This fits (at least for me it does), because throughout this I got the distinct feeling that I am not even smart enough to *assess* how stupid I am compared to Phistomefel.
Same. While he’s amazed by the design, I’m amazed he even worked out the first part. He does such a good job of explaining that it seems obvious once said, but I’ve never been able to work out any of these on my own.
Pro tip: If you want to feel 50% less stupid, set the playback speed on the video to 0.5. As a bonus, it appears that Simon is sloshed as he solves these.
Can you just take 5 minutes to contemplate about how it feels to have every grand-master puzzle constructor in the whole world competing against each other to impress you with their marvellous creations? Come up with some new adjectives and epithets to describe that. It's got to be whatever the polar opposite of "lugubrious" happens to be. The true beauty of it is how EVERYBODY WINS. We all get to play-along and enjoy watching / solving the best puzzles in the world while a middle-aged English poet teaches us about X-Wings and Sword-Fish, just like we're hearing about them for the very first time.
It really is amazing what they woke up in all of us. I have never been that good at sudoku, and have mostly tried to solve it because my dad likes them. The viral one with diagonals and the middle magic square caught my eye, and I sent it to my dad. We competed for a few days who is going to finish it first! (we both didn't get a lot of time to do it, so we solved in multiple sittings) That was my first hard sudoku solve, and I already have an idea for a constraint that I think Simon will love! I've been trying to construct it for a few days, but no luck. Just have to try harder 😊
Honestly. I discovered this channel in the last month or so, haven't done a sudoku in years. And never above a casual intermediate puzzle from a super market book. The way that he teaches complex concepts from the ground up is fantastic. I'm the guy hearing about the X-Wings and the Sword-Fish for the very first time.
@@WizardlyTim Same here. I stopped playing because the sudoku books just became too easy and boring. After finding Simon though and him showing me a whole new universe of various kinds of puzzles, I just can't stop doing them again!
Grats! This is one I should have tried before watching, because I saw the first few steps that Simon went through before he was done talking. I haven't actually done a soduku in, like, ever. The symmetry made this puzzle very easy compared to some other crazy shenneagians Simon usually goes through.
@@vvalph9483 I was actually terrible at sudoku up until a month or 2 ago. Then he released a video with a sodoku with no numbers that went viral and I suddenly watched like 15 of these sodoku videos, with all different intricacies and crazy logic to get through them. Now, I'm starting to see things as Simon does and it's pretty cool.
As someone who's been watching your videos for a full month now (thanks quarantine), I feel like I've graduated from understanding the puzzle-SOLVING process to being desperately curious to understand how the heck these puzzles are DESIGNED to unfold in specific ways in the first place. Please encourage Phistomefel and any other puzzle-creators to make videos about how they accomplish this! I imagine that it must be deeply complementary to the process of solving these, but I absolutely can not see or imagine how. In this respect a series on puzzle design would be extremely illuminating, I'm sure.
This is the first puzzle I managed to complete! I did it in 31 min!! That was easily the most breathtaking experience of my life and as I kept going I started audibly shrieking because this puzzle was just so beautiful and mindbending.
Simeon Ivanov you can do that but for most of the ones shown on this channel it’s not like this. Simon sometimes says it as well. If a sudoku is constructed by a computer it’s not as beautiful as when done by humans. There is just a lack of things like flow, symmetry or beauty. This here is a hand-set Sudoku and I have no clue how you do it. But I certainly know that a computer can’t do that
Mark Jacobs I’m actually not sure if you could do that. How do you get a computer to give you a certain way of solving a puzzle. If someone is able to program something like a “beautiful” sudoku maker or even a helper for sudoku Setters, you’ll have my money.
I only discovered this channel a week or so ago and have been binging a lot of the videos and I just wanted to say I really appreciate how even after you've spotted an apparent pattern to the solution, you always double check that any digits you place still have a logical reason to be there beyond "it fits the pattern"
Yeah, I completely agree. And in this case it would've completely blown up in my face, because I saw the 1, 2, 3 in the bottom left diagonal, and the 7, 8, 9 in the top right diagonal, and went "well that obviously means that the middle bit is 4, 5, 6!" Meanwhile it turned out to be 6, 5, 4.
I looked at the thumbnail and predicted that the puzzle would be symmetrical with the centre number being 5, because it has to. It would be interesting to understand the maths behind this.
@@jaylawhorn5198 It's something that is common in very restricted puzzles. I could see by the layout that it would hold true for this one. The more prescriptive the rules, the more regular the structure. I shall have to give this some consideration. It would be interesting to see how the puzzles are constructed.
If you're interested, here's the journal article on it, found on jstor: www.jstor.org/stable/27642500 The discussion of symmetric sudokus starts on page 390 (page 8 of the article, or page 9 of the pdf if you get it from the link I gave). But be warned the math is not trivial, even if it seems like it should be.
@@ronmatthews1738 Ph.D. student in electrical engineering here, currently developing technology leveraging symmetry... If every number included in the puzzle abides by some symmetry (say opposite positions add up to 10), you cannot rule out a number n in a certain position without being able to symmetrically rule out (10-n) in the opposite position. Because you have a unique solution (this is an important condition), at some point you should be able to rule out all numbers but one (the correct), in any position. While you do this, the same happens in the opposite position. For the record, by "opposite" position I mean the position who's column and rows, each, add up to 10 with the columns and rows of the position it is opposite to. Yes, I'm a nerd. :)
It IS quarter-turn symmetrical! And Gurth would apply for that case as well! I can't believe what I'm seeing. Also, "Phistomefel plans to make a video": honestly the best news so far in 2020
I admit I only had a cursory glance at the grid when I wrote this. But I just tried, and I can say with 100% certainty that it actually is quarter-turn symmetrical. tl;dr: I'm gonna use notation from math (yuck!) to prove that this makes sense. It's actually easy to see, just keep in mind that for quarter-turn symmetry, if 1 maps to 4 then 4 does not map to 1. Symmetry in Sudoku requires not just the symmetry transformation, but also some permutation of the digits. Here that would be (1,9)(2,8)(3,7)(4,6), if denoted as a product of switching two numbers in the brackets (5 is not part of the notation, because it is left unchanged). In the case of half-turn symmetry, applying two half-turns gets you back to the original grid, and the permutation needs to reflect that: i.e. applying it twice leaves the digits unchanged. But it doesn't have to be that way: for quarter-turn symmetry, applying it twice is not the same as the original, it's a half-turn. The permutation reflects that: it doesn't just swap two digits (back), but does something a bit more tricky. The permutation here is (1,4,9,6)(2,3,8,7), which you can see by looking at the corners/edges of the center box. The notation just means that when the grid is turned 90° clockwise (i.e. when the permutation is applied), 1 must turn into 4, 4 turns into 9, 6 turns into 1, 3 turns into 8 etc. Which is what we can observe in the final solution. Just as an intuition: the subcycles (1,4,9,6) and (2,3,8,7) both have length/order 4, that means applying them four times gets you back to where you started. Just like the underlying quarter-turn would suggest. Oh hi you found my secret cookie stash. 🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪
@@ilonachan ok fine, with the additional permutation. Number mirroring is already obligatory because of sudoku and so doesn't really need specification. BTW I'm as good as certain that this is the most symmetrical sudoku one can get. Bonus question: how many essential different sudoku's of this type are there? Answer: 80 {:-)
what really surprised me was how easy it was. At first it seemed nearly impossible, but after a few minutes of thinking differently it became one of the easier puzzles lately. These large cage killers really require a different thought process
@@mauer1 This one actually has a 4-fold symmetry, so you only need to solve a quarter. It's even easier than that actually since Sudoku rules interact with symmetries. Symmetries make a lot of things very easy.
