@@samexell7242 In your sentence "a lot" should be either in quotations and spelled in same manner as the person you're referencing, or italicized with the correct spelling. "Allot" is actually a word though, so it's likely an autocorrect failure. Keep up the good work.
Hi @@dalaube , I am sorry to hear that you are from America; I have deduced this from the use of the letter 'Z' in a word which should be spelt with an 's'. I respect that you've made an effort to reply but unfortunately you have done qhite the opposite. You completely ignored my point, given that allot is still a word; however, not used in this context and neither a Apple nor Samsung keyboard would correct to this. It's nice you've tried, but sadly you have come out of this looking silly. Kind Regards, Sam
@@samexell7242 If you have a phone that has never corrected the right usage of a word to the wrong one, I would love to know what that is. You also completely missed the irony of the situation, and why I pointed it out. Theres much better things to be doing, so please go on and keep insulting peoples intelligence for making grammatical mistakes while doing the same.
This is the purest form of RUclips. Really old school. It's just one person doing something they enjoy, and an audience becoming invested, not because they may care about the topic at hand (some of you sure do but I think many of us didn't really care about Sudoku solving before this two "Miracle Sudoku" videos) but because you can see how passionate that person is about it. To me, RUclips doesn't get any better than this.
Most of us came here that way - I’m here for two month maybe and pretty addicted both to the videos from both of you guys and also to sudoku, although I’m still at mediocre level and most of the puzzles here on the channel are not solvable for me, but very very enjoyable to watch.
Xyzzyx I actually solved it in the time since, but had to study the patterns of the first two miracle sudokus for a good bit to figure it out. Once I did that, it was just a matter of plugging all the numbers in.
I was able to find the solution by simply taking this same pattern, shifting some rows, and rotating it, these shift it to fit the constraints, basically take the 1st and 2nd row from this solve and move them to the 8th and 9th rows, shifting every other row up, then you take what is now row 4 and move it to row 6, shifting rows 5 & 6 up to rows 4 & 5. take this new grid and turn it clockwise once, that is the solution. Doing it with logic rather than previous knowledge of these patterns is beyond me however.
I always thought watching strangers solve puzzles would be the epitome of boredom. Because it would be! But here I am, watching an artist mastering his art with admiration and humility. And that certainly is one of the best things I've ever been able to see on RUclips! Please NEVER stop doing these ☺️
That's the thing about spectator sport. Watching someone about as good as you do anything is boring, but watching someone do something demonstrably better than you is fascinating. That's why E-Sports in general are a growing industry, and as games literacy goes up, you'll see E-sports fly ahead in leaps and bounds.
I think I've watched about 4-5 hours of these now. I don't understand how I keep falling into them. I've never in my life decided to watch half an hour of someone else do Sudoku...
@@colindaviddick I don’t even like Sudoku and yet I keep falling in this hole too. I think it’s Simon’s charisma at play here. It’s just so nice to watch him solve and go through a puzzle like this
This is very deceptive. It seems like it should be boring, but it just hooks me and doesn't let go. Especially if you start seeing a move that the master doesn't see yet.
It drives me mad how he sees such intricate pieces of logic and then misses things as blatant as normal sudoku rules. And I notice it all the time because I can't see the advanced logic yet so all I do is look for the aforementioned easier restrictions.
I think it's just the way his brain works- like he has to finish off one piece of logic to its conclusion before he can look at anything else. And also I think he likes to get the difficult bits done because he knows he can fill the givens in easily afterwards.
I really like this guy, and especially how he explains his thought process. I watch these videos at 2x speed because then I can watch twice as much in the same amount of time, and still I can follow along with his logic, even though it gets quite advanced and I am far from a sudoku expert. He simply explains it so clearly and concisely that I can easily follow his thought process, even sped up.
The problem with miracle sudoku is that each row is in the exact same order. Once you place a number in one row, you know it's relation to every single number. Let's say you place a 6 two spaces after a 3. The 6 will ALWAYS be two spaces after a 3, in every single row.
Yeah this is actually the exact same puzzle as the first miracle sudoku except column one has been shifted to column nine with col 2 becoming col 1, 3 becoming 2 etc.
Noticed this as well. Pattern of number are all the same on every row a variation of 948374615 horizontal then vertically first number from each block then second number then third then that pattern repeats vertically.
A couple of people below have noticed that each row is just a translation (sideways shift) of the first row. That was true for the other miracle sudoku as well. I think it is a necessary result given the king and knight moves ... maybe? OK, start with the cell 6 in a block - the number that is in each of those cells must have its corresponding position in cell 3 or 9 in the next block to the right. Now consider cell 4 in a block - that number must be in position 1 or 7 in the next block to the left. Similarly, whatever is in cell 8 in a block must be in cell 7 or 9 below, and whatever is in cell 2 must be in cell 1 or 3 above. I think if you work through the logic, that will force enough cells into position that you will end up with either this pattern *or* the same pattern but with horizontal and vertical swapped (because there are no constraints that apply in one direction but not the other): ▶ every row of 3 cells will be repeated in anagram form in the other two blocks in that row, and each of the 3 rows will have the same transformation applied. ▶ every column of 3 cells will be repeated in anagram form in the other two blocks in that column, and each of the 3 columns will have the same transformation applied. ▶ this forces _either_ the rows _or_ the columns to have a 'zero' transformation applied, meaning that in one direction the group is just shifted and not shuffled. ▶ this in turn means that either the complete rows or complete columns become simple translations of each other, and within each block that means it has to be translated by 3 (ie a whole block). I have a truly marvellous proof of this, which this margin is too narrow to contain 😜.
You could make as many puzzles with these constraint as you want by giving just about any two different nearby digits. That's just the nature of how these constraints work, since antiking + antiknight together require that all rows or columns be translations of one another.
I don't think a puzzle without full symmetry (all digits have a pairing in the counterpart, except the one in the middle, which has itself) would be possible with this constrain and this amount of givens either. With more digits maybe you could get a semi-symmetrical (all digits have themselves or their pairing in the counterpart), but I believe you need at least one repeated given to force the semi-symmetrical solution against the full symmetrical one.
Wecoc1 you only need a repeated given to prove that a puzzle does *not* have full symmetry since uniqueness would otherwise prove it must (assuming there is indeed one solution). A rotationally symmetrical puzzle with these constraints is not impossible. For example, the “miracle” sudoku is one itself.
