The "Empty Grid" Sudoku
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- čas přidán 20. 10. 2021
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We suspect you won't have seen a sudoku like today's ever before. Not even The Miracle Sudoku was quite so sparse. That's right Empty Grid by Jodawo literally has nothing in the grid at all. What is going on?!?! You can play the puzzle at the following link:
app.crackingthecryptic.com/su...
Rules:
In this puzzle ‘2-digit numbers’ read from left to right or downwards. Box 1 (NW) will contain all the 2-digit square numbers (16, 25, 36, 49, 64, and 81), which may overlap but must be entirely contained within the box. Box 9 (SE) is a clone of box 1, rotated through 180°. In each of boxes 3 (NE), 5 (centre) and 7 (SW), each digit will contribute to at least one 2-digit prime number contained within that box. Box 4 (W) is a magic square, with each row, column, and 3-digit diagonal summing to the same total. In each of box 6 (E) and 8 (S), the two 3-digit diagonals sum to the same number (NB box 6's number may be different from box 8's number).
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As mentioned in the video, we have a bonus puzzle today from the brilliant Botaku. It's called Euclidean Sudoku! You can play it at the link below and watch a video of Simon solving it on our Patreon page.
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Play the puzzle here:
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Rules:
Normal sudoku rules apply. Given two cells which both contain the digit N, the Euclidean distance between (the centres of) those cells must be at least √N times the sidelength of a single cell. In other words, if moving from one such cell to the other takes X horizontal steps and Y vertical steps, then √(X^2 + Y^2) ≥ √N.
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Genuinely stunned that a sudoku with no digits, and only rules which apply to entire boxes, could have a unique solution AND a logical path to reach it. Incredible setting!
Actually there’s a 5 in the center of Box 4, since every 3×3 magic square has to have a 5 in the center.
Given that the solution is unique, by the same logic there are 81 given digits
The setter got the idea to try to do it when he was reading the comments on another puzzle. Someone had said one day Simon's going to open up the puzzle and it'll just be an empty grid. Many setters have tried with the constraints that we have to develop a similar puzzle. This one is the first of its kind that has been featured.
If there is a unique solution, there is always a logical path to reach it.
if you understand the mathematics then the rules become like hints
The fact that he never realized that box 3 and 5 were exactly the same amuses me.
That’s exactly what I was thinking!
I did not notice that either somehow
I used that fact in order to somewhat cheat. Before trying to work out the logic for box 5, I had noticed that the digits of box 3 fit all the sudoku constraints of box 5. So as an experiment I tried just copying box 3 into box 5, not really expecting it to work and thinking I'd have to rewind after it lead to a contradiction. But then the puzzle solved easily from there.
Right when I was thinking about it, I found this comment. What a coincidence.
Wow!!!! i didn't notice
I just have to say that normal sudoku rules apply is not one of the specified rules
Maybe the solution was wrong, then! Considering normal sudoku rules don't apply... Lol
@@katieschroeder7620 Either the puzzle was wrong (by having multiple non-sudoku solutions) or the solution was indeed the one he got (regardless of the sudoku rules Simon applied ; but I doubt very much it was solvable without them)
What I mean is: as long as the solution Simon found is respecting all the specified rules, he absolutely got the intended one ; except if the puzzle is broken/ambiguous
Came here for this. Nowhere does it say it's a sudoku at all!
maybe there was a character limit lmao
since normal sudoku does not apply, you could put letters in the grid instead of numbers 😜
This is by far the best explanation of a magic square I've ever heard.
YES! SET meets magic.
Same here. You could even keep going with the sum logic. e.g. if 1 was in the corner then we would have to make 14 in two cells three different ways, and using the secret the remaining two cells would have to add to 2.
Another thing I would add is,
Do evens go in corners or the odds?
If odds went in the corners, then you'd have a odd-even-odd row (or column)
Odd+even+odd gives a even number, 15 isn't even.
So odds don't go in corners. Evens do...
Another nice way that also immediately gives which numbers are in the corners is this:
•Write all possible partitions of 15 with 3 distinct numbers from 1 to 9
9+5+1 ; 9+4+2 ; 8+6+1 ; 8+5+2 ; 8+4+3 ; 7+6+2 ; 7+5+3 ; 6+5+4
•Separate the numbers 1-9 by how many times they each appear:
{4 times} = 5 || {3 times} = 2,4,6,8 || {2times} = 1,3,7,9
The middle number has to appear 4 times, the corners' three, and the ones adjacent to the middle two, so you got an idea of how the square looks like just from this.
There’s an even easier way to discern what the middle digit should be - it’s simply the mean number between 1 and 9. :)
I knew you'd eventually get a blank grid!!!!! The next level set of rules from the setter could be "read my mind!" 😅
I'd love it xD
Really, Tippy? The sudoku scene is the next step in the evolution of humankind? Mind you, it could be 😍
@@amoswittenbergsmusings 😄
Next step: you have to build the grid too!
@@juggernaut93 Good one!! 👍
26:53 "51, that's not prime, all darts players will know that"
The casualness and confidence with which he makes these comments simply delight me. It's as if it's such a simple, elegant truth that naturally everyone knows by heart, this man's intelligence is absolutely unfathomable
Like at 14:00 "if the three was in the corner, we would have 3,6,9 and could do the song"
@@yellowyoda274 hahaha very true
That's not intelligence. That is education.