You guys are amazing, and these constructors that send you puzzles are amazing also. For the first time in my life, this is the only channel that i haven't missed a single video you uploaded for 3 months straight. This puzzle is amazing, it took me 42 minutes, and it was a nice figuring the puzzle out and figuring the similarities and mirrored digits. This is the most fun i had while solving a sudoku. Well done Phistomofel.
My first time solving a Phistomefel puzzle without Simon's help!! I'm happy it was such an awesome puzzle. Can't wait to see more of this guys works of art.
i love this. when you add up the sum of the symmetry it is 10. the whole puzzle thats the case. the moment you figure that out the puzzle becomes a bit easier. or to me it does anyways. this is the type of puzzle that makes me feel good about the world. there is order, the chaos of normal sodoku vanishes. absolutely love it.
Amazing puzzle! After a couple of months watching every video of this channel, being able to solve this puzzle by myself felt like a graduation. Thanks, Simon, Mark and all those brilliant constructors!
There's a lovely way to complete the puzzle without "checking" the 5 in the top-left corner at 15:46 - look where the digits 3,4,8,9 can go in column 6. Then likewise look where 1,2,3,4 go in row 4. Do the same for column 4 and row 6 (using the symmetry) and you find that the only possible place a 5 can go in the middle box is at the very center, and the puzzle solves beautifully. Thanks SO much for sharing this gorgeous puzzle with us, you bring so much joy!!
I watch every single thing you guys put out. I wasn't sure I was going to like this, but I did. I started by coloring the cages and immediately saw the symetry. After the two solavable cages gave 1,2 and 9,8, I knew this was going to be like a pinwheel. It didn't disappoint. Just beautiful to see the numbers staying true to the pattern.
This is just another level construction. Each time, Phistomefel impresses me. What's so beautiful about this is it takes 15-20 mins to find one digit but once we do it just finishes so beautifully.
really beautiful puzzle, I went back to this after a year because I remembered how lovely the construction is. I remembered it was one of the first times I've seen a setter take advantage of the geometry of the killer cages in such a unique way. Outstanding indeed
I fell upon one of your videos last week and I have never been more intrigued. It is such a joy to see the excitement and wonder in your eyes as you solve these puzzles with incredible wit. Wish I was here from the start! Definitely have some binging to do. Love the work you’re doing Simon, can’t wait for more.
The logic and the symmetry behind this was gorgeous! When you look at it first, it seems like it's impossible to get even started... but once you grasp the logic, it all blooms out beautifully. :)
When I tried this on logic masters Germany, I found the central 5 a different way; when you list all the possibilities in boxes 2, 4, 6, and 8, you can deduce that there must be a 5 in the side 3 cells in box 2, a five in the top 3 cells of box 6, a five in the bottom 3 cells in box 4, and a five in the 3 side cells in box 8. Using sudoku, that eliminates a five in all cells except for the center in box 5!! That’s how I progressed in the puzzle at that point. As always, great job Phistomefel. You are definitely the best puzzle setter I’ve come across!!!
I noticed that rows 4&6 and columns 4&6 have quintuples(?) that all combine to force 5 out of every middle box square except dead center. 5 was actually the first digit I placed :P it's cool that there's multiple ways of finding that square I can't tell if you found it the same way as I did, so forgive me if I just worded your method differently haha
I found a 5 directly in the center as well although not by listing all possibilities. Rather I noticed the opposite squares of numbers shared no common digits. This makes the 6,7,8,9 in box 4 a 'new york times' quadruple. Where do they go in row 6? There are only 4 positions outside of box 4, which limits where the 5 can be placed. Thinking about quadruples helped a ton as well because in box 5 you have intersecting quadruples. So without writing in a ton of stuff, I was able to place a 12, 34, 67, and 89 pair in the central box on the corner cells without cluttering up the grid with possibilities.
My time was 19:36. I do find most puzzles on this channel to be well constructed, but never are there any that leave me this stunned by the construction. This puzzle is legitimately brilliant.
It's due to the symmetric nature of the puzzle. Every number, when added to its symmetrical opposite, makes 10. So whatever 7-sized cage you're looking at, even ones that are not given in the puzzle, makes 10 x 7 = 70 . Any N-sized cage actually adds up to 10N when added to its symmetrical opposite.
@@RaimbetteLB But not all symmetrical puzzles add to 10. Check out today's puzzle, where 6 is the pivot, meaning that some pairs add to 10 while others add to 11.
@@sabinrawr In no way is yesterdays puzzle symmetrical. Sure, the path to solving it uses the same "trick" several times in a rotation, but if you look at what comes after as well as the solution itself theres nothing left of said symmetry. 6s are facing 6s, 2 are facing 8s, nothing actually goes right in the end ! Unfortunately because the middle digit (1 - 9) is 5 you cannot have anything symmetric around a digit other than 5
@@RaimbetteLB The problem is your definition of symmetry. If a digit always appears opposite of another digit, it's symmetrical. The mathematics of Killer Sudoku can change the value upon which te puzzle is rotated, but that doesn't make it any less symmetrical.
Quite phenomenal that someone can create such a puzzle. I've been watching different puzzles in the channel and trying them out. Always gets stuck so I need to use the video for help, but always a pleasure to see you so joyful with these puzzles. Thanks!
That was a beautiful puzzle. I love the quick pairs and symmetry that runs around the puzzle. Took me quite a while to get an actual number. Then, when I started getting them, I couldn't fill them in fast enough and kept losing myself because of the way the logic worked in so many places at the same time! Wow.
My method of determining the central square to be a 5 was to look at the numbers available for the diagonals in the opposing corner boxes. The lower left had 12345, and the upper right had 56789. Thus the central square had to include the 2 missing numbers from each corner with only 3 squares, 5 was the only overlap so it had to be in center portion of the diagonal. The same logic also worked on the other pair of opposing corners, with 5 as the only overlap. Which meant that the central box had to have a 5 on the each diagonal, which put 5 in the central square.
I used to solve sudokus every day, but since I discovered this channel some six months ago, I haven't done a single computer-generated one and enjoyed the beauty of handcrafted grids.