You're right. It's just the same sequence of numbers shifted 3 cells to the left for each row (plus another cell when it reaches a new box). Talk about ruining the magic! ;-) Do the givens have to be consecutive for it to work or could you start with any two numbers?
Agree, this is a style of puzzle you can only do once. After you know the translation constraint, there is no work/fun other than the first set of digits.
Started watching your videos a week ago. This is the first one I've been able to solve on my own without getting any hints from the video, and managed in about 40 minutes! Thank you for the very entertaining videos! You do a great job explaining the logic behind your moves.
Treat it as a refresher and watch over two or three sessions and you will soon realise you don't have a lack of knowledge. You simply need an opportunity to flex your mental muscles now and again.
I'm nowhere near his level of genius but have been doing sudoku since I was a child. I'm so, so proud of myself for solving this in 36 minutes!! The feeling of elation when I figured our where a number that's not on the grid yet goes was immense! Can't wait to keep practicing my sudoku skills thanks to this channel
For someone who learned Sudoku by himself, I REALLY APPRECIATE how you solve this and how your mind works on so many things at the same time. Watching you solving it gives me excitement and goosebumps especially when you find multiple numbers on a row. As for the ones who created it, NO COMMENT is able to give enough RESPECT & ADMIRATION of how they came up with these puzzles and others👏 I just came across your channel and watched two videos (this is the third one). I decided to try solving this one before I watch you solving it. Tbh, I double checked with your video a few times just to make sure I’m on the right track, I had an early mistake in four cells only, 4s & 1s. Other than that, it was all completed by myself. I completed it in 1:14:54 , to me, it’s a good record since this is this first time I solve a non conventional Sudoku puzzle. It gave me a feeling similar to the first time I solved a Sudoku puzzle. I rarely comment, but here I wanna share my story with Sudoku: The first time I came across Sudoku was in 2009 when I saw it at a local neighbourhood newspaper with a prize for the first person to solve it. I read the rules and thought it was easy to solve. I’ve started by writing random figures then to find out there was an error. I’ve tried to solve it for couple hours but since I didn’t know the methods and the ways of how it’s solved I just got fed up with it and threw the newspaper. The Second time, a few years later, I saw a guy playing Sudoku from a newspaper on the train and it was the first time I saw someone is solving it, then I got triggered and I made a promise to myself that I have to learn and to solve one at least. That time, I had a Nokia phone (no judging😝) which had the game installed, I started playing and checking if my answers were correct. The moment I finished the first Sudoku I felt so relieved and fulfilled, as if I had believed this could never happened, (even though it was an easy level 😅) Since then I became addicted to the game and whenever I buy a new phone it’s the first game I download 😇 My only source of learning is through mobile phones. I came to know by myself different ways of solving the puzzles without searching or looking how to solve them, I just gave it time and follow trends of the ones I solved. Ever since, I encourage everyone around me to play it and sharpen their minds and I appreciate anyone who does play it. I usually play it the moment I open my eyes before I get out of bed😅 Thank you for the videos and making me re-live my old memories Simon. And Thank you ,to whomever read my comment, for reading all the way here 🙏 😊 Peace & Love to u all ✌️❤️
Each of these types of puzzles is a sequence of fixed integer sequence shifted. Once you find one of the numbers in the sequence, you can ancher the rest. Notice how the 3 is always two to the right of 4 with wraparound. This is the same as the previous puzzle. Each digit has a fixed "shift" using the previous rows. So example at 20:42 once the 2 has been found you can go through and place all other 2's two boxes shifted to the right of 3. You only need to find a single new digit through logically and the rest all fall into place.
@@CB-lh4ph Has to be the case in all antiknight&no-touch Sudokus. Another fellow "detuned" put it like this: "With no given digits, and no non-consecutive constraint, the combination of anti-knight and no touch constraints gives a unique solution (up to relabelling of digits and symmetries of the square) ". So all the two given digits and the non-consecutive restraint do is fix the rotation and labeling of numbers.
@@alexharkler I'd say maybe the latter if you read right to left like the Japanese but here in the west we tend to read left to right so I'd opt for the former. The reason I say only "maybe the latter" is because although the Japanese do read from right to left they don't read from bottom to top. I don't think anyone does... you do you though.
This is the first puzzle featured on your channel which I managed to complete without needing help, the most satisfying thing ever, all thanks to the techniques I learned due to watching your channel, sudoku isn't often find on 17 year old's hobby list, but definitely it's starting to be on mine, love your videos, keep up the good work!
I like comments like this because they let me brace for it, otherwise it would bug me the whole way through :D I'm compulsive with my pencil marks, I find such great joy in setting them and tidying them up, especially in Anti Knight puzzles, so Simon sometimes being a "sloppy" pencil marker makes me shake my head (adoringly though!) In any case, shouting at the screen is half the fun 😁
First ever special Sudoku I've solved without watching the video. Really happy with the solve. I realised you have to solve them yourself to appreciate the beauty of the construction.
Theres more than that! Each digit is only in a certain position relative to the sub squares exactly once! For example, a 4 can only be in the gop right corner of 1 square. This is a property of all sudoku actually, not just the miracles!
and then there's me who can never fall asleep easily and so sometimes I just end up playing sudoku until I end up like passing out at like 5 am it's fun uwu
I found one of these videos a few days ago and thought why did I watch this for 25 minutes... I think I've watched so many hours now and it just makes me happy when you realise how to get it done
Once you have the 3 and 4's placed, look at the offset of each row, starting at the top and working down. Makes it pretty easy to add each number once you have one of them. Feels like the restrictions force this pattern offset.
Yeah, that's what I instantly noticed with the first one. This one still took me 22 minutes, but finding the first few digits was fairly enjoyable. I'll be going after this nightmare next.
Finally, the first time I needed less time than Simon (ok, more like the time the video lasts) . And although it was just 12 seconds and I'm aware that he takes his time to explain the rules in the beginning and every step while solving I'm happy. Have a nice sunday and stay safe :)
god, i've spent last 1.5 hours trying to solve it and i keep making mistakes, and now im watching you do it so effortlessly. there is much to learn for me. thank you for your amazing channel
Just wanted to say I've been watching your videos for the past 6 weeks or so (not sure how I got here in the first place. thanks YT algorithm!) But i finally had a go at solving one of these on my own, before watching you do anything. Took me quite a while but so satisfying to finish it without any clues or help! Thanks Simon!