@@NinjaOnANinja intelligence is understanding the difference between merely being educated, and being able to make sense of all the information after having been educated. Amusing to see you comment this, good try though.
@@StormBurnX not really. Robots can be just as logical. Be serious plz.
This is the last type of channel I ever thought I’d get hooked on but I’ve been binging this for the past two days.
Still watching this channel?
Same
@@user5214is it possible to just stop watching CTC? Hahaha
Just started watching these solves. He's so good at pacing his explanation of his thought process while figuring out the logical solve at the same time. Also he's so invested I get glued to the screen. This content is so satisfying 😅
26:06 Am I the only one that found it weirdly wholesome that he got slightly upset at himself and apologised to the eights for missing them lol
When I saw and heard him do that about the 8's, It made me think about Oliver Twist for some reason.
Same.
I don’t know what’s more constricting, the prime rules or the sudoku rules 😂
@@griffinshorts785 The Prime Box has 288 different combinations. The Square Box has 4 different combinations. The Square Box is more restrictive. Even more restrictive than the Magic Square which has 8 different combinations.
@@Jodawo interesting. It just seemed to me that he used the prime rules a lot more than anything else
"I'm just struck by how little sudoku I did" - To be fair, Sudoku is usually the last thing you try as soon as there's any sort of variant rule that's not a standard variant...
He filled in 81 numbers though, so that that seems like doing quite a lot of sudoku!
@@matthewkaseman7457 I think you completely missed the point.
@@christopherknight9960 I mean, I might be approaching his point obliquely, sure, but I'm not completely wrong! The platonic ideal of a sudoku is filling digits into boxes, and this puzzle let the player do that 81 times, which is quite a lot more than getting to do 65 or 70 digits. I'd argue that this puzzle was the maximum amount of sudoku per sudoku possible!
"Doing sodoku" in this context means using the uniqueness constraints on each column, row, and box to affect other rows, columns, or boxes.
@@matthewkaseman7457 (Didn't spot this until just now)
What isHavvy said - "Doing sudoku" in this context is "sudoku logic" - The things that being a 9x9 Latin Square with 9 additional 3x3 regions tells you. At its simplest, pointing pairs, naked and hidden singles, and the like. At it's more advanced, stuff like X-Wings, Y-Wings, continuous nice loops, skyscrapers, SET stuff, and more obtuse techniques I don't have the foggiest what they are yet alone how to spot them.
All sudoku variants add additional constraints - additional possible logical paths - to that, but those variants are using additional, non-sudoku, logic that interacts with the logic of sudoku.Taking kropki dots, for example, since one of the GAPPs (a companion series to GAS, which features non-sudoku puzzles, posted daily on the CTC discord) was a 7x7 Kropki - No sudoku, just a 7x7 latin square with kropki dots, and which I believe predates the Kropki sudoku variant, they give a logic that exists outside of Sudoku logic all on their own, and as such when doing a Kropki Sudoku, it's not really 'doing sudoku' when the logic you're using is currently only the logic that you get from Kropki, not from the additional 3x3 boxes from Sudoku (Although, obviously, since both Sudoku and Kropki puzzles are types of Latin Squares, there's a lot of overlap with the logic that's Sudoku logic, and the logic that's Kropki logic)
What Simon meant when he said 'I didn't do much sudoku' and I was riffing on is that he was almost entirely using the variant ruleset rather than any of the logic that comes from the grid just being a sudoku (Which his mind seems to instinctively do as soon as he has any variant for as long as possible, sometimes doing something a far more complicated way using the variant rules when a simpler method using sudoku would have sufficed)
I feel sorry for box 2 :(
I felt sorry for box 5 - it looks to be the same as box 3 at first glance. Yes - the same triplets, so Simon melting his brain when the answer is already there...
So incredibly focused that he got tunnel vision - not for the first time.
7 minutes of solving and he never noticed the box 3/5 clone even at the end.
Mind you - he finished the puzzle - I never even started it. My brain melted reading the 'manual'!
BOX 2 SOLIDARITY ✊✊
@@CJ_squared Go box 2 ftw
@@itsmeagain1745 nice observation but I m affraid he didn't have vision tunnel at all there : it ended up being clones but through different logic, there was no inherent logic forcing box 5 being a clone just from having the same row triplets (as far as I can tell, I might have tunnel vision too ^^).
@@emphyriohazzl1510 You could well be correct - it just seemed to me that the triples would give the same logic as he worked out earlier. But what do I know - these puzzles are usually way beyond my skill level.
It would be interesting for Simon to comment on this.
A year ago, Simon probably would've thought Mark was trolling with this empty grid. Now he just gets right into it
The thing that should have amazed you is before he put it up the puzzle he said one of the possibilities was "a grid with nothing in it". I think that's amazing because this is the only empty grid Sudoku that has ever been featured. It would be like him going to a zoo and having to guess what the next cage is going to have in it and him commenting it'll probably be a unicorn and it's a "🦄".
Never ever apologise for taking a long time to solve a puzzle. Watching you blitz through puzzles would not be as enjoyable. I look forward to watching the channel every evening.
You finally did it, you absolute madman. You solved a completely empty grid. Kudos to the setter for managing to find a ruleset that allows a unique solution with absolutely no clues.
