me the "wait, that would make an extra Latin square" step was the very last one).
What a gorgeous puzzle. I would like to highlight that nowhere in the rules does it state that you have to put the digits 1-8 in every row and column, nor does it state that every digit has to appear 8 times, that's just the logic that follows from the 3 nested latin squares determining that the minimum size of the third square is 8x8.
Had trouble wrapping my mind around a puzzle that wraps around. Enjoyed watching Simon figuring it out, though! I don’t usually try to do the monthly puzzle packs, but snack-adoku sounds like something I can handle - right??? 🤔
What a great puzzle! Slow (and nicely unusual) start for me working-out if x3 and x5 and x7 grids were even possible (x3 and x7 fairly easy to eliminate) but then struggling to find where the 4x4 would fit! Once found, the puzzle flows relatively easily from there.
Great puzzle, and a very entertaining solve as usual. If it wasn't clear already, I think the latter part of this video proves Simon's aversion to "Goodliffing". I do enjoy all the coloring though, so it's all fine I guess.
I read the rules: "This puzzle contains exactly three Latin Squares ...": wait, wait, wait, exactly, it says? That's the one word that will probably solve this puzzle...
I struggled to figure out this puzzle because though I knew the latin squares had to be a 2x2, 4x4, and 8x8. The title of the puzzle was misleading because I was assuming that each square had to be COMPLETELY nestled within the next. It maybe would be nice if the rules explained that this did not have to be true because it was confusing and I'm likely not the only one that understood it that way. No matter what I still love this channel and I will continue trying all the puzzles myself ☺
Have to say that I find it a little misleading to say there are only 3 Latin squares. By definition in the final result there are many 2X2, so why could the 3 and 4 pair in R3-4C5-6 not be considered a Latin square to fulfil the rules? As always absolutely enjoy Simon's solve, and his painstakingly thorough investigation of multiple options to both teach and solve the puzzle in an entertaining manner.
If you think about it carefully, a Latin square in this puzzle is defined as an NxN grid with the digits 1 to N in each row and column without repeats. So 1's and 2's in a 2x2 grid is valid, and 1's, 2's, 3's and 4's in a 4x4 grid is valid. But two 3's and two 4's in an X pattern doesn't count as a 2x2 Latin square with this definition. Either it would have to be made from 1's and 2's, or if it involves a 4, you could only consider a square at least 4x4 in size and including all the digits from 1-4. So however you look at it, it's never one of the Latin squares under this definition.
The rules specifically state: In this puzzle, a Latin Square is defined as an NxN grid of cells that contain only the digits 1 to N where N>1, in which digits do not repeat in a row or column.” The patterns you describe don’t match the definition of the rules.
It will depend on the type of display you are watching on, and the amount of Dow processing of the video that is done in either editing, or UA-cam converting for your display. I don’t know if Simon checks for how many viewers are watching on different display types, but the display of RGB is different on computer screens versus mobile devices versus TV screens. Computer screens without processing will show this contrast no problem, but after webm conversion for UA-cam it gets harder to see, and then on mobile or TV screens it will be worse again. I get about 60% views on mobile devices, and about 15% on TVs, so I always try to check my colour grading after processing, but it’s a lot of work.
Disambiguating based on avoiding a Latin square was not even in my brain at all! Finding that little thing was the very last thing for me, and that was tricky! Brilliant puzzle!