Holy cow I cannot believe I was able to do that without Simon’s help! That was a wonderful solve, and it all built up to one beautiful moment when the first digit was placed in the center square.
I’m not really a puzzle solver myself but I have just stumbled across your channel and think I’ll start giving it a try! Your excitement about sudoku is so fun and makes me excited! Your channel has been a pleasure to stumble upon.
Beautiful Puzzle!!! I love the simple rule set and the logic of going around in circles around the grid for the very linear deductions. Truly a masterpiece!
Simon, I'm not sure if you'll see this, and I know it may seem excessive to say, but your videos really do help with my depressive tendencies. There is something so genuinely wholesome in your almost child-like elation at a wonderfully-constructed puzzle that brings a warmth to me that reminds me of Christmas mornings in my youth. It's inspiring to see someone find real joy in something seemingly so innocuous, it really is good for my soul.
Holy shit! This is stunning beauty! took me 30min overall. first 15 min - I was in disbelief, and didn't know how to make progress. Then I saw the beautiful interaction of the cages, and the logic flowing through the whole grid. And when i saw the rotational symmetry - my jaw dropped! INSANE! Loved it
There is a stunning beauty in this puzzle. Without doing anything else you can immediatly fill in the 5 in the middle because of the symmetry. The puzzle is unchanged if you rotate over 180 degrees and replace all numbers by their "opposite" (i.e. 1 by 9, 2 by 8 etc. ). This means that the middle square can only be the number that is its own opposite!
I am absolutely stunned by the beauty of this puzzle. The way that the creator has figured out the symmetry is amazing. Thank you for making a video of this! (I know I'm commenting late, sorry).
The killer sudoku part of the puzzle had some absolutely beautiful logic - it's not often I react to puzzles with quite the same untempered joy as Simon, but I did this time. I made it up to the "can I prove that the centre is 5?" point easily enough, but stalled there hard - it didn't even occur to me to just try all of the other possible values and check for contradictions, even though I'd already had to use that logic earlier in the puzzle. In the end, before resorting to the video, I took advantage of the apparent symmetry of the puzzle to just place the 5 and see if I could solve it from there, which I did, but I'm still frustrated I wasn't able to make that one last deductive jump to solve the entire thing without assumption. I was kicking myself when I then watched the video and saw what I'd missed.
I'm absolutely amazed by this puzzle, and I managed to finish it in an hour which is by far my fastest time on any of the puzzles on the videos that I've tried.
so happy to see your recent success with views and subscribers. this was an incredible puzzle and entirely deserving of the title you gave it. keep up the good work
I assigned a colour to every 1/2 square, and 3/4, and 6/7, and 8/9, since they appeared so often as locked to those 2. The symmetrical rainbow you got as a results was quite lovely
This took me an extremely long time, picking up tiny scraps of information along the way, until I finally placed the first digit and suddenly everything fell into place. Incredible!
After watching I’m noticing that all of this symmetry leaves a board where every digit but the center 5 has a mirror that adds to 10. Absolutely magical!
I just wanted to say, I've seen puzzles with 180 degrees of symmetry but I don't think I've seen one with such symmetry _and also_ logical inferences that work every 90 degrees like this. Singularly beautiful. Phistomefel has outdone himself and that's saying something.
My solving process: Open the link. Get completely stuck. Watch 3 minutes of this video, then make some of my own progress and get stuck again. Watch another 3 minutes... get stuck again. After Simon went through the logic of putting a 5 in the middle (which was absolutely brilliant), I was finally able to crack the rest. There are so many crazy logical leaps that I've never seen in any other killer sudoku. Love this so much.
Right away I picked up on the symmetrical placement... and by right away, I mean after staring at it for almost 30 minutes... I ended up determining the 12,34... etc pairs via a different (albeit slower) method. I noticed what cells had to contain the same pairs before identifying what those pairs had to be. After coloring those in each in their own color, I was then able to make some algebraic equations along the lines of 2 orange + 2 green + 2 yellow = 90, and then green + orange = 38, and ultimately deduce what each pair had to be from that. I wish I had seen it the way you did, as getting those pairs took several hours of staring and trial/error, but the puzzle fairly quickly collapsed after that. In any manner, Phistomefel has once again proven to be my favorite setter, and I cannot wait to see more of his work!
This puzzle was amazing! I could solve it without hints and was super rewarding. I love Phistomefel's style this was the first puzzle I could do from him
After publishing several point-symmetrical galaxy sudoku puzzles, Phistomefel creates a sudoku that is defined by its point-symmetry. I really appreciate the beauty of this.
I might have missed if this was mentioned in the vid, but from the start you can use uniqueness to place a 5 in the center square; everything is rotationally symmetric up to replacing x with 10-x, which can be seen from the empty starting grid. Hence any deductions obtained from the start must abide by this symmetry.
The symmetry in this puzzle is absolutely mesmerising. I mean at 18:00, the digits are perfectly aligned which also surprisingly all equal 10 when you add the box and it’s symmetrical counterpart.
Wow. That logical still applies even when i’m near the end of the video. This combination of a sudoku grid is art let alone the puzzle which has no given digits!
You are totally right, indeed you can apply Gurth's symmetrical placement from the start of this grid: as you noticed the cages are symmetrical, but that would not be enough. But if you notice all the number given for the cages are "symmetrical". Look for example at the first cages you considered, summing to 42 and 28, this numbers are symmetrical, meaning that for each cell you should change a number x with 10-x (1 with 9, 2 with 8 etc), so the sum of a 7 cells large (let's call it S) should reflect to 70-S. Indeed 42=70-28, and so on for all the cages. So, yes the solution is symmetrical and indeed you could apply Gurth's symmetrical placement. This puzzle is just amazing!
Like many people I suspect, I got stuck right where you did before you figured out that the 5 *had* to be the middle box where the diagonals intersect. I think we all suspected it, but I was unable to prove it without Simon's help! Once I confirmed that, it all blew open. What a great puzzle.
YEAH ! Finally did it in around 1:30:00 (2:13:52 on the timer and at least 45 minutes of break.) What a cool puzzle ! I didn't have seen your logic but I'll check it out tomorrow, it's 01:40 now...
At 12:24 we can place the 5 in r5c5. In box 6 r5c7 and r6c7 contains the contents of r4c1 and r4c2. So the 5 in box 6 is in row 4. By similar logic 5 in box 4 is in row 6, box 2 is in column 4 and box 8 in column 6. This forces 5 in middle box to r5c5. Rest of the puzzle unwinds easily...
01:06:06 solve time for this, about 3/4 of which was spent spotting the pattern and the symmetry of the grid, much like the video solve. After figuring out the eight corner cells the rest of the puzzle went smoothly, but I was pretty slow getting there. Another clever construction from Phistomefel.
5 must always be in the centre as you said, “the puzzle is turned 180°”. Therefore, when the 5 in centre turns 180, it lands on itself; adding them together will get you 10, which is what all other numbers add up to with their counterpart.