Wait till you see Empty Grid 2. It'll only have specific rules for 3 Boxes instead of 8 that this one had. There will be less rules. Also when you finish the puzzle, there's a huge Easter Egg.
An empty grid that doesn't need a lot of Sudoku to solve it, but you must have good knowledge of primes, addition and know how magic squares work.
I love CtC, where else can you find such great content?
And we have Mark and Simon sowing us how to solve them.
I suggest you go watch "mind your decisions". It's similar, not cryptic, but similar.
@@WatchOnYT I like both. 😀
I would argue there is a lot of Sudoku done in this puzzle. Remember all the triples for Boxes 2, 6, 7, & 8? Getting triples is doing Sudoku. Box 3 had quite a bit of Sudoku also he used Box 1 and Box 9 to help figure that one out by eliminating digits before he used the constraint. Also at the end Boxes 2 and 8 had a flurry of Sudoku to narrow down the possibilities before the constraint in Box 8 was used. After that constraint was used it was all Sudoku to finish it off. It could be easily argued that over 50% of this puzzle was Sudoku.
so you need to know what is a prime number (everyone knows it no metter age), how to add 2 numbers (not even gonna talk about it) and how magic squares work (also eveyone knows and its even explained)... this speeks for itself
Thank you for the magic square proof, I was solving with a few friends yesterday who aren’t as familiar and my proof was basically “5 is always in the middle and evens in the corner because that’s what the sudoku gods say.”
Of the 362,880 possible layouts for a block, 288 (exactly 1/1260th) are valid entries for the two-digit-prime squares, and half are diagonal mirror reflections of the others (for instance, 235 489 167 vs 241 386 597). I find it funny that blocks 3 and 5 turn out exactly the same!
Are there sudokus where blocks 3 , 5 and 7 ( or 1 5 9 ) are the same or does that break at least one of the other boxes ? (not with these rules added etc)
Oh, expletive. And here I spent a good 30 minutes stuck trying to find a solution for block 5 that would fit the constraints from the other blocks, and the solution to it was right there for me to look at. That's hilarious!
@@highpath4776 It can have three clones. You can also put clones in boxes 2, 4, 9 | 2, 6, 7 | 1, 6, 8 | 3, 4, 8 . That would be the boxes that could hold three clones because the center squares do not see each other. Not only that but I have created a puzzle that has three clones in it purely by accident and one of them is in a box while the other two is offset and crossing more than one box. In fact this puzzle will be going into the archive very soon. The puzzle having clones is not even part of the ruleset I had said the arrangement was purely accidental so now I tell the solvers there is an "Easter Egg" in the puzzle.
@@highpath4776 Yes, and even if you were provided with that box, that still isn't enough to get a unique solution. There are still so many options it isn't funny.
You can even try for more symmetry (but I don't have a solution count checker to check for it)
It is possible for all the boxes to be in groups of 3.
e.g. boxes 1, 5 & 9 are identical; boxes 2, 6 & 7 are identical and boxes 3, 4 & 8 are identical.
And even then you can still have loads of solutions, as you can permute all the different numbers (362880 different possibilities), as well as permuting the rows within boxes, the rows of boxes, the columns within boxes and columns of boxes.
What I want to know is there only 1 possible solution with trivial permutations, or are there more, non-trivial permutations?
And how many clues need to be provided to solve it with this constraint?
Actually... There are not THAT many possibilities when introducing prime rules. I have layouted what looks to be a key to it of some sorts. Now, in addition to this, the top left corner of a box always is even (or 5 I think). So really limited in terms of setting.
000/000/258
000/258/039
258/039/017
Where in the diagonal two digits have to be next to each other and form an L-shape with either 3 or 9. I.e.
0/0/8
0/5/3
0/0/0
And bottom right has to be either 1 or 7.
I've never played a game of sudoku in my live and yet it's oddly relaxing to just follow the logic that's being explained
Let's get cracking: 04:52
And how about this video's Simarkisms?!
Sorry: 10x (04:16, 12:27, 22:30, 26:06, 26:42, 27:18, 35:14, 37:40, 37:40, 39:17)
Clever: 5x (12:39, 13:42, 20:44, 36:18, 52:37)
Hang On: 4x (02:42, 14:20, 26:25, 31:32)
Surely: 3x (35:20, 36:59, 41:20)
Bobbins: 2x (22:30, 30:14)
Good Grief: 2x (02:19, 03:42)
Naked Single: 2x (29:16, 50:07)
Three In the Corner: 2x (14:14, 14:36)
Lovely: 2x (17:01, 30:53)
Beautiful: 2x (14:55, 23:54)
What on Earth: 1x (35:27)
Useless: 1x (10:14)
Secret: 1x (05:37)
The Answer is: 1x (22:57)
Break the Puzzle: 1x (36:07)
By sudoku: 1x (18:49)
FAQ:
Q1: What is a Simarkism?
A1: A Simarkism is something that Simon and Mark typically or frequently say.
Q2: How do you do this so fast?
A2: I'm not made of flesh and blood, but of sand ...
Q3: Why don't you include 'XX' and 'YY'?
A3: Probably it's already on the list ('Scooby-Doo' for example), but not mentioned in this video. But if you think it's not, tell me what you'd like me to include and there's a good chance I'll add it!