10.37 for me. Surprised myself with that one. Usually takes me an age. The kropki dots in row one will only work with the 2x2 starting in column 5 to 6
Rules: 01:36 Let's Get Cracking: 09:20 Simon's time: 32m19s Puzzle Solved: 41:39 What about this video's Top Tier Simarkisms?! Bobbins: 3x (03:24, 03:29, 23:36) Phistomefel: 2x (02:38, 02:38) Three In the Corner: 1x (33:37) And how about this video's Simarkisms?! Hang On: 11x (11:48, 16:23, 17:01, 23:44, 29:56, 32:00, 32:17, 32:17, 32:17, 32:51, 33:43) Sorry: 6x (06:48, 15:05, 20:47, 26:50, 28:59, 41:11) Brilliant: 6x (02:29, 04:34, 05:39, 07:13, 41:47, 41:50) In Fact: 5x (10:44, 13:12, 24:01, 27:36, 30:23) Ah: 5x (16:17, 19:17, 26:09, 38:45, 41:20) Horrible Feeling: 3x (13:30, 13:55, 38:37) Beautiful: 3x (05:26, 21:02, 25:41) Deadly Pattern: 3x (34:57, 37:28, 38:39) Clever: 2x (19:21, 19:21) Obviously: 2x (10:18, 22:02) Cake!: 2x (05:05, 06:22) Good Grief: 1x (35:51) Goodness: 1x (41:08) Naughty: 1x (35:58) Stuck: 1x (04:26) Break the Puzzle: 1x (25:11) Fascinating: 1x (42:08) Incredible: 1x (01:16) Ridiculous: 1x (30:35) First Digit: 1x (31:25) Gorgeous: 1x (04:03) By Sudoku: 1x (34:31) Progress: 1x (20:51) Wow: 1x (07:39) Have a Think: 1x (15:08) Weird: 1x (08:29) Most popular number(>9), digit and colour this video: Thirty Eight (3 mentions) One (65 mentions) Black (8 mentions) Antithesis Battles: Even (6) - Odd (2) Black (8) - White (5) Row (21) - Column (15) FAQ: Q1: You missed something! A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn! Q2: Can you do this for another channel? A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!
If the largest Latin square in the puzzle had N < 8, then there would be nothing in the rules to prevent me from filling the outer squares (that weren't in any Latin square) with 9, 10, 11, 9000, etc! So the lack of any rules about what digits were allowed in the puzzle was a big hint about how big the largest Latin square was going to have to be.
26:15 finish. I definitely was a bit slow on the uptake with some of the logic on this one. Once I got into it, however, everything dropped quite nicely. Excellent!
I wish the rules were more specific. Since we don’t have “normal sudoku rules apply”, I had no idea whether digits could repeat outside of the square, or go to 9 or higher, like in, say, a fillomino, or if zero was allowed, that sort of thing. Edit: Never mind, it seems that actually isn’t necessary.
What a brilliant puzzle! Mind-boggling how the “exactly three Latin squares” condition led to the unique solution. Also there couldn’t be a 3x3 Latin square could it?
Well, I looked at this for like twenty minutes to get the 2x2, 4x4, 8x8 logic and it took Simon like one! (I didn't get beyond that.) Edit: lol a 1.5x1.5 can't be a Latin square because it's less than 2 and not because it involves half a cell?
For once I actually solved this faster than Simon T-T. But that was only cuz I always get rid of my pencil marks as soon as I can XD. He did the actual logic much *much* faster than me.
That was so satisfying even with forgetting the knights move constraint for a while. I sure wish Sven had a series of common rule icons visible along the top of the grid or something.
hmm...I'm going to have to watch the video to figure out why what I did didn't work. I put a 2x2 in the bottom right corner and a 4x4 also in the bottom right corner - basically, all my squares share the bottom right 4 squares. All the dots worked out fine, but I came up with like 20 deadly patterns. There must be something wrong with how I put the squares, but if it violates the rules then I don't understand why. Edit: oooooh! I missed the word "exactly." Got it!
i reached a different solution, except it was wrong, i didn't take enough notice of the "EXACTLY" three latin square.. my 2x2 latin square repeated inside of it T.T
Just a small bit of feedback from someone who is not colourblind as far as I know, but the combination of blue number, white outlines and the dark grey background is really hard on the eyes.
The rules specify that, for this puzzle, a Latin Square specifically contains the digits 1 to N. But you're right, the usual definition of a Latin Square allows for any selection of digits, symbols, letters etc.