I gave a try on this puzzle and managed to do it without any assistance... took me about 90 mins... and feeling pretty accomplished! Really enjoying your material and looking forward to improving my logic.
I also stumbled across your channel a few days ago and just bought your classic and knights app, I’ve loved sudoku for many years but since watching you I can now complete most classic in about 30 minutes 😀🤪😜
This is the same sudoku as Mitchell Lee's, just relabeled and with a different choice of starting digits. If you compare the ending states you'll see that everywhere a 9 appears in this puzzle, a 4 appears in his. And everywhere a 3 appears in this puzzle, a 7 appears in his. Etc.
As far as I can tell the Miracle constraints mean every box is the same arrangement with a different offset... which also means they all are the same solution (up to mirror/rotation/relabeling) I solved it using that method and it went quite quick.
In truth, just one filled in box with these rules creates a unique solution because the constraints are what results in the symmetry. It would just make the start more of a headache.
(23:00) I thought dominos did secure even more squares. All around as you marked. But then also two extra steps away from the long edge. So in the example domino with 1s you showed. It should secure all squares two steps up and two steps down, as those squares are captured by normal sudoku rules and the knights rule. What you get is this shape: [ ][X][X][ ] [X][X][X][X] [X][dom][X] [X][X][X][X] [ ][X][X][ ] Where "dom" is the domino. Rotate the shape for a rotated domino.
I paused, I studied it, I used what you've taught me (over the past couple weeks) and I finally solved one without having to see you do it! Thanks for teaching us how to Crack the Cryptic!
Similarly to the previous one, this one is also symmetrical, however opposites do not add up to 9 but 10
4 года назад+2
there is always a space between the numbers. f.e. is always 2 spaces to the right of 1. It just goes over to the border. I wonderd early on, why he didnt notice, because once you realize that the puzzle ist just on autosolve
Very happy with myself... I clicked on the puzzle, and went for a solve myself... and only took twice as long as you did to nail it. Thank you for showing me how to get some of these done.Now... my brain needs a nap.
Following the solve of the first miracle sudoku helps with solving this by myself. It’s amazing, especially when placing 8 and 9 in the grid; it’s like... your pen is just dancing across the puzzle!
Never in a million years did I think I'd be watching a sudoku puzzle being solved while shouting at the screen where numbers go getting excited that the puzzle is revealing itself. 😂this was brilliant!
Immediatly clicked the video and the link as soon as I got the RUclips notification. The last miracle sudoku was SO fun to solve, and so was this one (even though I had to restart twice because of hasty mistakes... whoops). Thanks for making sudokus part of my daily life! I always have to restrain myself to not just spend the whole day solving sudokus...
After watching the last miracle sudoku, I went to solve this one before watching the video and it took me nearly an hour and a half because I kept messing up the 3s and 4s but realizing too late and just having to completely restart. These insane sudokus are absolutely enchanting to me!
The trick being the repeating digits or closer to the way he solved it? I tried to solve it using logic like he does, but it took me twice as long as you. Maybe I'm just slow.
Imo one way to possibly make it more interesting is to have starting numbers 1 apart (like 1 and 3) and having to work out all three numbers we would have info about (so 1s, 2s and 3s in this case) at the same time. The initial logic to fill in the two starting digits is fun but once you know that, the puzzle is basically over ^^
@@user-vb3jg1zc9g no it's literally the matter of being thorough, I've not used ANY logic Simon didn't mention in the previous video. Thing is, Simon is unbelievably good at spotting mad logic patterns but he is I'd say pretty avreage (at least for a puzzle fan) at spotting what's already there. There were multiple instances in that video (seen it after my solve) where Simon finds great logic... that's just not needed because he didn't squeeze out 100% out of that 4 he just put in :)
Back in May I saw this Sudoku. It was shortly after I started following your channel. I was like "nah, never will I be able to solve a puzzle like that". Today I stumbled across it again and gave it a try. It took me a little more than an hour but I made it. Thanks Mark and Simon for being such good teachers and good companions during this year! Wish you all the best for Christmas!
I watched a lot of videos on your channel, despite not knowing how in the world to solve a sudoku. I watched a previous miracle sudoku puzzle and thought "Wow, that actually looked kind of easy, I wish I had done it" and saw you'd done this one and thought I'd give it a shot myself before watching your video. This is the first time I've ever managed to solve a sudoku. I only had to consult your video about 2 or 3 times, and only for a little nudge in the right direction. Otherwise, it was almost entirely on my own. I've never even managed to do a standard sudoku where almost all the numbers are given to you. I'm not sure I'm going to take a dive into solving more complicated or other kinds of sudoku puzzles, but I think miracle sudoku like this is more my speed. Thank you!
When I tried to solve this puzzle on my own, I made a mistake with the sixes. But something amazing happened. With the incorrect sixes, it seemed like there was no way to place the sevens in a contradictory way so I was struggling to make progress. That is until I realized that I needed to place the sevens in such a way that the left over squares do not touch each other, since that would lead to consecutive eights and nines. I thought it was a surprisingly neat ending that got more difficult at the end. I was a bit sad that it was not part of the real puzzle.
This one took me a week. I never watch the videos until I have mine solved, and then to see him fly through what I agonized over in less than half an hour... Well, you'd think it would be disheartening, but it's such a celebration! He gets so very happy with every success, and I get to relive all the joy without the frustration. 😊
And 5 goes next to the 1, next to the 1, next to the 1, 6 goes next to the 2, next to the 2, next to the 2 7 goes next to the 3, next to the 3, next to the 3 I was waiting for him to notice. The repeating pattern by row (you could do it by column I suppose) is an interesting outcome of these rules for the game. It could make for an extremely fast solve if the pattern is fully understood and anticipated right from the start.
This just popped up in my recommend feed, never done a single Sudoku before but I decided to try this after hearing the instructions, it took me an hour of mostly process of elimination but at the end it's so rewarding, definitely going be doing more but rn I need to go to bed
Saw the video, waited for the rules to be sure it was the same, paused and solved. Little over half an hour but I managed it! You're right, these are really nice to solve. You just have a huge hurdle at the beginning and then it's all smooth sailing.
I solved it in 2 hours and 23 minutes, around 2 hours in I made a mistake and briefly thought I would have to restart the whole thing but thank goodness I realised where I messed up and could easily fix it
@@alipareedanse12 That's good that you noticed where you made the mistake! It would have been sad if you had to do the whole thing again just because a little mistake 😬
Love the miracle sudoku. It's such a fun solve, and I love listening to you help guide me through when I get stuck. It's a great soothing and relaxing way to end my night.