Q4: You missed 'XX' at 'YY:ZZ'!
A4: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn!
Q5: Could you turn these statistics into videos?
A5: I've been playing around with the idea and I'm open to input as to what people would like to see. Let me know if you are interested in this and/or have suggestions.
This is beautiful, you legend
I don't know how I could have missed this one. I was looking for it. I'm glad I took another look.
This is hurting my eyes with all that blue
Open puzzle.
Read rules.
Close puzzle.
Watch video.
I don't think you are alone. With the quality of puzzles that they get most of the time watching the video is the default mode... LOL
While I am in constant admiration of your reasoning skills, I wish I had the skill to even attempt to set a puzzle like this. It boggles my mind that someone can think of a logical path to create a puzzle like this.
Simon: "Probably it's going to be a grid with nothing in it, or some crazy stuff in it"
Me:
(I'm shocked that I got this one to solve, though I did take a lot longer than Simon -- not surprisingly.)
I think it was crazy how he guessed it was going to be a grid with nothing in it. It was one of his two choices that he had guessed. This channel has never seen a completely empty grid so for it to be the first thing out of his mouth is quite a prediction. The last huge video I can remember where he was asked to open it when the camera was running was one called "Chaotic Wrogn". He took one look and basically said "No, I'm not doing that!?". It turned out to be one of his best videos. This puzzle and that puzzle are polar opposites of each other. One is clean and completely devoid of anything while the other looks like Pollock set the puzzle.
27:59 for me. That was awesome. I can’t believe this is solvable at all. Incredible. I thought it was going to be much harder, but some of the constraints are more restricted than what I initially thought. Kudos to the setter for being able to create such a thing like this.
There is another one in the Discord CTC fan page by the same setter. It is called "Disjointed Primes". It is in testing right now but should be very soon in the archive. Imagine just three 3x3 killer cages, zero given digits and a little killer with no value. All of this with a much easier ruleset. There is also an Easter egg in it. If you are on Discord then you can find it in the testing area but like I said it should be going into the archive very soon.
Great puzzle. (1) I note with amusement that "j" and "w" are both letters with many pronunciations across languages, so having a name with them is a good metapuzzle for everyone! (2) Somehow, I am reminded of my crazy puzzle idea: "reverse sudoku" - the idea would be the player would be given a full grid of digits, but have to place rules that entailed them in the right way. E.g, you'd be told there was a three cell arrow, 3 black kropki dots, etc.
In this case the pronunciation is :
Jo which will sound like "jaw". Da will sound like "duh". Wo will sound like "wa"ter. [ Jodawo = JawDuhWa ]
@@Jodawo Nah, I don't care if it's actually your name, the correct pronunciation is obviously "Yoda Foe."
😀
@@Tfin I got the pronunciation straight from the horse's mouth.
The letter 'r': "Hold my uvular trill"
@@jayrs1528 You mean the Japanese L?
I came so close - right up to the final few steps. Then, tragically, I discovered a contradiction that had remained hidden for ages. I made a hasty assumption when doing box 5 that didn't cause a problem until the very end! I was almost proud of myself. Regardless, amazing puzzle.
Thats a learning moment, great job!
Your videos are really addicting… never thought I’d spend an hour watching someone else do sudoku without me getting distracted but here I am!
I have to wake up at 530am for work. I found this channel 2 weeks ago, so i havs quite the backlog of videos. I often find myself watching CtC until midnight. Even as late as 1am some nights. For example, I was up until 1230 last night. It's 1130 as I type this and I swore I would be in bed by 10... the problem is I'm addicted to football and this, so on Sunday, Monday, and Thursday, football goes until 11 at the earliest. Then for some reason I have to watch CtC and that's an hour. And all the sudden it's 1230am smh. This channel is highly addictive and I love every second of it and don't regret an ounce of sleep I've lost.
Congratulations Jodawo, you just made the most visually minimal and empty Sudoku grid ever set in the history of Cracking The Cryptic!
No big digits.
No tiny digits.
No Cages.
No Thermos.
No colored hints.
Nothing in the grid.
Nothing outside the grid.
Nothing.
Just a grid.
One of the longest rule sets though, but I don’t think can be helped
It could have been an irregular, and also had no thick lines.
next video: no grid
Wait till you see Empty Grid 2. It'll only have specific rules for 3 Boxes instead of 8 that this one had. There will be less rules. Also when you finish the puzzle, there's a huge Easter Egg.
@@Jodawo *gulp*
This is the absolutely last channel I thought I’d ever watch! This guy is a genius, I get stuck on easy puzzles 😂, and I’m bowled over by magic squares, geometry and special rules! Total respect!
When you get to 41:31, you can quickly rule out 569 and 659 in b5's lower row. Neither 5 nor 6 can appear in the ones digit of a two-digit prime. So the 5 and 6 must both make their prime entirely in the row, but they cannot both be in the other digit in the row's tens position, so if you put 569 in the bottom row of b5, you are saying that either 56 or 65 is a prime number, but neither of these is prime.
This is the first puzzle I was able to solve in one session without having to get any clues/encouragement from the video. Thanks for making these, it’s been a great spring break trying, and mostly failing, but learning a lot. Took me just under an hour.
I feel like there's still a little too much grid in this sudoku... how about one where there's just an audio clip describing a sudoku that you need to construct yourself?