Understanding the constraints were relatively simple as was finding the solution Proving the 2nd branch wasnt valid was a bit more difficult . Well it shouldnt have been ... 2x2 of 4x4s and ur staring at the color cfg thinking If the 2nd Low 4x4 didnt contain the 2x2 latin then its not nested and thus a valid branch even though the 4x4 itself is latin...funtimes wasted
Old "pick the highest-hanging fruit first" Simon re: taking so long and doing so much harder stuff before getting to the white dot between a 1234 and a 5678...
10:09 for me. I don't understand the point of this puzzle. It's not even GAS level. I mean, it's kind of an interesting concept that it fills like that, but the whole thing solves itself.
Thank you for featuring another of my puzzles! It's actually exactly a year since the first ThePedallingPianist feature on this channel, so this is a lovely way to celebrate - and Orla has had a lovely nap while her daddy watched this video!
Spoilers below...
The solution path was pretty much exactly as intended! Once you've worked out that the grid effectively contains four 4x4 Latin Squares (albeit two contain the digits 5-8 and two wrap around the grid), there are a couple of "secrets" I found very interesting that can help speed things up, though they don't really alter the solve path.
Firstly, you know that digits exactly 4 orthogonal steps in a straight line away from each other will be opposite polarity (especially helpful in conjunction with the very deliberately placed black dots in rows 4/5). Secondly, within each 4x4 Latin Square (even the ones that wrap around the grid), digits exactly 2 diagonal steps away must be the same.
As for that disambiguator near the end - I don't think you're alone in thinking it was horrible! If I'd replaced the row 8 white kropki dot with a black one just to the left, that disambiguation wouldn't have been necessary and the solution would still have been the same... but I decided it was too long since I made the solver consider the theme of the puzzle, and after all, I am horrible!! :D
I thought that the disambiguation near the end was genius! I saw the deadly pattern developing as Simon was solving, and knew that he would apply the rule immediately (especially since he had so thoroughly considered the placement options for the 2x2 Latin square early on) - and was very amused that he did not catch on to it right away! Brilliant in every way, thanks for creating the puzzle (and for your year's worth of contributions!)
@@emilywilliams3237 This was my favourite part of the puzzle too, and I definitely didn't catch it right away - took me a while too. But loved it because as Stuart said, it made you reconsider the theme of the puzzle when you thought that part was done and dusted. Lovely
What’s your favorite puzzle you’ve created?
Another lovely construction from you!! Appreciated the insight into your mind a bit!! The ending was indeed fantastic and fabulous!
@@martysearsit was lovely indeed and fabulous as to how it tied into the title of the puzzle!!
Probably worth mentioning that a 3x3 latin square can't exist no matter what simply because it violates the knight's move condition
This is how I figured it out in the first 30 seconds or so. You just can't do a 3x3 with knight's move.
great point!
i don't think I've ever seen as much fear in Simon's eyes than when he thought he had that deadly pattern! The resolve was genius though. This whole puzzle is just brilliantly coherent, the peddling pianist creates art once again! A little outside of my comfort zone so I didn't try it this time, but as always I thoroughly enjoyed watching your solution :)
It really is hilarious many times Simon does an anti-knight puzzle and doesn't instantly realize that's how he's going to resolve a deadly pattern.
When I was in college, the pure math professors would call that wrap-around thing Toroidal Boundary Conditions, like Simon does, but the applied math professors would call it Pac-Man Boundary Conditions.
Whatever you call it, it's lovely stuff. The lower green 4x4 has all four copies of the same digit on the same positive diagonal (with wrapping), while the upper has the 1s and 4s on the positive diagonal, and the 2s and 3s on negative diagonals. The lower black 4x4 has the even digits repeating along positive diagonals, and the odd digits repeating along negative diagonals. The upper black 4x4 reverses it, with the even digits on negative diagonals and the odds on positive diagonals.