25:35 that's a five (Stares at R8C7) "Oh no, I don't want to put a five there" Simon looks like he accidentally angered the sudoku gods looking down from above XD
Can I please stress that both you and aad are wizards, this has been one of the fastest half hours of my life. Love your work, keep up the amazing solving!
I love it when I spot something a few steps ahead of where you are at because 99% of the time I'm about 10 steps behind and just dumbfounded. Makes me feel smart for just a second hahaha
phew, the beginning was extremely annoying, it took me around an hour and a half to clear this. I already watched him clear the last miracle one, but still didn't expect to take 1 hour and 30 minutes to clear it XD.
From 13:15 you can already see some symmetry in the middle 3 boxes. The 3s are exactly 2 cells right of 4s Even the row2 column8 4 cell loops around the edge and keeps a distance of 2 cells. Absolutely love this content!
I don't really like this puzzle to be honest. It's exactly the same as the other one, just labeled differently. The 5's have become 1's in this one, the 6's have become 2's, the 7's have become 3's and so on..
Its the ruleset, you can get all possible valid solution by moving the board down, left, or rotating it. The constraints are too restrictive to make anything else. Thats why the first one was a miracle, it was a miracle that it ended up that way and it can't be repeated.
Super Happy! Solved in about 2 hours. Getting all the 3s and 4s was super tough, But once I had them I also started with 2s and then the rest just came along a lot quicker. This is great. Discovered your page today, and spent around 3 hours on a different puzzle earlier. Absolutely hooked. Subscribed. :-)
It's basically the same Sudoku as the Mitchell Lee version but all numbers are staggered one step to the right. I'm more amazed over how it's still solvable though from this position.
I actually managed to do this one on my own after seeing your first miracle solve! I watched this video after successfully solving it myself! Really enjoyed it :) Thanks!
I love how happy he sounds when he solves allot in a row
You're clearly not smart enough to be watching sudoku videos if you think a lot is one word.
@@samexell7242 In your sentence "a lot" should be either in quotations and spelled in same manner as the person you're referencing, or italicized with the correct spelling.
"Allot" is actually a word though, so it's likely an autocorrect failure.
Keep up the good work.
Hi @@dalaube ,
I am sorry to hear that you are from America; I have deduced this from the use of the letter 'Z' in a word which should be spelt with an 's'. I respect that you've made an effort to reply but unfortunately you have done qhite the opposite. You completely ignored my point, given that allot is still a word; however, not used in this context and neither a Apple nor Samsung keyboard would correct to this. It's nice you've tried, but sadly you have come out of this looking silly.
Kind Regards,
Sam
@@samexell7242 quite*
@@samexell7242 If you have a phone that has never corrected the right usage of a word to the wrong one, I would love to know what that is.
You also completely missed the irony of the situation, and why I pointed it out.
Theres much better things to be doing, so please go on and keep insulting peoples intelligence for making grammatical mistakes while doing the same.
This is the purest form of RUclips. Really old school. It's just one person doing something they enjoy, and an audience becoming invested, not because they may care about the topic at hand (some of you sure do but I think many of us didn't really care about Sudoku solving before this two "Miracle Sudoku" videos) but because you can see how passionate that person is about it. To me, RUclips doesn't get any better than this.
what about our sponsor shadow raid legends though?
I stumbled across you guys just a week ago and I’m already addicted. I love your videos and they bring me so much happinesses
The Same happened to me yesterday :)
Jonas nuranders every single video is just lovely
Most of us came here that way - I’m here for two month maybe and pretty addicted both to the videos from both of you guys and also to sudoku, although I’m still at mediocre level and most of the puzzles here on the channel are not solvable for me, but very very enjoyable to watch.
I just got here a few days ago
I’m the same! :)
I was screaming at the screen when you highlighted two squares that you thought could be 2 even though they were connected to a 3
16:15 this?
i saw it too but he’s still way smarter than me
me too!
Same and then he keeps clicking on the one on the right side and I am so angry he hasn't noticed it despite having his cursor there over and over!!!
ORTHOGONALS
We absolutely have to see the blank puzzle with only two little thermometers in a live solve!
I’m having trouble believing it’s actually possible
@@swappingparts I worked on it and you get some interesting patterns. but the disambiguation is a bit tricky, and might require brute-forcing it
Xyzzyx I actually solved it in the time since, but had to study the patterns of the first two miracle sudokus for a good bit to figure it out. Once I did that, it was just a matter of plugging all the numbers in.
Mark Broesamle wow good job I don’t think I’d ever be able to do that
I was able to find the solution by simply taking this same pattern, shifting some rows, and rotating it, these shift it to fit the constraints, basically take the 1st and 2nd row from this solve and move them to the 8th and 9th rows, shifting every other row up, then you take what is now row 4 and move it to row 6, shifting rows 5 & 6 up to rows 4 & 5. take this new grid and turn it clockwise once, that is the solution. Doing it with logic rather than previous knowledge of these patterns is beyond me however.
4 hours ago I thought "I'm not watching a 30 min long video on sudoku"
That was 8 sudoku videos ago now.
Same dude same
I always thought watching strangers solve puzzles would be the epitome of boredom. Because it would be! But here I am, watching an artist mastering his art with admiration and humility. And that certainly is one of the best things I've ever been able to see on RUclips! Please NEVER stop doing these ☺️
Couldn't agree with you more, it's memorising!
That's the thing about spectator sport. Watching someone about as good as you do anything is boring, but watching someone do something demonstrably better than you is fascinating. That's why E-Sports in general are a growing industry, and as games literacy goes up, you'll see E-sports fly ahead in leaps and bounds.
Me: "Haha! This guy thinks I'm gonna watch him play sudoku for the best part of half an hour!"
Me after 28 minutes: 👀
I think I've watched about 4-5 hours of these now. I don't understand how I keep falling into them. I've never in my life decided to watch half an hour of someone else do Sudoku...
@@colindaviddick I don’t even like Sudoku and yet I keep falling in this hole too. I think it’s Simon’s charisma at play here. It’s just so nice to watch him solve and go through a puzzle like this
Anyway I sped up video
This is very deceptive. It seems like it should be boring, but it just hooks me and doesn't let go. Especially if you start seeing a move that the master doesn't see yet.
Me a week ago: "wAT iS SudoKU"
Me today going along with the video: "So THAT can't be a 5!"