You joke now, but we’ll see who’s laughing in 2031 when Simon takes 12 hours to place the first line of the grid.
@@felipevasconcelos6736 "We'll use blue for major box lines, because they both begin with b, and orange for minor cell lines"
In 2040 Simon solves a Sudoku from first principles.
Underrated comment
@@jonahcomstock3061 In 2050 Simon takes 23 days to come up with 3 possible sets of rules to form the upper left pixel of box 1, and afterwards takes 46 days to construct the rest of the single cell so he can solve a sudoku from first principles, those principles you have to figure out yourself of course
Stumbled across this just before bed, and instead stayed up an extra hour. Genuinely riveting, absolutely delightful watching you puzzle through this. You explain your thought process wonderfully.
Your cheerfulness in receiving this puzzle and working your way through it is awesome!
Simon’s reaction to puzzles like this changed after he solved “Chaotic Wrogn” (a.k.a. The Second Movie).
@@Y_Llew_Tew When was that?
@@longwaytotipperary About 9 months ago - czcams.com/video/zfIomUELg6c/video.html
@@Y_Llew_Tew Thanks!
@@Y_Llew_Tew I think that video was probably one of his best videos ever. It seems when Mark slips Simon a puzzle and tells him not to look at it until the video is on usually turns out to be a great video. I think Simon even though he may say differently truly enjoys the challenge of the surprise.
It always seems weird to me when a puzzle gets like 2/3 of its digits in and we're still using non-sudoku rules to make progress. If i saw a classic sudoku with 2/3 of the digits given, i'd assume it'd be elementary to solve it.
I would argue there is a lot of Sudoku done in this puzzle. Remember all the triples for Boxes 2, 6, 7, & 8? Getting triples is doing Sudoku. Box 3 had quite a bit of Sudoku also he used Box 1 and Box 9 to help figure that one out by eliminating digits before he used the constraint. Also at the end Boxes 2 and 8 had a flurry of Sudoku to narrow down the possibilities before the constraint in Box 8 was used. After that constraint was used it was all Sudoku to finish it off. It could be easily argued that over 50% of this puzzle was Sudoku.
The point of the advanced rules, other than upping the difficulty, is to constrain to a unique solution.
Once you get to that stage, yes, you could "solve" it by using normal Sudoku rules. But the result would not necessarily follow the specified non-sudoku rules, which is why it takes so much extra effort even if most of it is filled out.
I think it would be really cool to see you and Mark react to a solve from last year, before this sort of thing was even feasible! It would be interesting to see what your reaction is to the early variants.
Even more interesting (but sadly impossible) would be Simon and Mark from 2019/20 reacting to one of the latest puzzles. All it requires is someone inventing a time machine…
@@Y_Llew_Tew The implication of a time machine is that the second law of thermodynamics is broken. If entropy can be reversed, the dead can rise again - bodily. And all of a sudden Mahler's 2nd symphony is in my head: "Aufersteh'n, ja aufersteh'n wirst du mein Herz, in einem Nu!"
@@Y_Llew_Tew I'm on it.
@@amoswittenbergsmusings Your comment is way above my pay grade, mate
its impressive how you can stay focused for such long time and not get distracted.
"There may be a better way of doing it." 47:37. I think I've got a cleaner solution for you all. I'll put it below for spoilers. Pausing at the current time should give you a pretty good picture of my logic, I hope:
So if you consider the top row and ask yourself how 6 can make a prime it cannot horizontally as 56, 65, 69 & 96 are all composite (not prime). Therefore 6 has to make a prime vertically with the second row and the only valid number in the second row is the only odd number: 7. Therefore 6 is above 7. Now, consider if 6 is above 7, 5 and 9 must be above even numbers (2&4) so they can't make a prime vertically and will have to make a prime horizontally with each other as 59. Therefore 6 cannot be in the top-middle box or it would split up 5 and 9 and because 6 is above 7, 7 is also out of the center box in its row.
Let's talk about the middle row now. Simon already eliminated the 2 from the left middle box. Let's consider 4 and if it could be a horizontal prime. It could only be that if it were 47, but now that 7 is out of the middle box the only valid 47 would place 4 in the middle and 7 on the right. But placing that 47 would prevent the 2 from being able to be placed anywhere as 2 is already out of the left box. Therefore 4 MUST be a vertical prime and because it's even it must make a prime with a third row digit. Which digit? Well not 8, that's even. And not 2 because we've already proved that 2 is above the 3. 4 therefore must be above the 1, 2 above the 3 and by elimination 8 MUST be above the 7.
If you examine the square at the time stamp you and imagine there's no 7 in the middle box you can now see that the only column in box 5 that could place a 7 above an 8 is the left column. 7 in the middle left square, 8 in the bottom left. 6 goes above the 7 in the top left placing 59 in the remaining two top squares. We know 8 must make 83 so 3 is in the bottom middle, 1 in the bottom right, 4 above it in the middle left and 2 in the middle. There: clean. Simple? Nah.
Hopefully that's easy to follow along. That was the logic I used to solve the middle square in any case.
Very nice deductions. One thing that might help when doing the Prime Box is that the middle square is always a 258. 258 only has two prime Enders 39. That means two out of three of the 258 have to share one of the Prime ender 39. If you experiment, you'll find the only way the puzzle does not break is that one of the sharing cells is in the center. That would have made Simon put the 2 in the center cell. Everything else would have fell into place with much simpler deductions.