Omg saw that negative constraint step near the bottom left coming and was so happy it did indeed not only show up but was necessary to the solve, so delightfully clever
It's such a conceptual idea, less about unwinding logical "knots" in the grid and more about sitting back and contemplating the nature of the thing. Such a unique idea and as always from ThePedallingPianist so beautifully executed (and with 60% less pulling your hair out! which is the usual case for the mad genius).
The fact that this puzzle can exist is just *chefs kiss*
These puzzles in puzzles in puzzle
They tend to confound and confuzzle.
They leave my brain reeling
And leaving me just feeling
Like I need a hug and a snuzzle.
Love the outro music!
(Eats all your carrots and leaves a Father Christmas matroishka)
I must say, I would have just plonked the initial 2x2 right in the middle of the grid, assuming that of course that must be it, and then gotten very far away from the actual solution. Thanks for being thorough, Simon, and demonstrating this not only on this puzzle, but in several others. And thanks for this lovely video!
One of the umpteen things I've learned over the past three years or so of watching CtC is to re-read the rules when I get stuck. Sure enough, suddenly the word 'exactly' gave me the the way forward.
Finding the other potential 2x2 latin square before Simon made my day! I feel so smart today. 😄
Ah yes, just as I was sitting down to do my work. You always post at the perfect time to make me procrastinate the most! In all seriousness though, you guys videos are great to have on in the background while I work, so I thank you for your consistency and amazing solves!
1,000 copies of me in 1,000 rooms with 1,000 pencils could not have solved this in 1,000 hrs, much less been able to set something lke this. You really are very talented, Simon, and the setter is a true genius!
Thank you for the birthday greetings! Pronounciation and geographie were spot on 😊
And such a beautiful puzzle this is.
This puzzle was more than good, it was fun!
I have no idea how you were able to solve that with the chosen colour scheme. The blue pencil marks on the dark green and black highlighted squares were very difficult on my eyes.
Funny(now) Story: At the very beginning, I got so stuck and confounded that the checker was telling me some digits were wrong. I rechecked my logic twice, before giving up in a huff and coming back to the video to pout in defeat. I assumed the rules were written strangely, and Simon would tell me what grammar technicality I'd missed. And then, watching Simon's elimination of the corners, I got even more confused because he was doing it exactly as I was, and found the location of the 4x4!
It was at this moment, after staring at the two squares I had filled in, and clicking the check button a few times in case it would change its mind, that I realized a black dot crossing the edge of the 4x4 could have 4/8, and not just 3/6.
I have reached the skill level just past novice, where my confidence flies too close to the sun; it must be a broken solve checker, before it could be my still-developing kropki instincts!
Back to the basics for me, while I complete this solve extra carefully. You are the best teachers one could ask for ❤
Even though I couldn't solve it entirely myself - needed to listen Simon's explanations in the beginning to get anywhere - I still loved this puzzle, the way you needed to figure the next steps. I particularly liked how knight's move and the square limit were used to solve the deadly patterns. Took me about an hour.
i would love more puzzles of this type.
What a beautiful puzzle 👍
I have to say that I absolutely love your videos. I've been watching for a while and have been pausing the video right after you start the puzzle and give it a shot myself. I managed to get this one on my own today. Watching it afterwards and seeing you be like "wait something is wrong" in regards to the 1/3 in the bottom was the exact same thought process I had. Appreciate everything you and the team do with this channel!
256 pencil marks simultaneously. This must be some kind of record
For the double clicking to work, you’d have to remove the black. When you double click a square that is both blue and black, the software will highlight any squares that contain blue or black.
Yes.
You can get away with temporarily removing the black from just one black/blue cell, so that it's just blue, then double-clicking it to select just the cells that contain any blue.
But there wasn't really any need to keep any black at all, and it would have made reading pencil marks and digits a lot easier had it been removed earlier (or even better, never used at all - it's too dark!).
@@RichSmith77 Yes, the black background with the digits being outlined in white was literally giving me a headache.