Mathematical skeletons of games are quite addicting
same
Dilon and Kody are bots dont fall for it
@@phillt.coiler8769 I get a lot of joy out of reporting bots.
It only took me a video from one point to another
I love how infectious his enthusiasm is. I never get as excited by a puzzle as a do watching him.
when Simon keeps clicking on the one that could never be a 2
It drives me mad how he sees such intricate pieces of logic and then misses things as blatant as normal sudoku rules. And I notice it all the time because I can't see the advanced logic yet so all I do is look for the aforementioned easier restrictions.
that was so frustrating, those 2 errors would have made the 2s much easier for him
Simon doesn't even need to fix his errors. He still solves it anyway via other means!
I think it's just the way his brain works- like he has to finish off one piece of logic to its conclusion before he can look at anything else. And also I think he likes to get the difficult bits done because he knows he can fill the givens in easily afterwards.
I was literaly shouting inside :D
every time you see something before he does but also knowing you could never finish the puzzle
I really like this guy, and especially how he explains his thought process. I watch these videos at 2x speed because then I can watch twice as much in the same amount of time, and still I can follow along with his logic, even though it gets quite advanced and I am far from a sudoku expert. He simply explains it so clearly and concisely that I can easily follow his thought process, even sped up.
Ikr I can’t even do a medium sudoku he explains it’s so good
The problem with miracle sudoku is that each row is in the exact same order. Once you place a number in one row, you know it's relation to every single number. Let's say you place a 6 two spaces after a 3. The 6 will ALWAYS be two spaces after a 3, in every single row.
Yeah I noticed this too. Its a pity really
Yeah this is actually the exact same puzzle as the first miracle sudoku except column one has been shifted to column nine with col 2 becoming col 1, 3 becoming 2 etc.
Noticed this as well. Pattern of number are all the same on every row a variation of 948374615 horizontal then vertically first number from each block then second number then third then that pattern repeats vertically.
that's a great strategy to solve it very quickly then
I’m going to try to forget this…😂
A couple of people below have noticed that each row is just a translation (sideways shift) of the first row. That was true for the other miracle sudoku as well. I think it is a necessary result given the king and knight moves ... maybe?
OK, start with the cell 6 in a block - the number that is in each of those cells must have its corresponding position in cell 3 or 9 in the next block to the right.
Now consider cell 4 in a block - that number must be in position 1 or 7 in the next block to the left.
Similarly, whatever is in cell 8 in a block must be in cell 7 or 9 below, and whatever is in cell 2 must be in cell 1 or 3 above.
I think if you work through the logic, that will force enough cells into position that you will end up with either this pattern *or* the same pattern but with horizontal and vertical swapped (because there are no constraints that apply in one direction but not the other):
▶ every row of 3 cells will be repeated in anagram form in the other two blocks in that row, and each of the 3 rows will have the same transformation applied.
▶ every column of 3 cells will be repeated in anagram form in the other two blocks in that column, and each of the 3 columns will have the same transformation applied.
▶ this forces _either_ the rows _or_ the columns to have a 'zero' transformation applied, meaning that in one direction the group is just shifted and not shuffled.
▶ this in turn means that either the complete rows or complete columns become simple translations of each other, and within each block that means it has to be translated by 3 (ie a whole block).
I have a truly marvellous proof of this, which this margin is too narrow to contain 😜.
Ah yes, we’ll probably wait for 300 years before someone else can provide the proof then
Love this puzzle, the fact that all the rows are the same, just offset, and the rotational symmetry adding to 10. A work of art
You could make as many puzzles with these constraint as you want by giving just about any two different nearby digits. That's just the nature of how these constraints work, since antiking + antiknight together require that all rows or columns be translations of one another.
I don't think a puzzle without full symmetry (all digits have a pairing in the counterpart, except the one in the middle, which has itself) would be possible with this constrain and this amount of givens either. With more digits maybe you could get a semi-symmetrical (all digits have themselves or their pairing in the counterpart), but I believe you need at least one repeated given to force the semi-symmetrical solution against the full symmetrical one.
Wecoc1 you only need a repeated given to prove that a puzzle does *not* have full symmetry since uniqueness would otherwise prove it must (assuming there is indeed one solution). A rotationally symmetrical puzzle with these constraints is not impossible. For example, the “miracle” sudoku is one itself.
You're right. It's just the same sequence of numbers shifted 3 cells to the left for each row (plus another cell when it reaches a new box). Talk about ruining the magic! ;-)
Do the givens have to be consecutive for it to work or could you start with any two numbers?
What I was wondering is if it's really possible one *without* full symmetry and still with only one valid solution... I'll try it on JSudoku.
Agree, this is a style of puzzle you can only do once. After you know the translation constraint, there is no work/fun other than the first set of digits.
Started watching your videos a week ago. This is the first one I've been able to solve on my own without getting any hints from the video, and managed in about 40 minutes! Thank you for the very entertaining videos! You do a great job explaining the logic behind your moves.
Found this channel last night and watched till 5:00 in the morning. I’m addicted to my lack of knowledge.
Treat it as a refresher and watch over two or three sessions and you will soon realise you don't have a lack of knowledge.
You simply need an opportunity to flex your mental muscles now and again.
I'm nowhere near his level of genius but have been doing sudoku since I was a child. I'm so, so proud of myself for solving this in 36 minutes!! The feeling of elation when I figured our where a number that's not on the grid yet goes was immense! Can't wait to keep practicing my sudoku skills thanks to this channel
Watching him leave the square by the 3 highlighted as a 2 nearly broke my brain LOL
Which one? There's two.
@@Xeridanus Center right box specifically.
@@antonioliles5027 The other one was in center left.
@@Xeridanus LOL I completely missed seeing that he did not deselect that one as well.
i was screaming the whole time trying to get his attention XD it almost feels like he can't hear me lol
For someone who learned Sudoku by himself, I REALLY APPRECIATE how you solve this and how your mind works on so many things at the same time. Watching you solving it gives me excitement and goosebumps especially when you find multiple numbers on a row.
As for the ones who created it, NO COMMENT is able to give enough RESPECT & ADMIRATION of how they came up with these puzzles and others👏
I just came across your channel and watched two videos (this is the third one). I decided to try solving this one before I watch you solving it.
Tbh, I double checked with your video a few times just to make sure I’m on the right track, I had an early mistake in four cells only, 4s & 1s. Other than that, it was all completed by myself.