Another characteristic of the Prime box is that there's only four Prime Enders 1379. Two of those numbers need to be in the bottom row. In the other two rows, there needs to be one in each to create a valid Prime Box. Knowing those two characteristics would make disambiguating the Prime Box much easier.
My favourite thing you do in all your videos is you never assume we know something that is obvious to you. Like you were just explaining the magic square and you said there are three ways of making 6 but in sudoku you can't use a 3 twice. That's obvious but I really Appreciate you clarifying things like that when explaining the process of solving these puzzles. I have to really concentrate on understanding your puzzle solving and often have to pause the video and listen to you word by word to understand what you're saying lol. (Not saying you're bad at explaining, your very good at explaining but sudoku doesnt come naturally to me) Also other times you've explained something that is so obvious to me now I know it but wasn't obvious to me when I first started. Iv watched your videos for years. I'm quite good at sudoku now.. not as good as you tho 🤣. Thanks for making sudoku fun for everyone even the beginners and the not so academic like myself. And I mean this is the best possible way, your videos do send me off to sleep most evenings. I think it's your therapeutic voice. The annoying thing is I never make it to the end to see the solution. 🤣
This man’a just thinking out loud and I’m here for it
53 minute Simon video with an empty grid...yeah I think I'll just watch this one 🤣
As someone who took 2 and a half hours to complete the puzzle, I felt personally offended every time he said "you probably saw this before I did"
I just discovered your channel and told my friend about you and he was like "this guy sounds like the Bob Ross of puzzles" and I was like yes!!!! Nailed it
I’m not a huge fan of puzzles where the rules aren’t the same across the whole puzzle, but I will still enjoy watching Simon solve it.
well it's hard to have a completely blank grid AND universal rules since you need to break the symmetry somewhere or else the puzzle will have multiple solutions and be unsolvable.
@@HopUpOutDaBed
You can have a directional rule that applies to the whole grid, and that’s fine.
I guess the rules could have been worded more generically (instead of "in box X", it could just have been some marker in the grid for each), but then you wouldn't have a completely empty grid at the beginning. (Some restrictions are needed to break the symmetry and make it uniquely solvable.)
@@PauxloE
You can’t get a unique solution with a blank grid unless the rules have some kind of asymmetry to them. They can still be the same for the whole grid.
@@ragnkja True, the "two-digit numbers are read from left to right or top-down" is already such a kind of asymmetry in this example (though it still allows mirroring across the diagonal). Do you have an example of an empty puzzle with just global rules?
This channel has woken up sleeping giants around the world who are outdoing one another to come up with more and more incredible number arrangements to fit into a sudoku grid. Very enjoyable!
Do we call them Matth Daemons!
I never cease to be amazed by Simon's genius
I'm probably the LEAST math inclined person you'll ever meet.
However I am trying SO HARD to keep up. This is so fun to watch be solved!!
no need to apologize about taking too long to solve! this is the third one-hour long video i watch from you and it's really entertaining following your train of thought to solve them, even if it takes a while there's absolutely no rush
I'm glad I didn't look at the video length before trying this one... it took me a looong time but I did finish it. This is now my new record for length of video of a puzzle I solved. What a pleasure.
"Satisfying video" as they says on the web, just watching the genius you are solving them! Bravo.
At first I was like, nah I'll just watch Simon do it, and after he started coloring it, I foolishly thought I'd give it a try first...
It took me 50:20 and I'm glad I went for it, this was so weird and amazing.
It probably was the correct way to do that. Watching Simon in the beginning so he can give you a clearer assessment of the rules. Sometimes if you're solving and you misunderstand a rule it can cause quite a headache trying to figure out what's going on or why it's not working. Sometimes it's good to try a puzzle before you watch the whole solve on video. If you do end up finishing it it's actually more exhilarating then if you watched someone else do it even if the video turned out great. I actually think that's why people will say the book was better than the movie because our minds can fill in so much and do what CGI just cannot do. For this puzzle, being able to finish it in under an hour looks like a great accomplishment and you should be proud of yourself.
@@Jodawo Yeah, I've made that mistake.
And yet again I watched the whole video without realising
"So now, with a bit of visualization you can see..."
*cries in Aphantasia*
I’m impressed how someone can make such a sudoku
It is absolutely fascinating and pure joy watching you work through these, thank you for sharing your gift.
Loved this one! I foolishly tried it myself and gave up after staring at my incomplete magic square; resigning myself to watching the genius of Simon cracking it instead. Time excellently spent.
In this puzzle where to start is well hidden. Once you find the starting point it logically pushes you in the right direction. It's almost like the puzzle does not allow you to stray from the path once you find the start.
I love how humble you are. Great work as always!
One of the best puzzles. the way Simon solves it is amazing..
I thought "I know primes, let's try this one."
I started with the squares - wrote down the (directed) graph from the pairs, and noted that it has a path of length 5, which can only go into the (3×3) grid starting at the top left and ending on the bottom right (so 8 and 9 were fixed, 1 and 4 had two places left). Due to the 6 also getting the 3, this fixed the 6, and then I got the two options for the 25.
Next I took on the magic square, but remembered the logic wrong, which got me into a contradiction after another long time (and then I restarted it).