That was another goos solve Simon, but yout persistent use of dark colours made it practically impossible to visually follow the solve, even on a 22" inch screen. Totally impossible on an iPhone. Please try to delete unneeded colours, thank you.
This was great, really liked it. The break in is tough!
The simple way to rule out a 3 x 3 latin square from the start is to realise that it would immediately break the anti-knight rule
One of those problems where every word of the instructions is crucial. I went around in circles with a 3 and 4 "2x2" square until I realised it wasn't breaking the rules. Nice solve
Took me a bit to understand the rules, but once I got them, the puzzle to me 10:32. Very nice.
One of the best!
Don’t know how. But it’s the first time my brain got a puzzle instantly. 17:22 finish
I did this puzzle late the other night and was sure it would make its way here. There is one deduction that just eluded me for way too long (it was so obvious in hindsight), and i fully expect Simon to just get it within the first few minutes.
Yup, I got the deduction that you can't fit an N square in an N+1 square, but I missed that the minimum nesting size was 2N. I also concluded that a 2×2 couldn't live in the corner of a 4×4, but I forgot to explore putting a 2×2 anywhere else in the 4×4. Simon is, as expected, shooting well ahead of my 11pm brain
You literally had the solution for the N*N grid being limited to exactly 3, but somehow forgot it immediately. Maybe it was way under your radar. Love your videos.
19:58 for me. That puzzle was a lot of fun to solve, even if I did take way too long to recognize that no Latin square could be embedded in the corner of another.
My solve path ended with that nearly deadly pattern of 1s and 3s in the lower left, and I found the way that that disambiguated to be an absolutely beautiful ending to the puzzle.
Brilliant. I worked backwords from 8X8, because to go down from there you need to go to 4x4. And there are no 1:2 ratios in the 5-8 sets, so the 4X4 needs to incorporate as many black dots as possible and land any others on a line between regions.
That was a beautifully mind-blowing puzzle. Thanks for featuring it wow
I figured one of the Latin squares had to be 8x8 because otherwise there would be no way to know how to fill the outer perimeter.
This was so clever. Just when I thought I'd get stuck with just one xwing remaining, I realized that one possible solution would drop a second 2 by 2 Latin square in the grid, and that was the final disambiguation. Just when you thought you were done with thinking about those boxes. 00:24:39, now I've got to see Simon solve it just to see if he runs into the exact same situation.
And he panics over the 13 xwing just like I did.
And just once I even beat Simon. Makes one feel good, that's 2 days in a row I solve something. Thanks goodness we've got these wonderful teachers.
The way I determined the 4X4 is this: (suppose we use the same color scheme as Simon)
- On each black dot, there is at least one green square.
- Since each row must have 4 consecutive (potentially wrapping) greens, r1c5, r1c6, and r1c7 must be green.
- This implies the blackness of r5c5, r5c6, and r5c7.
- We then need a green at r4c5.
- This fixes a rectangular region of greenness at r1-r4 X c5-c7.
- If the last column of the 4X4 is at c8, then there would be two 4X4 in the puzzle. Thus, the 4X4 must be r1-r4 X c4-c7.
I spent twenty or so minutes just playing around in the grid, and thought I had one of seemingly multiple solutions. Then I realised the importance of there being *exactly* three Latin squares, and no more! I had a 4x4 in one corner, so naturally had an extra Latin square in the opposite corner. But it took me a few minutes of head scratching to work out why I hadn't stumbled on a valid solution.
So then I restarted the puzzle and did it a lot more methodically, finding the right spot for the 4x4 the same as Simon. I completed that 4x4, then all the 5678s, and finished with the seemingly deadly 13 pattern. I also couldn't see immediately how it could possibly be resolved, yet I was so close! Felt great when it dawned I couldn't create a second 2x2 Latin square.
Another point, having sussed there must be an 8x8 Latin square surrounding the whole lot - you could choose a purple frame, so if there's no three in the corner at least you get a sing-song.