I completed it in 1:14:54 , to me, it’s a good record since this is this first time I solve a non conventional Sudoku puzzle. It gave me a feeling similar to the first time I solved a Sudoku puzzle.
I rarely comment, but here I wanna share my story with Sudoku:
The first time I came across Sudoku was in 2009 when I saw it at a local neighbourhood newspaper with a prize for the first person to solve it. I read the rules and thought it was easy to solve. I’ve started by writing random figures then to find out there was an error. I’ve tried to solve it for couple hours but since I didn’t know the methods and the ways of how it’s solved I just got fed up with it and threw the newspaper.
The Second time, a few years later, I saw a guy playing Sudoku from a newspaper on the train and it was the first time I saw someone is solving it, then I got triggered and I made a promise to myself that I have to learn and to solve one at least.
That time, I had a Nokia phone (no judging😝) which had the game installed, I started playing and checking if my answers were correct. The moment I finished the first Sudoku I felt so relieved and fulfilled, as if I had believed this could never happened, (even though it was an easy level 😅)
Since then I became addicted to the game and whenever I buy a new phone it’s the first game I download 😇
My only source of learning is through mobile phones. I came to know by myself different ways of solving the puzzles without searching or looking how to solve them, I just gave it time and follow trends of the ones I solved.
Ever since, I encourage everyone around me to play it and sharpen their minds and I appreciate anyone who does play it.
I usually play it the moment I open my eyes before I get out of bed😅
Thank you for the videos and making me re-live my old memories Simon.
And Thank you ,to whomever read my comment, for reading all the way here 🙏 😊
Peace & Love to u all ✌️❤️
Each of these types of puzzles is a sequence of fixed integer sequence shifted. Once you find one of the numbers in the sequence, you can ancher the rest. Notice how the 3 is always two to the right of 4 with wraparound. This is the same as the previous puzzle. Each digit has a fixed "shift" using the previous rows. So example at 20:42 once the 2 has been found you can go through and place all other 2's two boxes shifted to the right of 3. You only need to find a single new digit through logically and the rest all fall into place.
Does that have to be the case, or does is just happen to be the case for the two Sudokus featured on this channel?
948372615
once you have one digit just fill in the rest of the sequence.
@@CB-lh4ph Has to be the case in all antiknight&no-touch Sudokus. Another fellow "detuned" put it like this: "With no given digits, and no non-consecutive constraint, the combination of anti-knight and no touch constraints gives a unique solution (up to relabelling of digits and symmetries of the square)
". So all the two given digits and the non-consecutive restraint do is fix the rotation and labeling of numbers.
@@bobleonheart9600
948372615 or 162738495
@@alexharkler I'd say maybe the latter if you read right to left like the Japanese but here in the west we tend to read left to right so I'd opt for the former.
The reason I say only "maybe the latter" is because although the Japanese do read from right to left they don't read from bottom to top. I don't think anyone does... you do you though.
This is the first puzzle featured on your channel which I managed to complete without needing help, the most satisfying thing ever, all thanks to the techniques I learned due to watching your channel, sudoku isn't often find on 17 year old's hobby list, but definitely it's starting to be on mine, love your videos, keep up the good work!
me staring at column 2 row 6 screaming internally about how it can’t be a 2
I was screaming the same thing at column 7 row 6
@@borkursig24 same for both. Ever since he penciled them in, lmao. (Granted he does other things so much quicker than I ever could :p)
I like comments like this because they let me brace for it, otherwise it would bug me the whole way through :D I'm compulsive with my pencil marks, I find such great joy in setting them and tidying them up, especially in Anti Knight puzzles, so Simon sometimes being a "sloppy" pencil marker makes me shake my head (adoringly though!)
In any case, shouting at the screen is half the fun 😁
i wouldnt be able to contain my internal screaming without being able to commiserate in the comments
Same for column 3 row 1 :D
I have never played a single sudoku puzzle, but love how he figures these out.
I genuinely love how excited and passionate Simon gets about solving puzzles! Watching him get excited about a solve gets me so pumped
First ever special Sudoku I've solved without watching the video. Really happy with the solve. I realised you have to solve them yourself to appreciate the beauty of the construction.
This is the first puzzle you've done that I was actually able to solve completely on my own!
I like the fact that there is a hidden restriction being "the middle digit of each square can not repeat". Love your videos!
Theres more than that! Each digit is only in a certain position relative to the sub squares exactly once! For example, a 4 can only be in the gop right corner of 1 square. This is a property of all sudoku actually, not just the miracles!
I was just about to sleep but here i am..
*solving sudoku on my bed at 3 am*
same for me but 10:30 pm
to be honest, staying up to puzzle isn't the worst reason to lose a bit of sleep. as long as it doesn't become a habit.
and then there's me who can never fall asleep easily and so sometimes I just end up playing sudoku until I end up like passing out at like 5 am
it's fun
uwu
5am at the moment and I started watching this, here we go again
same but at 6am
It is a pleasure to listen to you approach a puzzle and watch it collapse so effortlessly! Thank you for sharing your gift.
You know you’re becoming a real fan of the the channel when you get excited for an Aad van de Wetering puzzle
I found one of these videos a few days ago and thought why did I watch this for 25 minutes... I think I've watched so many hours now and it just makes me happy when you realise how to get it done
Once you have the 3 and 4's placed, look at the offset of each row, starting at the top and working down. Makes it pretty easy to add each number once you have one of them. Feels like the restrictions force this pattern offset.
Yeah, that's what I instantly noticed with the first one. This one still took me 22 minutes, but finding the first few digits was fairly enjoyable. I'll be going after this nightmare next.
If the pattern if forced for rows, why isn't it forced for columns. And how to tell for which column or row it is fixed
Doesn't hold for the columns, though. I think that pattern just happened to occur for this sudoku.
@@andrewzmorris in the other "miracle sudoku" video he did a week ago, it was pretty much the same (an offset pattern on the rows).
With the numbers beeing in the exact same order, but a different offset.
His enjoyment and candid attitude when discovering what number goes where is so contagious
Finally, the first time I needed less time than Simon (ok, more like the time the video lasts) . And although it was just 12 seconds and I'm aware that he takes his time to explain the rules in the beginning and every step while solving I'm happy. Have a nice sunday and stay safe :)
had that happen for the first time on the spiral galaxy one the other day for the first time. all my time practicing spirals finally paid off!
god, i've spent last 1.5 hours trying to solve it and i keep making mistakes, and now im watching you do it so effortlessly. there is much to learn for me. thank you for your amazing channel
I love how they get exponentially easy! This is the fastest puzzle I’ve solved! In 22 mins...