For the primes, I wrote down all combinations of digits which make primes, and noted that all of 2, 5, 8 only give primes as first digits with 3 or 9 as their second digit (and therefore 3 and 9 needed to serve 1 and 2 of the others each). "This must be significant!" - it means that those 5 digits were quite restricted in where they could go (relative to each other, and at all). (Also, the 6 only forms a prime as 61 and 67, which can be later used for box 5.)
I somehow didn't get the "there are 3 digits left in each column" idea (I don't usually solve Sudokus, this shows), so it took me a lot longer to fill the bottom left box, but I got it (and then also the top left box) correctly (with the 28 pair still unresolved).
I managed to partially fill box 6 and 8, like Simon had at 33:35 (with several more corner pencil marks in Box 8 - and I managed to find out that R9C5 could not be a 3, because it was needed in the sum). I then tried the middle box, and got a lot of pencilmarks in there, but was stuck for a long time. I gave up, watched the video until Simon showed that there must be a 7 in the middle row, and from there succeeded on my own. [After knowing that there is a 569 row, it's clear that the 9 must be the last digit and before it a 5 to make that one a prime (the 3 was in the other row too far away), so you can only go 659. And then the 6 needs a 7, so this row needs to be on the top, which fixes the 7 in the middle row. Then both the 8 and the 2 need the 3, and the only way for the 4 to get a prime was with the 1, which fixes the remaining digits.]
Took me 162:06 after the restart due to the wrong magic square (including watching half of the video).
I worked on this on and off for a few days and just cracked it. I tripped myself up majorly very early in the logic by doing most of the magic square and box 1, but failed to do the tiniest bit more logic on the magic square to disambiguate the 1 and 3 in box 1, which made much the other solving a true headache.
The trick I used for the prime boxes was the idea of ending and beginning digits. A two-digit prime can never end in 2, 4, 5, 6, or 8, so it must instead always end in 1, 3, 7, or 9. From there it was some nice colorful logic in each box, placing where beginning and ending digits must go. I didn't do any digit logic (what primes can be which) until I had the color map filled out, at which point the digit logic was easy. In the case of box 5, I had to disambiguate via trying the digit logic for two possible colorings, which was only necessary because I failed to realize how to place 6 in box 6. Remarkably, I didn't have the same trouble as you with the 7 logic in box 5. My deduction is incredibly hit or miss.
My math brain is VERY pleased with this puzzle. I'm amazed at the great solve! Lovely work
I just found your channel, and I'm glad i did. Your brilliance is an inspiration. The way puzzles refine the mind and encourage lateral thinking is incredible!
I started this video out of bored curiosity. But watching you slowly logic it out, I became absorbed. Watched the whole video and I don't even play sudoku. 😂
There is one called "Chaotic Wrogn" by Undar Beyond. Simon's reaction to seeing it is priceless. When you look at it, you will probably think to yourself how is this solvable.
This was so weird and different from pretty much every sudoku I've solved before.
I loved it!
Very cool puzzle. I paused at 47:00 to see if there was an easier way to sort out the central box. 8 must be part of 83 so 1 can't go in the middle. 5 must be part of 59 so 5 can't go on the right, 9 can't go on the left, and 6 can't go in the middle. 6 must be part of 67 so 7 can't go in the middle. Now we try to put 2 on the right and quickly see 4 doesn't get a partner.
This is the first time that Simon had to work with this kind of constraint. He got through box 7 and box 3 without much problem. It also meant that he only learned a minimal amount about the characteristics of a Prime Box when he finally got to box 5. I think that's why it was difficult for him. It was like seeing it for the first time, which meant he had to slow down and learn more about it.
these videos bring me great joy
No need for an apology! Every minute of that was very enjoyable to watch.
When you mentioned 3-6-9 in box one and said you might be able to do "the song," my first thought was that the song was "Get Low" by Lil Jon
Wow. Simply, amazingly, wow.
46:30 its not bifurcating if i bifurcate in my head :). words of wisdom by the great Simon
I have been watching since the beginning of the pandemic, and I have to say that these videos fill a very specific spot in my entertainment library. I dont always watch them, but I do come back to them whenever I just need to turn my brain both completely off and also activate whatever math/logic it takes to get the answer one second before you 20% of the time.
I cant really explain it, but its very specific and can only be found here.
this was dope af. like a mathmatical mic drop on sudoku. im stunned this was doable at all
I'm frustrated that Simon seemed to skip over an entire rule (box 1: all square numbers must be entirely contained within the box) but it's good to see that he guessed that rule anyway.
The fact that I was completely focused and engaged in an hour long video with no edits says a lot. You're awesome!
I had a long train ride to go on, so I brought pencil and paper, wrote down the rules and tried my hand at this Sudoku. It took me a total of 6 hours to solve (because I got stuck for quite a while halfway through) but I managed to solve it and had a blast.
Love your logical and calm approach to these puzzles!
Simon did have a little problem with Box 5. It was his first time really working with this constraint. If I told you, that in all cases the center cell of a Prime Box will have the numbers 2, 5, or 8. Those numbers have only 3 or 9, as a prime ender, that they can use to be a 2-digit Prime. That means that two of those numbers has to share a prime ender. You will find that one of those three digits that has to share will have to occupy the center cell. The right bottom cell will always be a prime ender (1379). I have a feeling with these two pieces of information it would have made the solve a little bit easier.