18:21 for me. Absolutely incredible. Loved this one so much!!
What a mesmerizing puzzle! I remained baffled for a long time, more or less tracing out all the same exploratory dead ends Simon did (but more slowly). Even when I finally found the right track, I was prepared to learn I'd gone horribly wrong. I've never been so happy to reach the end of a puzzle (after overcoming the beautifully-baked-in deadly pattern panic at the end; for me the "wait, that would make an extra Latin square" step was the very last one).
Such a nice and logical path to solution...once you locate the squares
I, as a russian, really love it when english speakers struggle to pronounce "Matryoshka"
What a gorgeous puzzle. I would like to highlight that nowhere in the rules does it state that you have to put the digits 1-8 in every row and column, nor does it state that every digit has to appear 8 times, that's just the logic that follows from the 3 nested latin squares determining that the minimum size of the third square is 8x8.
Had trouble wrapping my mind around a puzzle that wraps around. Enjoyed watching Simon figuring it out, though! I don’t usually try to do the monthly puzzle packs, but snack-adoku sounds like something I can handle - right??? 🤔
I absolutely believe you can do the snack-adokus!! 🙂
@@davidrattner9 thank you for your confidence!!! ❤️
What a great puzzle!
Slow (and nicely unusual) start for me working-out if x3 and x5 and x7 grids were even possible (x3 and x7 fairly easy to eliminate) but then struggling to find where the 4x4 would fit! Once found, the puzzle flows relatively easily from there.
Great puzzle, and a very entertaining solve as usual.
If it wasn't clear already, I think the latter part of this video proves Simon's aversion to "Goodliffing". I do enjoy all the coloring though, so it's all fine I guess.
Nice puzzle rule set. took me a bit of time but was able to solve it. Great work
I read the rules: "This puzzle contains exactly three Latin Squares ...": wait, wait, wait, exactly, it says? That's the one word that will probably solve this puzzle...
It's frightening how far above my head this puzzle and the solution went.
I struggled to figure out this puzzle because though I knew the latin squares had to be a 2x2, 4x4, and 8x8. The title of the puzzle was misleading because I was assuming that each square had to be COMPLETELY nestled within the next. It maybe would be nice if the rules explained that this did not have to be true because it was confusing and I'm likely not the only one that understood it that way.
No matter what I still love this channel and I will continue trying all the puzzles myself ☺
I am a new father, and I barely have the time to SOLVE two puzzles a day. No idea how he can create them.
So interesting to watch this solving.
Have to say that I find it a little misleading to say there are only 3 Latin squares. By definition in the final result there are many 2X2, so why could the 3 and 4 pair in R3-4C5-6 not be considered a Latin square to fulfil the rules? As always absolutely enjoy Simon's solve, and his painstakingly thorough investigation of multiple options to both teach and solve the puzzle in an entertaining manner.
If you think about it carefully, a Latin square in this puzzle is defined as an NxN grid with the digits 1 to N in each row and column without repeats. So 1's and 2's in a 2x2 grid is valid, and 1's, 2's, 3's and 4's in a 4x4 grid is valid. But two 3's and two 4's in an X pattern doesn't count as a 2x2 Latin square with this definition. Either it would have to be made from 1's and 2's, or if it involves a 4, you could only consider a square at least 4x4 in size and including all the digits from 1-4. So however you look at it, it's never one of the Latin squares under this definition.
The rules specifically state: In this puzzle, a Latin Square is defined as an NxN grid of cells that contain only the digits 1 to N where N>1, in which digits do not repeat in a row or column.”
The patterns you describe don’t match the definition of the rules.
This was brilliant, but the blue pencil marks on grey were horrible. Wish Simon had removed the background color once he'd found the squares....
It will depend on the type of display you are watching on, and the amount of Dow processing of the video that is done in either editing, or UA-cam converting for your display.
I don’t know if Simon checks for how many viewers are watching on different display types, but the display of RGB is different on computer screens versus mobile devices versus TV screens.