@@oliolion For me I was able to determine that 5 must be in the middle. I filled in the 5 remaining digit possibilities for boxes 2, 4, 6, & 8. So, this means that in column 4, cells, 1,2,3,8,&9 are a 34589 pentuple. Similarly, there is a 12567 pentuple in column 6 (1,2,7,8,9) And in rows 4 & 6. In all cases, there is a 5 outside the middle box. Thus, 5 must be in the center.
@@oliolion if you look at the 4th row for example to two left most cells are 6/7 and 8/9. If you look at the three right most cells they are not 1,2,3, or 4 because of the pairs in the box. Therefore the top 3 cells must contain 5,6,7,8, or 9. Since 2 were being used on the left side the remaining three (which includes the 5) have to be used on the right. This pentuple idea repeats in the other 3 cases so the middle box can only have a 5 in the center.
I'm glad I found a solve path where the first digit I found was the 5 in the center, because seeing the whole grid solve from there was amazing. It required coloring, but I got it done in a reasonable time (25 min).
Usually I can follow just fine, but now I had no idea what was going on. Numbers were flying, all in symmetry, and all of a sudden it was all over. Mind blowing.
For me, the eureka moment and the moment I started placing down final answers in the boxes was when I noticed the symmetry and placed a 5 in the middle. Every single entry cascaded from that 5. It was beautiful. I wasn't nearly as fast as you, though, this took me about 46:39
I loved this puzzle. I used a different technique to solve it. At 15:40 , there are 4 quintuples. They are in row 4 and 6 and column 4 and 6. The quintuples all contain the number 5, which forces the 5 in the middle cell of box 5
I love how amazingly humble you are! Genuinely feeling like you're less than clever because of how difficult you find these puzzles sometimes. YOU ARE ASTOUNDINGLY SMART AT PUZZLES AND ITS AMAZING
I saw a puzzle by Phistomefel and I thought it would be a good day to just watch. Then I saw it was only 25 minutes, so I thought I might be able to get it. Got a whole lot of pencil marks after an hour and decided it was a good day to just watch Simon.
This puzzle is insane in the best possible way! The logic is just mesmerizing and awe-inspiring. Thanks to you guys for showcasing this and thanks to Phistomefel for creating such a piece of art, though I cannot wrap my mind around the creation process of such a masterclass sudoku without having to go through the fourth dimension (definitely looking forward to a potential setting video by him). Absolutely stunning! Edit: after watching Simon solve this I find myself astounded the central 5 wasn't his first digit in the grid as it was for me. Looking at the grid state at 15:30 what I found was that r4+5c3 would have to contain some combination of 1, 2, 3 and 4 because of the way box 6 was set up, thus pushing the 5 to row 6 and ruling it out of the bottom three cells in the center box. Applying this logic over all 90 degree rotations left r5c5 as the only position to place a 5 in box 5, which then got me kickstarted on all corners
This truly is a beautiful puzzle. Every square adds together to 10 with its symmetrical mirror square. And that's also why the central square must be a 5: It mirrors itself so that it can add up to 10.
just want to point Gurth's symmetrical placement (GSP) does not apply in killer sudokus, unless the killer clues are themselves symmetrical both in placement and in magnitude (number in top left corner). This is the case in this puzzle, but simply saying the 5 can be placed in the middle the second we have symmetrical digits would be wrong without verifying that constraint. Also, a reminder that GSP can apply in other cases than the 10-sum symmetry we've seen in quite a few videos recently, so complete symmetry (i.e. where every number but one has a counterpart) can't be assumed until there is information about every digit in the grid (except for the number with no counterpart, ofc).
Once you set up the pairs, you can set the 5 in the center by symmetry and then fill in the numbers in a big spiral. Set the number in the corner, follow around, repeat each cycle with the next disambiguated digit/pair. Lovely!
Another T-shirt idea:
"Oh. Now. Hang on. Yes."
Look.
@@nicklow4410 it's just.. gorgeous!
Hahahaha I love this and would buy it
"Now we're cooking with gas"
"Work of Aad"
Simon: "Phistomefel. He just makes me feel stupid, absolutely stupid..."
Me: "Whoa, wait a second, in that case I am unicellular" =)
Me: why are you united in a cellar?
This fits (at least for me it does), because throughout this I got the distinct feeling that I am not even smart enough to *assess* how stupid I am compared to Phistomefel.
I feel the same...
Same. While he’s amazed by the design, I’m amazed he even worked out the first part. He does such a good job of explaining that it seems obvious once said, but I’ve never been able to work out any of these on my own.
This is probably the only channel where I don't miss a SINGLE video...
me too, and i have seen them multiple times.
And I get disappointed when I see red "watched" lines on all the videos :D
Pro tip: If you want to feel 50% less stupid, set the playback speed on the video to 0.5. As a bonus, it appears that Simon is sloshed as he solves these.
Can you just take 5 minutes to contemplate about how it feels to have every grand-master puzzle constructor in the whole world competing against each other to impress you with their marvellous creations? Come up with some new adjectives and epithets to describe that. It's got to be whatever the polar opposite of "lugubrious" happens to be.
The true beauty of it is how EVERYBODY WINS. We all get to play-along and enjoy watching / solving the best puzzles in the world while a middle-aged English poet teaches us about X-Wings and Sword-Fish, just like we're hearing about them for the very first time.
It really is amazing what they woke up in all of us. I have never been that good at sudoku, and have mostly tried to solve it because my dad likes them. The viral one with diagonals and the middle magic square caught my eye, and I sent it to my dad. We competed for a few days who is going to finish it first! (we both didn't get a lot of time to do it, so we solved in multiple sittings) That was my first hard sudoku solve, and I already have an idea for a constraint that I think Simon will love! I've been trying to construct it for a few days, but no luck. Just have to try harder 😊
JohnPaul Adamovsky
Some of us ARE hearing about X-wings and Sword-Fish for the very first time! LoL
Antonym of lugubrious would, perhaps, be cheerful.
Honestly. I discovered this channel in the last month or so, haven't done a sudoku in years. And never above a casual intermediate puzzle from a super market book. The way that he teaches complex concepts from the ground up is fantastic. I'm the guy hearing about the X-Wings and the Sword-Fish for the very first time.
@@WizardlyTim Same here. I stopped playing because the sudoku books just became too easy and boring. After finding Simon though and him showing me a whole new universe of various kinds of puzzles, I just can't stop doing them again!
4 hours, 32 minutes and 7 seconds later, I can finally say I completed a Phistomefel puzzle for the first time without help.
Time to sleep.
Grats! This is one I should have tried before watching, because I saw the first few steps that Simon went through before he was done talking. I haven't actually done a soduku in, like, ever. The symmetry made this puzzle very easy compared to some other crazy shenneagians Simon usually goes through.
1 hour 23 minutes (give or take) for me. So much more satisfying, without help or hints!