I don't even play sudoku...my mom introduced me to sudoku years ago, I think because I like math and used to be addicted to crossword puzzles, but I was AWFUL at it and soon lost what little interest I had. I haven't tried in over a decade and only really spent a month or so on it anyway. I just happened to click on one of your videos where it looked like a blank puzzle with no numbers and obviously I was intrigued. Of course, with no additional information and an empty sudoku box you could fill it in however you liked - there would be no one right answer. But after learning it came with rather simple buy significant rules and forms and wasn't just an empty 9x9 grid, I was fascinated. That was a couple weeks ago, and now I'm hooked. It's almost hypnotic watching you solve the puzzles and go through your thought processes. Of course, you mention certain tricks and symmetries and "x-wings", and I have no idea what you're talking about, but I'm hooked and using some of your systematic basic methodologies I've started doing the puzzles again myself, and I'm really enjoying it, to my surprise. Thank you for the inspiration!
Just over an hour of my life which I will never get back, but that's fine, it was very happily donated to a very absorbing puzzle. The way the primes resolved was particularly magical, though box 5 took me much longer than Simon.
The other thing to consider is 2, 5, & 8 need to have a 3 or 9. That means someone has to share or the puzzle will be broken. After further analysis of this type of ruleset, you will find that the middle square will always have a 2, 5, or 8. The 2 would have been a write in as soon as he found the possibilities. Since 7 was proved to be in the fifth row in box 5, a 39 could be pencil marked into the cell below the 2 (r6c5). 58 could be pencil marked in cell r6c4 because the 39 needs to be shared. After that you can deduce r6c6 will be 1. After that the Magic Square and box 6 become disambiguated. No need for bifurcation.
55 minutes. But I am still learning the advanced reasoning from you. Got stuck several times. And I had the magic square right early on. Until I actually applied some Sudoku, and realized I had it inverted. Your reasoning is phenomenal. I find myself wanting to rush, and complete boxes; but end up in a cul-de-sac.
Can't believe I just spent an hour watching this and got thoroughly into it! Nicely done
For the prime boxes the main break into those is to realize that 2, 5, and 8 need either a 3 or a 9 as their end digit to make them Prime. You will then see that in the center Square there has to be a 2, 5, or an 8 because that number needs to share an ending digit with one of the other two that is left. So when he got two Box Five he would have been able to just write in the 2. He had a little trouble with that box but when you work with that type of constraint you will see that there are only a few ways to place the prime enders and non-prime enders.
I was glad to see Simon explain the magic square in detail because I can imagine when that first came up in a puzzle it was a concept that needed to be figured out now we can pretty much pencil mark the whole box without even thinking about it.
I think Simon did a marvelous job solving that puzzle for only seeing the constraint only once that is if he caught Mark's solve of the "Anniversary Sudoku" puzzle.
41:47 for me. spoiler:
2 of the prime boxes resulted to be clones!
Decided to give this one a try on a whim. 274 minutes and two pages of notes later and I've solved it. What an absolute joy of a puzzle!
Absolute banger. Watched start to finish.
Been waiting for a puzzle like this for a while where there are no given digits. Well done, Simon.
This is just sublime!
Every time I think they can't possibly create another miracle Sudoku, someone does. But surely there is nowhere else after this?
Can't believe I watched this in full. His explanations we're really good most of the time and kept things followable and engaging
That magic square logic baffled me. I had to watch it a few times to get it. Genious
One of the best I've seen. That was a nice way to end what has otherwise been a terrible day.
That took me 80 minutes and even though I got bogged down for a long while I'm quite happy with the time.
It was a fun puzzle that got the old, grey cells working.
That was a really fun solve to watch Simon, good job!
Commenting for the algorithm! Love following your logic through these puzzles. Watching you progress through the grid is always a joy :)
“That’s three in the corner”
box 3 and box 5 being the same numbers and positions was interesting
Phenominal. A true genius. Love the content. Very cozy to watch.
Before finding this channel, I thought of Sudoku as a puzzle I enjoy solving now and then. The puzzle in this video though.. it's a work of art!
Simon is a pure genius. I couldn't solve it if my life depended on it.
The titles always get me and I just want a look at the challenge and plan on skipping through to see some of the fun logic puzzles but I always get enthralled trying to get the logic along with you, very engrossing
I do very little sudoku, yet I find these videos totally mesmerizing, watching you work through the logic is astounding. Very fun.
Not sure why I'm on my couch at 22:44pm watching this.
Not sure why it was on my recommended videos
Not sure why I even continued watching since I struggle with standard Sudoku
But what I do know is, I loved it, you sir have a new subscriber
59:50. Whew. I think longest time spent on a puzzle. Quite enjoyable. Proudest solve yet! Now to watch the start of the video to see his reaction to it! 11.5/10.
Simon: slightly complains about not having enough sudoku in the puzzle.
Also Simon: rarely does sudoku anyways 🤣
Gotta love it!
Did very little sudoku. Literally entered all the triples into the boxes
I have been hypnotized into watching an hour long sudoku video and you cant make me believe otherwise, time flew by watching this, im baffled
I don’t know anything about sudoku puzzles but this was really fun to watch! Take a shot every time he says “this is really clever”