Computer screens without processing will show this contrast no problem, but after webm conversion for UA-cam it gets harder to see, and then on mobile or TV screens it will be worse again.
I get about 60% views on mobile devices, and about 15% on TVs, so I always try to check my colour grading after processing, but it’s a lot of work.
Did this one a couple of days ago and thought it might end up here. Took me 17 minutes
Congratulations to everyone who turned up on the October Roll of Honor -- lovely to see so many familiar names. 😺💚
Goodness me it takes a long time for your videos to start these days.
Disambiguating based on avoiding a Latin square was not even in my brain at all! Finding that little thing was the very last thing for me, and that was tricky! Brilliant puzzle!
10.37 for me. Surprised myself with that one. Usually takes me an age. The kropki dots in row one will only work with the 2x2 starting in column 5 to 6
Very strange puzzle for me as I am not familiar with Latin Square. But very good solve, I don't even dare to try it! 🐖
30:13 for me. Beautiful puzzle!
Rules: 01:36
Let's Get Cracking: 09:20
Simon's time: 32m19s
Puzzle Solved: 41:39
What about this video's Top Tier Simarkisms?!
Bobbins: 3x (03:24, 03:29, 23:36)
Phistomefel: 2x (02:38, 02:38)
Three In the Corner: 1x (33:37)
And how about this video's Simarkisms?!
Hang On: 11x (11:48, 16:23, 17:01, 23:44, 29:56, 32:00, 32:17, 32:17, 32:17, 32:51, 33:43)
Sorry: 6x (06:48, 15:05, 20:47, 26:50, 28:59, 41:11)
Brilliant: 6x (02:29, 04:34, 05:39, 07:13, 41:47, 41:50)
In Fact: 5x (10:44, 13:12, 24:01, 27:36, 30:23)
Ah: 5x (16:17, 19:17, 26:09, 38:45, 41:20)
Horrible Feeling: 3x (13:30, 13:55, 38:37)
Beautiful: 3x (05:26, 21:02, 25:41)
Deadly Pattern: 3x (34:57, 37:28, 38:39)
Clever: 2x (19:21, 19:21)
Obviously: 2x (10:18, 22:02)
Cake!: 2x (05:05, 06:22)
Good Grief: 1x (35:51)
Goodness: 1x (41:08)
Naughty: 1x (35:58)
Stuck: 1x (04:26)
Break the Puzzle: 1x (25:11)
Fascinating: 1x (42:08)
Incredible: 1x (01:16)
Ridiculous: 1x (30:35)
First Digit: 1x (31:25)
Gorgeous: 1x (04:03)
By Sudoku: 1x (34:31)
Progress: 1x (20:51)
Wow: 1x (07:39)
Have a Think: 1x (15:08)
Weird: 1x (08:29)
Most popular number(>9), digit and colour this video:
Thirty Eight (3 mentions)
One (65 mentions)
Black (8 mentions)
Antithesis Battles:
Even (6) - Odd (2)
Black (8) - White (5)
Row (21) - Column (15)
FAQ:
Q1: You missed something!
A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn!
Q2: Can you do this for another channel?
A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!
If the largest Latin square in the puzzle had N < 8, then there would be nothing in the rules to prevent me from filling the outer squares (that weren't in any Latin square) with 9, 10, 11, 9000, etc! So the lack of any rules about what digits were allowed in the puzzle was a big hint about how big the largest Latin square was going to have to be.
26:15 finish. I definitely was a bit slow on the uptake with some of the logic on this one. Once I got into it, however, everything dropped quite nicely. Excellent!
I wish the rules were more specific. Since we don’t have “normal sudoku rules apply”, I had no idea whether digits could repeat outside of the square, or go to 9 or higher, like in, say, a fillomino, or if zero was allowed, that sort of thing.
Edit: Never mind, it seems that actually isn’t necessary.