Now that's a lot of persistency. Congrats for that!
Wow, you people are impressive. My brain will probably stop working after 4 minutes.
@@vvalph9483
I was actually terrible at sudoku up until a month or 2 ago. Then he released a video with a sodoku with no numbers that went viral and I suddenly watched like 15 of these sodoku videos, with all different intricacies and crazy logic to get through them. Now, I'm starting to see things as Simon does and it's pretty cool.
As someone who's been watching your videos for a full month now (thanks quarantine), I feel like I've graduated from understanding the puzzle-SOLVING process to being desperately curious to understand how the heck these puzzles are DESIGNED to unfold in specific ways in the first place. Please encourage Phistomefel and any other puzzle-creators to make videos about how they accomplish this!
I imagine that it must be deeply complementary to the process of solving these, but I absolutely can not see or imagine how. In this respect a series on puzzle design would be extremely illuminating, I'm sure.
As a left-handed person I cannot relate to the feeling of the man who commented on this puzzle
Haha, same for me! :D
Don't worry, it's just a rather colourful hyperbole.
Unless that person was also left handed in which case the puzzle is even better than you thought!
It’s in the thumbnail
This is the first puzzle I managed to complete! I did it in 31 min!! That was easily the most breathtaking experience of my life and as I kept going I started audibly shrieking because this puzzle was just so beautiful and mindbending.
Yeah the real puzzle now is how these are constructed.
You encode the rules and make the computer fit the digits
@@sbIvanov But how do you pick a set of rules that will be solvable, or will have an intuitive flow to them and be challenging for a human?
Simeon Ivanov you can do that but for most of the ones shown on this channel it’s not like this. Simon sometimes says it as well. If a sudoku is constructed by a computer it’s not as beautiful as when done by humans. There is just a lack of things like flow, symmetry or beauty. This here is a hand-set Sudoku and I have no clue how you do it. But I certainly know that a computer can’t do that
@@otta3680 It probably could be done by a computer, but it'd be faster doing it by hand 🤔
Mark Jacobs I’m actually not sure if you could do that. How do you get a computer to give you a certain way of solving a puzzle. If someone is able to program something like a “beautiful” sudoku maker or even a helper for sudoku Setters, you’ll have my money.
I only discovered this channel a week or so ago and have been binging a lot of the videos and I just wanted to say I really appreciate how even after you've spotted an apparent pattern to the solution, you always double check that any digits you place still have a logical reason to be there beyond "it fits the pattern"
Yeah, I completely agree. And in this case it would've completely blown up in my face, because I saw the 1, 2, 3 in the bottom left diagonal, and the 7, 8, 9 in the top right diagonal, and went "well that obviously means that the middle bit is 4, 5, 6!"
Meanwhile it turned out to be 6, 5, 4.
Phistomefel is quickly becoming my favorite constructor. He's got such an elegance to the way he makes his puzzles.
Him and Aad vd Wetering are absolute geniuses
Aad, Phistomefel and what's his name... Sam Cappleman-Lynes.
puzzle: is symmetrical
Simon: STUNNING! :) :)
so wholesome
I looked at the thumbnail and predicted that the puzzle would be symmetrical with the centre number being 5, because it has to. It would be interesting to understand the maths behind this.
Well if you do a few million standard sudokus, the symmetric ones must stand out!
@@jaylawhorn5198 It's something that is common in very restricted puzzles. I could see by the layout that it would hold true for this one. The more prescriptive the rules, the more regular the structure. I shall have to give this some consideration. It would be interesting to see how the puzzles are constructed.
If you're interested, here's the journal article on it, found on jstor: www.jstor.org/stable/27642500
The discussion of symmetric sudokus starts on page 390 (page 8 of the article, or page 9 of the pdf if you get it from the link I gave). But be warned the math is not trivial, even if it seems like it should be.
@@ronmatthews1738 Ph.D. student in electrical engineering here, currently developing technology leveraging symmetry... If every number included in the puzzle abides by some symmetry (say opposite positions add up to 10), you cannot rule out a number n in a certain position without being able to symmetrically rule out (10-n) in the opposite position. Because you have a unique solution (this is an important condition), at some point you should be able to rule out all numbers but one (the correct), in any position. While you do this, the same happens in the opposite position.
For the record, by "opposite" position I mean the position who's column and rows, each, add up to 10 with the columns and rows of the position it is opposite to.
Yes, I'm a nerd. :)
It IS quarter-turn symmetrical! And Gurth would apply for that case as well! I can't believe what I'm seeing.
Also, "Phistomefel plans to make a video": honestly the best news so far in 2020
no it's only half-turn symmetric, and that follows immediately from the clues since the solution should be unique;-)
I admit I only had a cursory glance at the grid when I wrote this. But I just tried, and I can say with 100% certainty that it actually is quarter-turn symmetrical.
tl;dr: I'm gonna use notation from math (yuck!) to prove that this makes sense. It's actually easy to see, just keep in mind that for quarter-turn symmetry, if 1 maps to 4 then 4 does not map to 1.
Symmetry in Sudoku requires not just the symmetry transformation, but also some permutation of the digits. Here that would be (1,9)(2,8)(3,7)(4,6), if denoted as a product of switching two numbers in the brackets (5 is not part of the notation, because it is left unchanged).
In the case of half-turn symmetry, applying two half-turns gets you back to the original grid, and the permutation needs to reflect that: i.e. applying it twice leaves the digits unchanged. But it doesn't have to be that way: for quarter-turn symmetry, applying it twice is not the same as the original, it's a half-turn. The permutation reflects that: it doesn't just swap two digits (back), but does something a bit more tricky.
The permutation here is (1,4,9,6)(2,3,8,7), which you can see by looking at the corners/edges of the center box. The notation just means that when the grid is turned 90° clockwise (i.e. when the permutation is applied), 1 must turn into 4, 4 turns into 9, 6 turns into 1, 3 turns into 8 etc. Which is what we can observe in the final solution.
Just as an intuition: the subcycles (1,4,9,6) and (2,3,8,7) both have length/order 4, that means applying them four times gets you back to where you started. Just like the underlying quarter-turn would suggest.
Oh hi you found my secret cookie stash.
🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪
@@ilonachan ok fine, with the additional permutation. Number mirroring is already obligatory because of sudoku and so doesn't really need specification.
BTW I'm as good as certain that this is the most symmetrical sudoku one can get.
Bonus question: how many essential different sudoku's of this type are there?
Answer: 80 {:-)
what really surprised me was how easy it was. At first it seemed nearly impossible, but after a few minutes of thinking differently it became one of the easier puzzles lately. These large cage killers really require a different thought process
Well you only have to solve one half. The restraints to force the symmetry do rest
@@mauer1 This one actually has a 4-fold symmetry, so you only need to solve a quarter. It's even easier than that actually since Sudoku rules interact with symmetries. Symmetries make a lot of things very easy.
You guys are amazing, and these constructors that send you puzzles are amazing also.