Just wanted to say I've been watching your videos for the past 6 weeks or so (not sure how I got here in the first place. thanks YT algorithm!) But i finally had a go at solving one of these on my own, before watching you do anything. Took me quite a while but so satisfying to finish it without any clues or help! Thanks Simon!
It's like Oprah: "You can't be a two! And you can't be a two! And you can't be a two! You all can't be a two!"
Astounding logics, gently delivered. Even an occasional missed decision which leaves room for us to discover items along the way. Well done.
I swear if Mitchel Lee now makes one with a 5 and a 6 I'm gonna laugh myself to death lol
I gave a try on this puzzle and managed to do it without any assistance... took me about 90 mins... and feeling pretty accomplished! Really enjoying your material and looking forward to improving my logic.
“I feel like I’m missing something here...”
*staring at the naked single 4 in column 6* indeed
Thank you! Those can't be 3's in column 5 because the 4 is locked there.
I also stumbled across your channel a few days ago and just bought your classic and knights app, I’ve loved sudoku for many years but since watching you I can now complete most classic in about 30 minutes 😀🤪😜
This is the same sudoku as Mitchell Lee's, just relabeled and with a different choice of starting digits. If you compare the ending states you'll see that everywhere a 9 appears in this puzzle, a 4 appears in his. And everywhere a 3 appears in this puzzle, a 7 appears in his. Etc.
As far as I can tell the Miracle constraints mean every box is the same arrangement with a different offset... which also means they all are the same solution (up to mirror/rotation/relabeling) I solved it using that method and it went quite quick.
And yeah... just did the thermometer one by figuring out the mapping (It's a 90 CCW rotation and subtracting 2 from all digits of this one)
Matthew Karr That's a very interesting observation, however in order to use it you should proof why it is true..., imo
Not only that, but whenever a number appears the surrounding numbers are always the same. Though at the edges they may wrap.
In truth, just one filled in box with these rules creates a unique solution because the constraints are what results in the symmetry. It would just make the start more of a headache.
I AM ADDICTED TO THESE VIDEOS!!! The energy it gives from seeing everything falling in place!!! Amazing!!
(23:00) I thought dominos did secure even more squares. All around as you marked. But then also two extra steps away from the long edge. So in the example domino with 1s you showed. It should secure all squares two steps up and two steps down, as those squares are captured by normal sudoku rules and the knights rule. What you get is this shape:
[ ][X][X][ ]
[X][X][X][X]
[X][dom][X]
[X][X][X][X]
[ ][X][X][ ]
Where "dom" is the domino. Rotate the shape for a rotated domino.
Yup makes sense to me
I paused, I studied it, I used what you've taught me (over the past couple weeks) and I finally solved one without having to see you do it! Thanks for teaching us how to Crack the Cryptic!
14:59 Another incredible puzzle, but since the idea has been done, it made the solve that much easier.
I've never thought it would be that fascinating to watch someone solve a Sudoku for half an hour
Similarly to the previous one, this one is also symmetrical, however opposites do not add up to 9 but 10
there is always a space between the numbers. f.e. is always 2 spaces to the right of 1. It just goes over to the border. I wonderd early on, why he didnt notice, because once you realize that the puzzle ist just on autosolve
It's exactly the same, only the individual numbers have switched.
I gave it a try and took me 57 minutes but I managed. Thank you Simon for preparing me for this moment through previous videos.
"Work of Aad" should be on a t-shirt 🤣🤣
Very happy with myself... I clicked on the puzzle, and went for a solve myself... and only took twice as long as you did to nail it. Thank you for showing me how to get some of these done.Now... my brain needs a nap.
I like how he says "cracking the cryptic"
One the most British sentences I've ever heard.
Cracking the enigma
Following the solve of the first miracle sudoku helps with solving this by myself. It’s amazing, especially when placing 8 and 9 in the grid; it’s like... your pen is just dancing across the puzzle!
Never in a million years did I think I'd be watching a sudoku puzzle being solved while shouting at the screen where numbers go getting excited that the puzzle is revealing itself. 😂this was brilliant!
Immediatly clicked the video and the link as soon as I got the RUclips notification. The last miracle sudoku was SO fun to solve, and so was this one (even though I had to restart twice because of hasty mistakes... whoops). Thanks for making sudokus part of my daily life! I always have to restrain myself to not just spend the whole day solving sudokus...
Simon's always like a 10 year old opening his christmas presents when he finally cracks a puzzle.
After watching the last miracle sudoku, I went to solve this one before watching the video and it took me nearly an hour and a half because I kept messing up the 3s and 4s but realizing too late and just having to completely restart.
These insane sudokus are absolutely enchanting to me!
11:58 speedsolve... In my opinion this is a one off - once you know the trick, it's not satisfying anymore.
Yeah, 26:09 on my end. I remembered the last time this happened and knew what needed to be done.
The trick being the repeating digits or closer to the way he solved it? I tried to solve it using logic like he does, but it took me twice as long as you. Maybe I'm just slow.
Imo one way to possibly make it more interesting is to have starting numbers 1 apart (like 1 and 3) and having to work out all three numbers we would have info about (so 1s, 2s and 3s in this case) at the same time. The initial logic to fill in the two starting digits is fun but once you know that, the puzzle is basically over ^^
I think it's satisfying up to the point where no major logic acrobatics are longer needed. For me it's when 3 digits are filled completely. (21:30)
@@user-vb3jg1zc9g no it's literally the matter of being thorough, I've not used ANY logic Simon didn't mention in the previous video. Thing is, Simon is unbelievably good at spotting mad logic patterns but he is I'd say pretty avreage (at least for a puzzle fan) at spotting what's already there. There were multiple instances in that video (seen it after my solve) where Simon finds great logic... that's just not needed because he didn't squeeze out 100% out of that 4 he just put in :)
Back in May I saw this Sudoku. It was shortly after I started following your channel. I was like "nah, never will I be able to solve a puzzle like that". Today I stumbled across it again and gave it a try. It took me a little more than an hour but I made it. Thanks Mark and Simon for being such good teachers and good companions during this year! Wish you all the best for Christmas!
16:06 Well, that's just the 3's pattern from the first puzzle rotated by 180°. It's basically the same Sudoku.