Yep, I definitely took the fact that the rules had no clarifications about that as a big hint about how big the largest Latin square would be!
Yes, I got stuck at the 1,3-x wing.
Will this puzzle steal my washing machine?
What a brilliant puzzle! Mind-boggling how the “exactly three Latin squares” condition led to the unique solution. Also there couldn’t be a 3x3 Latin square could it?
Can anyone share what the closing song is? It's such a beautiful string, I'd love to hear more. 🎶
Be careful about the 5s and 7s so they don't grow into black dots.
Be careful about the 3s and 4s too so they don't attach to the 6s and 8s too quickly.
Well, I looked at this for like twenty minutes to get the 2x2, 4x4, 8x8 logic and it took Simon like one!
(I didn't get beyond that.)
Edit: lol a 1.5x1.5 can't be a Latin square because it's less than 2 and not because it involves half a cell?
For once I actually solved this faster than Simon T-T. But that was only cuz I always get rid of my pencil marks as soon as I can XD. He did the actual logic much *much* faster than me.
That was so satisfying even with forgetting the knights move constraint for a while. I sure wish Sven had a series of common rule icons visible along the top of the grid or something.
hmm...I'm going to have to watch the video to figure out why what I did didn't work. I put a 2x2 in the bottom right corner and a 4x4 also in the bottom right corner - basically, all my squares share the bottom right 4 squares. All the dots worked out fine, but I came up with like 20 deadly patterns. There must be something wrong with how I put the squares, but if it violates the rules then I don't understand why.
Edit: oooooh! I missed the word "exactly." Got it!
18:00 Did you just invest toroidal regions??? You can use toroidal regions together with killer cages probably!
Question of definition - does "nested" mean on all 4 sides or just held in the crook of an L, like in Simon's initial demonstrations?
The only way to figure out the 1s and 3s at the bottom is indeed to realize you would be creating a 4th Latin Square.
Is anyone else bothered by the fact Simon destroyed the coloring pattern of the 3 Latin squares by making all 1234 in rows 5-8 green? 😢
i reached a different solution, except it was wrong, i didn't take enough notice of the "EXACTLY" three latin square.. my 2x2 latin square repeated inside of it T.T
Just a small bit of feedback from someone who is not colourblind as far as I know, but the combination of blue number, white outlines and the dark grey background is really hard on the eyes.
Does anyone know what the outro music is? (Some kind of Pachabel arrangement?)
Green and black aren't the best colours for readability of small digits!
15:35 I freely admit that was a fluke. I should probably stop using bifurcation.
I solved this almost exactly 21 minutest faster than Simon.
49:56 for me. guessing game
I see too many additional 2*2 Latin squares, starting at R1C2, R2C1, R3C2, R5C4, R5C6, R6C5, R6C4, R6C6
Am i missing something ?
The rules specify that, for this puzzle, a Latin Square specifically contains the digits 1 to N. But you're right, the usual definition of a Latin Square allows for any selection of digits, symbols, letters etc.
@@ThePedallingPianist Fair Enough 👍
Funny how obvious patterns doesn´t cross his mind though he is talking about it.
Understanding the constraints were relatively simple as was finding the solution
Proving the 2nd branch wasnt valid was a bit more difficult . Well it shouldnt have been ...
2x2 of 4x4s and ur staring at the color cfg thinking
If the 2nd Low 4x4 didnt contain the 2x2 latin then its not nested and thus a valid branch even though the 4x4 itself is latin...funtimes wasted
Old "pick the highest-hanging fruit first" Simon re: taking so long and doing so much harder stuff before getting to the white dot between a 1234 and a 5678...
the rules did not trensalte for me to human thoughts. i had to watch the video and am still on the fence about understanding.
Maryland is pronounced very close to Marylebone, just drop the B and add a D.
10:09 for me. I don't understand the point of this puzzle. It's not even GAS level. I mean, it's kind of an interesting concept that it fills like that, but the whole thing solves itself.