For the first time in my life, this is the only channel that i haven't missed a single video you uploaded for 3 months straight.
This puzzle is amazing, it took me 42 minutes, and it was a nice figuring the puzzle out and figuring the similarities and mirrored digits.
This is the most fun i had while solving a sudoku. Well done Phistomofel.
My first time solving a Phistomefel puzzle without Simon's help!! I'm happy it was such an awesome puzzle. Can't wait to see more of this guys works of art.
i love this. when you add up the sum of the symmetry it is 10. the whole puzzle thats the case. the moment you figure that out the puzzle becomes a bit easier. or to me it does anyways. this is the type of puzzle that makes me feel good about the world. there is order, the chaos of normal sodoku vanishes. absolutely love it.
That’s a wondrous puzzle, solved with such enthusiasm. And that’s why we keep coming back for more.
Even someone who is only a little better than a beginner can love and learn everything you put out! The more I watch, the more i want to play Suduko!
Amazing puzzle! After a couple of months watching every video of this channel, being able to solve this puzzle by myself felt like a graduation. Thanks, Simon, Mark and all those brilliant constructors!
There's a lovely way to complete the puzzle without "checking" the 5 in the top-left corner at 15:46 - look where the digits 3,4,8,9 can go in column 6. Then likewise look where 1,2,3,4 go in row 4. Do the same for column 4 and row 6 (using the symmetry) and you find that the only possible place a 5 can go in the middle box is at the very center, and the puzzle solves beautifully.
Thanks SO much for sharing this gorgeous puzzle with us, you bring so much joy!!
I don't think I've ever slowed down the solving of a puzzle before just so I could inspect and admire how it's all put together.
I watch every single thing you guys put out. I wasn't sure I was going to like this, but I did.
I started by coloring the cages and immediately saw the symetry. After the two solavable cages gave 1,2 and 9,8, I knew this was going to be like a pinwheel. It didn't disappoint. Just beautiful to see the numbers staying true to the pattern.
This is just another level construction. Each time, Phistomefel impresses me. What's so beautiful about this is it takes 15-20 mins to find one digit but once we do it just finishes so beautifully.
really beautiful puzzle, I went back to this after a year because I remembered how lovely the construction is. I remembered it was one of the first times I've seen a setter take advantage of the geometry of the killer cages in such a unique way. Outstanding indeed
What leaves me baffled is not only the way of solving - it's the construction. This puzzle is indeed a beauty.
I fell upon one of your videos last week and I have never been more intrigued. It is such a joy to see the excitement and wonder in your eyes as you solve these puzzles with incredible wit. Wish I was here from the start! Definitely have some binging to do. Love the work you’re doing Simon, can’t wait for more.
His whole presence and sheer joy is out of this world, I cannot agree with you more. Welcome to the club!
The logic and the symmetry behind this was gorgeous! When you look at it first, it seems like it's impossible to get even started... but once you grasp the logic, it all blooms out beautifully. :)
When I tried this on logic masters Germany, I found the central 5 a different way; when you list all the possibilities in boxes 2, 4, 6, and 8, you can deduce that there must be a 5 in the side 3 cells in box 2, a five in the top 3 cells of box 6, a five in the bottom 3 cells in box 4, and a five in the 3 side cells in box 8. Using sudoku, that eliminates a five in all cells except for the center in box 5!! That’s how I progressed in the puzzle at that point. As always, great job Phistomefel. You are definitely the best puzzle setter I’ve come across!!!
I noticed that rows 4&6 and columns 4&6 have quintuples(?) that all combine to force 5 out of every middle box square except dead center. 5 was actually the first digit I placed :P it's cool that there's multiple ways of finding that square
I can't tell if you found it the same way as I did, so forgive me if I just worded your method differently haha
I found a 5 directly in the center as well although not by listing all possibilities. Rather I noticed the opposite squares of numbers shared no common digits. This makes the 6,7,8,9 in box 4 a 'new york times' quadruple. Where do they go in row 6? There are only 4 positions outside of box 4, which limits where the 5 can be placed.
Thinking about quadruples helped a ton as well because in box 5 you have intersecting quadruples. So without writing in a ton of stuff, I was able to place a 12, 34, 67, and 89 pair in the central box on the corner cells without cluttering up the grid with possibilities.
I was going to reply with the same comment, because that's how I solved it too.
@@simpleman4251 the way you did it is what I did.
Each day there are new superlatives for the puzzles that top the superlatives from the day before. It seems we are in the Golden Age of puzzles!
Finally, the world's best puzzle constructors have a way to get mainstream recognition. And everybody wins.
My time was 19:36. I do find most puzzles on this channel to be well constructed, but never are there any that leave me this stunned by the construction. This puzzle is legitimately brilliant.
Me: Oh, when you rotate the cages and sum them, they sum to 70, always.
Also me: I have no idea how this information helps me in any way.
This.
It's due to the symmetric nature of the puzzle. Every number, when added to its symmetrical opposite, makes 10. So whatever 7-sized cage you're looking at, even ones that are not given in the puzzle, makes 10 x 7 = 70 . Any N-sized cage actually adds up to 10N when added to its symmetrical opposite.
@@RaimbetteLB But not all symmetrical puzzles add to 10. Check out today's puzzle, where 6 is the pivot, meaning that some pairs add to 10 while others add to 11.
@@sabinrawr In no way is yesterdays puzzle symmetrical. Sure, the path to solving it uses the same "trick" several times in a rotation, but if you look at what comes after as well as the solution itself theres nothing left of said symmetry. 6s are facing 6s, 2 are facing 8s, nothing actually goes right in the end ! Unfortunately because the middle digit (1 - 9) is 5 you cannot have anything symmetric around a digit other than 5
@@RaimbetteLB The problem is your definition of symmetry. If a digit always appears opposite of another digit, it's symmetrical. The mathematics of Killer Sudoku can change the value upon which te puzzle is rotated, but that doesn't make it any less symmetrical.
This one was just brilliant. Few rules, logical progression, beautiful layout and just the right difficulty.
Quite phenomenal that someone can create such a puzzle. I've been watching different puzzles in the channel and trying them out. Always gets stuck so I need to use the video for help, but always a pleasure to see you so joyful with these puzzles. Thanks!
I'm really hyped for that Phistomefel video where he shows how he sets puzzles.
Because this was really amazing.
That was a beautiful puzzle. I love the quick pairs and symmetry that runs around the puzzle. Took me quite a while to get an actual number. Then, when I started getting them, I couldn't fill them in fast enough and kept losing myself because of the way the logic worked in so many places at the same time! Wow.
I love the way the center box played out. If you move along diagonals you can go from one to nine sequentially.
My method of determining the central square to be a 5 was to look at the numbers available for the diagonals in the opposing corner boxes. The lower left had 12345, and the upper right had 56789. Thus the central square had to include the 2 missing numbers from each corner with only 3 squares, 5 was the only overlap so it had to be in center portion of the diagonal. The same logic also worked on the other pair of opposing corners, with 5 as the only overlap. Which meant that the central box had to have a 5 on the each diagonal, which put 5 in the central square.