I watched a lot of videos on your channel, despite not knowing how in the world to solve a sudoku.
I watched a previous miracle sudoku puzzle and thought "Wow, that actually looked kind of easy, I wish I had done it" and saw you'd done this one and thought I'd give it a shot myself before watching your video.
This is the first time I've ever managed to solve a sudoku. I only had to consult your video about 2 or 3 times, and only for a little nudge in the right direction. Otherwise, it was almost entirely on my own.
I've never even managed to do a standard sudoku where almost all the numbers are given to you.
I'm not sure I'm going to take a dive into solving more complicated or other kinds of sudoku puzzles, but I think miracle sudoku like this is more my speed.
Thank you!
When I tried to solve this puzzle on my own, I made a mistake with the sixes. But something amazing happened. With the incorrect sixes, it seemed like there was no way to place the sevens in a contradictory way so I was struggling to make progress. That is until I realized that I needed to place the sevens in such a way that the left over squares do not touch each other, since that would lead to consecutive eights and nines. I thought it was a surprisingly neat ending that got more difficult at the end. I was a bit sad that it was not part of the real puzzle.
This one took me a week. I never watch the videos until I have mine solved, and then to see him fly through what I agonized over in less than half an hour... Well, you'd think it would be disheartening, but it's such a celebration! He gets so very happy with every success, and I get to relive all the joy without the frustration. 😊
And 5 goes next to the 1, next to the 1, next to the 1,
6 goes next to the 2, next to the 2, next to the 2
7 goes next to the 3, next to the 3, next to the 3
I was waiting for him to notice. The repeating pattern by row (you could do it by column I suppose) is an interesting outcome of these rules for the game. It could make for an extremely fast solve if the pattern is fully understood and anticipated right from the start.
It's amazing that he was still able to solve when he misplaced the 2 coloring. You are brilliant
16:03 Pretty easy after having solved the previous one!
This just popped up in my recommend feed, never done a single Sudoku before but I decided to try this after hearing the instructions, it took me an hour of mostly process of elimination but at the end it's so rewarding, definitely going be doing more but rn I need to go to bed
25:40 “Hopefully I haven’t made a boo boo” I’m- 🥺 so cute
Never solved a sudoku featured on this channel, but tried this one and got it in 53 minutes. Cheers.
It's a work of Art.
*AND A WORK OF AAD.*
Saw the video, waited for the rules to be sure it was the same, paused and solved. Little over half an hour but I managed it! You're right, these are really nice to solve. You just have a huge hurdle at the beginning and then it's all smooth sailing.
his thinking process in solving these is faster than mine during panic attacks
I finally solved one with zero help from Simon! Usually I get stuck somewhere and have to watch part of the video. This is a good day indeed!
Imagine doing this sudoku, being at 5 and noticing, that you made a mistake... yep, that's me✋🏻
Edit: Omg I made it
Litterally me
Same🥲
I solved it in 2 hours and 23 minutes, around 2 hours in I made a mistake and briefly thought I would have to restart the whole thing but thank goodness I realised where I messed up and could easily fix it
@@alipareedanse12 That's good that you noticed where you made the mistake! It would have been sad if you had to do the whole thing again just because a little mistake 😬
I had already made a mistake at 2s so started over
Love the miracle sudoku. It's such a fun solve, and I love listening to you help guide me through when I get stuck. It's a great soothing and relaxing way to end my night.
25:35 that's a five
(Stares at R8C7)
"Oh no, I don't want to put a five there" Simon looks like he accidentally angered the sudoku gods looking down from above XD
Never enjoyed sudoku but find this oddly satisfying to watch and thoroughly enjoying it, youtube recommended helps me find stuff to watch again
Last time I was this fast I was still doing easy Sudoku just starting out.
Can I please stress that both you and aad are wizards, this has been one of the fastest half hours of my life. Love your work, keep up the amazing solving!
The more i watch this channel, the more i feel like i have the intelligence of a potato...
Still enjoy it immensely :)
I love it when I spot something a few steps ahead of where you are at because 99% of the time I'm about 10 steps behind and just dumbfounded.
Makes me feel smart for just a second hahaha
2s would have been faster if you didn't mark the cells next to the threes.
Yesh! My first time doing one of your featured puzzles under one hour and no peeking at the video! Keep doing these awesome videos!
phew, the beginning was extremely annoying, it took me around an hour and a half to clear this. I already watched him clear the last miracle one, but still didn't expect to take 1 hour and 30 minutes to clear it XD.
From 13:15 you can already see some symmetry in the middle 3 boxes. The 3s are exactly 2 cells right of 4s
Even the row2 column8 4 cell loops around the edge and keeps a distance of 2 cells.
Absolutely love this content!
I don't really like this puzzle to be honest. It's exactly the same as the other one, just labeled differently. The 5's have become
1's in this one, the 6's have become 2's, the 7's have become 3's and so on..
Yeah, as much as i loved the first one because of how ingenious it was, but now it feels identical and not as fun.
Its the ruleset, you can get all possible valid solution by moving the board down, left, or rotating it. The constraints are too restrictive to make anything else.
Thats why the first one was a miracle, it was a miracle that it ended up that way and it can't be repeated.
Super Happy! Solved in about 2 hours. Getting all the 3s and 4s was super tough, But once I had them I also started with 2s and then the rest just came along a lot quicker. This is great. Discovered your page today, and spent around 3 hours on a different puzzle earlier. Absolutely hooked. Subscribed. :-)
Well not that hard
Took me 40 minutes
But i’m dying to have more of those
this is the 3rd video ive watched in as many days, ive never been so riveted by sudoku. youre delightful to watch :)
Looks quite similar.
It's basically the same Sudoku as the Mitchell Lee version but all numbers are staggered one step to the right. I'm more amazed over how it's still solvable though from this position.
Just found your channel and I have quickly become addicted. I'm going to challenge my friend to one of these miracle sudokus 😁 thank you
who came from hazem code
Same
Me
Me lol
Bro they fr giving puzzles that requires 999 iq. Were literal 15 year olds bro 💀
Dude thinks were big brained
Me
I actually managed to do this one on my own after seeing your first miracle solve! I watched this video after successfully solving it myself! Really enjoyed it :) Thanks!
you made a fair few mistakes when calculating where the 2 could go
So nice to see you read that commenter's comment and fixed Aad's name by putting caps only where they're supposed to go :)