One of the best puzzle of this channel. That was not a clickbait (for once). I loved it, thank you very much !
I am completely mind boggled that not only is the puzzle mirrored, but that each counterpart to any given number also adds to 10
I used to solve sudokus every day, but since I discovered this channel some six months ago, I haven't done a single computer-generated one and enjoyed the beauty of handcrafted grids.
Holy cow I cannot believe I was able to do that without Simon’s help! That was a wonderful solve, and it all built up to one beautiful moment when the first digit was placed in the center square.
He missed that part though. He bifurcated instead and never saw it :(
@@shmojelfed9664 I know! I'm going to make a video and email him about it. Hopefully he'll have time to read it.
I'm so looking forward to Phistomefel's viedeo about how to create something like this!!!
I’m not really a puzzle solver myself but I have just stumbled across your channel and think I’ll start giving it a try! Your excitement about sudoku is so fun and makes me excited! Your channel has been a pleasure to stumble upon.
Beautiful Puzzle!!! I love the simple rule set and the logic of going around in circles around the grid for the very linear deductions. Truly a masterpiece!
Love it when simon feels stupid and theres a bunch of us still staring at the blank puzzle pulling our hair out xD
Simon, I'm not sure if you'll see this, and I know it may seem excessive to say, but your videos really do help with my depressive tendencies. There is something so genuinely wholesome in your almost child-like elation at a wonderfully-constructed puzzle that brings a warmth to me that reminds me of Christmas mornings in my youth. It's inspiring to see someone find real joy in something seemingly so innocuous, it really is good for my soul.
Holy shit! This is stunning beauty! took me 30min overall. first 15 min - I was in disbelief, and didn't know how to make progress. Then I saw the beautiful interaction of the cages, and the logic flowing through the whole grid. And when i saw the rotational symmetry - my jaw dropped!
INSANE! Loved it
There is a stunning beauty in this puzzle.
Without doing anything else you can immediatly fill in the 5 in the middle because of the symmetry. The puzzle is unchanged if you rotate over 180 degrees and replace all numbers by their "opposite" (i.e. 1 by 9, 2 by 8 etc. ). This means that the middle square can only be the number that is its own opposite!
I am absolutely stunned by the beauty of this puzzle. The way that the creator has figured out the symmetry is amazing. Thank you for making a video of this! (I know I'm commenting late, sorry).
The killer sudoku part of the puzzle had some absolutely beautiful logic - it's not often I react to puzzles with quite the same untempered joy as Simon, but I did this time. I made it up to the "can I prove that the centre is 5?" point easily enough, but stalled there hard - it didn't even occur to me to just try all of the other possible values and check for contradictions, even though I'd already had to use that logic earlier in the puzzle. In the end, before resorting to the video, I took advantage of the apparent symmetry of the puzzle to just place the 5 and see if I could solve it from there, which I did, but I'm still frustrated I wasn't able to make that one last deductive jump to solve the entire thing without assumption. I was kicking myself when I then watched the video and saw what I'd missed.
Until now i had never seen a puzzle like this and gone "This is beautiful"
I'm absolutely amazed by this puzzle, and I managed to finish it in an hour which is by far my fastest time on any of the puzzles on the videos that I've tried.
Thank you, Simon. I am sooo impressed by your ability to remember bits from early on, and then use them later. Also a VERY impressive setting !!
so happy to see your recent success with views and subscribers. this was an incredible puzzle and entirely deserving of the title you gave it. keep up the good work
I assigned a colour to every 1/2 square, and 3/4, and 6/7, and 8/9, since they appeared so often as locked to those 2. The symmetrical rainbow you got as a results was quite lovely
This took me an extremely long time, picking up tiny scraps of information along the way, until I finally placed the first digit and suddenly everything fell into place. Incredible!
After watching I’m noticing that all of this symmetry leaves a board where every digit but the center 5 has a mirror that adds to 10. Absolutely magical!
You are soon running out of superlatives in the video titles :-)
Ordinary sudoku? Lacklustre? Insipid?
I just wanted to say, I've seen puzzles with 180 degrees of symmetry but I don't think I've seen one with such symmetry _and also_ logical inferences that work every 90 degrees like this. Singularly beautiful. Phistomefel has outdone himself and that's saying something.
I am glad to see even Simon has those how could I miss that moments like when he had to clean up all the perimeter. Maybe there's hope for us yet!
My solving process: Open the link. Get completely stuck. Watch 3 minutes of this video, then make some of my own progress and get stuck again. Watch another 3 minutes... get stuck again. After Simon went through the logic of putting a 5 in the middle (which was absolutely brilliant), I was finally able to crack the rest.
There are so many crazy logical leaps that I've never seen in any other killer sudoku. Love this so much.
That center 5 was such an awesome find. I love when the diagonals have to contain all the numbers.
Right away I picked up on the symmetrical placement... and by right away, I mean after staring at it for almost 30 minutes...
I ended up determining the 12,34... etc pairs via a different (albeit slower) method. I noticed what cells had to contain the same pairs before identifying what those pairs had to be. After coloring those in each in their own color, I was then able to make some algebraic equations along the lines of 2 orange + 2 green + 2 yellow = 90, and then green + orange = 38, and ultimately deduce what each pair had to be from that. I wish I had seen it the way you did, as getting those pairs took several hours of staring and trial/error, but the puzzle fairly quickly collapsed after that.
In any manner, Phistomefel has once again proven to be my favorite setter, and I cannot wait to see more of his work!
This puzzle was amazing! I could solve it without hints and was super rewarding. I love Phistomefel's style this was the first puzzle I could do from him
21:07 I think I outdid myself figuring this out. Loved it, though I would probably pause before offering body parts for the recognition.
After publishing several point-symmetrical galaxy sudoku puzzles, Phistomefel creates a sudoku that is defined by its point-symmetry. I really appreciate the beauty of this.
16:57, this puzzle was a work of art from start to finish
Phistomefel is the Professor Moriarty to your Sherlock!
I might have missed if this was mentioned in the vid, but from the start you can use uniqueness to place a 5 in the center square; everything is rotationally symmetric up to replacing x with 10-x, which can be seen from the empty starting grid. Hence any deductions obtained from the start must abide by this symmetry.
Thank you! It wasn’t mentioned, I thought I was naive, but it does work!
The symmetry in this puzzle is absolutely mesmerising. I mean at 18:00, the digits are perfectly aligned which also surprisingly all equal 10 when you add the box and it’s symmetrical counterpart.
Wow. That logical still applies even when i’m near the end of the video. This combination of a sudoku grid is art let alone the puzzle which has no given digits!
You are totally right, indeed you can apply Gurth's symmetrical placement from the start of this grid:
as you noticed the cages are symmetrical, but that would not be enough. But if you notice all the number given for the cages are "symmetrical".
Look for example at the first cages you considered, summing to 42 and 28, this numbers are symmetrical, meaning that for each cell you should change a number x with 10-x (1 with 9, 2 with 8 etc), so the sum of a 7 cells large (let's call it S) should reflect to 70-S. Indeed 42=70-28, and so on for all the cages.
So, yes the solution is symmetrical and indeed you could apply Gurth's symmetrical placement. This puzzle is just amazing!
Like many people I suspect, I got stuck right where you did before you figured out that the 5 *had* to be the middle box where the diagonals intersect. I think we all suspected it, but I was unable to prove it without Simon's help! Once I confirmed that, it all blew open. What a great puzzle.
YEAH ! Finally did it in around 1:30:00 (2:13:52 on the timer and at least 45 minutes of break.)
What a cool puzzle ! I didn't have seen your logic but I'll check it out tomorrow, it's 01:40 now...
At 12:24 we can place the 5 in r5c5. In box 6 r5c7 and r6c7 contains the contents of r4c1 and r4c2. So the 5 in box 6 is in row 4. By similar logic 5 in box 4 is in row 6, box 2 is in column 4 and box 8 in column 6. This forces 5 in middle box to r5c5. Rest of the puzzle unwinds easily...
This is just pure genius. The symmetry and the way digits resolve each other.
Haven’t had a go at a sudoku for a while so happy with my 50 minute time for this. Beautiful construction.
01:06:06 solve time for this, about 3/4 of which was spent spotting the pattern and the symmetry of the grid, much like the video solve. After figuring out the eight corner cells the rest of the puzzle went smoothly, but I was pretty slow getting there. Another clever construction from Phistomefel.
5 must always be in the centre as you said, “the puzzle is turned 180°”. Therefore, when the 5 in centre turns 180, it lands on itself; adding them together will get you 10, which is what all other numbers add up to with their counterpart.
As someone with OCD, this is the most beautifully satisfying puzzle I have ever seen in my life. I want this carved on my grave!
16:20 I had a different solution for why 5 couldn't be in the corner. Had to do with finding pentuples in the 4th/6th rows//4th/6th columns
I haven't watched Simon's solve, but I also found these pentuples.
Can you please elaborate on that?
@@oliolion For me I was able to determine that 5 must be in the middle. I filled in the 5 remaining digit possibilities for boxes 2, 4, 6, & 8. So, this means that in column 4, cells, 1,2,3,8,&9 are a 34589 pentuple. Similarly, there is a 12567 pentuple in column 6 (1,2,7,8,9) And in rows 4 & 6. In all cases, there is a 5 outside the middle box. Thus, 5 must be in the center.
@@oliolion if you look at the 4th row for example to two left most cells are 6/7 and 8/9. If you look at the three right most cells they are not 1,2,3, or 4 because of the pairs in the box. Therefore the top 3 cells must contain 5,6,7,8, or 9. Since 2 were being used on the left side the remaining three (which includes the 5) have to be used on the right.
This pentuple idea repeats in the other 3 cases so the middle box can only have a 5 in the center.
@@oliolion imgur.com/gallery/3wJWw0E
I made a graphic out of it. I found the same method.
I'm glad I found a solve path where the first digit I found was the 5 in the center, because seeing the whole grid solve from there was amazing. It required coloring, but I got it done in a reasonable time (25 min).
23:44 Soon as you realise where certain paired cells are, it actually comes out fairly quickly but liking the symmetry.
Usually I can follow just fine, but now I had no idea what was going on. Numbers were flying, all in symmetry, and all of a sudden it was all over. Mind blowing.
For me, the eureka moment and the moment I started placing down final answers in the boxes was when I noticed the symmetry and placed a 5 in the middle. Every single entry cascaded from that 5. It was beautiful. I wasn't nearly as fast as you, though, this took me about 46:39
I love Phistomefels puzzles so much! As Simon always emphazises these puzzles are truly magical
I loved this puzzle. I used a different technique to solve it. At 15:40 , there are 4 quintuples. They are in row 4 and 6 and column 4 and 6. The quintuples all contain the number 5, which forces the 5 in the middle cell of box 5
I've never imagined that sudoku puzzles can be so fun! I am totally addicted to this chanel, and I enjoy every video! Thank You
I think I would gladly give my left hand to see a video of how Phistomefel made it! Another keyboard crackingly great video from Simon!
I love how amazingly humble you are! Genuinely feeling like you're less than clever because of how difficult you find these puzzles sometimes. YOU ARE ASTOUNDINGLY SMART AT PUZZLES AND ITS AMAZING
I saw a puzzle by Phistomefel and I thought it would be a good day to just watch.
Then I saw it was only 25 minutes, so I thought I might be able to get it.
Got a whole lot of pencil marks after an hour and decided it was a good day to just watch Simon.
What an absolute joy of a puzzle to get on Towel Day, especially with the whole key to the puzzle being the 42 box in the corner. Absolute genius.
Each pair of counterparts on the pivot add to ten. Brilliant!
Beautiful puzzle!
one of those puzzles that are actually way more beautiful at the stage where you can still see the symmetries in the possibilites and dependencies.
This puzzle is insane in the best possible way! The logic is just mesmerizing and awe-inspiring. Thanks to you guys for showcasing this and thanks to Phistomefel for creating such a piece of art, though I cannot wrap my mind around the creation process of such a masterclass sudoku without having to go through the fourth dimension (definitely looking forward to a potential setting video by him). Absolutely stunning!
Edit: after watching Simon solve this I find myself astounded the central 5 wasn't his first digit in the grid as it was for me. Looking at the grid state at 15:30 what I found was that r4+5c3 would have to contain some combination of 1, 2, 3 and 4 because of the way box 6 was set up, thus pushing the 5 to row 6 and ruling it out of the bottom three cells in the center box. Applying this logic over all 90 degree rotations left r5c5 as the only position to place a 5 in box 5, which then got me kickstarted on all corners
This truly is a beautiful puzzle. Every square adds together to 10 with its symmetrical mirror square. And that's also why the central square must be a 5: It mirrors itself so that it can add up to 10.
just want to point Gurth's symmetrical placement (GSP) does not apply in killer sudokus, unless the killer clues are themselves symmetrical both in placement and in magnitude (number in top left corner). This is the case in this puzzle, but simply saying the 5 can be placed in the middle the second we have symmetrical digits would be wrong without verifying that constraint. Also, a reminder that GSP can apply in other cases than the 10-sum symmetry we've seen in quite a few videos recently, so complete symmetry (i.e. where every number but one has a counterpart) can't be assumed until there is information about every digit in the grid (except for the number with no counterpart, ofc).
Once you set up the pairs, you can set the 5 in the center by symmetry and then fill in the numbers in a big spiral. Set the number in the corner, follow around, repeat each cycle with the next disambiguated digit/pair. Lovely!