The Ultimate Miracle Sudoku

** TODAY'S PUZZLE **
Some of you might remember the original Miracle Sudoku - a remarkable puzzle with just a couple of digits in the grid. We've seen other forms of Miracle sudoku since Mitchell Lee's original but today we feature what is surely the most extreme form! The setter is Emre Kolotoglu and there are no clues at all except for a few ? dotted around the edge of the grid!!! Good luck! Play the puzzle at the link below:
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Rules:
Normal sudoku rules apply. Clues outside the grid represent any positive integers and they show the sum of the first X digits from that direction where X is the first digit and they also show the sum of the digits sandwiched between the 1 and the 9 in that row/column.
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[@emrekolotoglu5133]

Thank you so much Simon for featuring my puzzle again, for this great solve, and for your very kind words. I am very happy to see that you enjoyed solving this puzzle.

[@thoughtbyte]

well done kolot, this is one of the absolute most amazing constructions ive ever seen

[@Screm01]

Holy Cow! What a Genius puzzle... You did an excellent job here! How can you even give less clues than that and the puzzle solves...

[@victormanjarinsala2253]

Amazing work! I think this puzzle is something very special... I think it deserves to be a new episode in the long lost series of constructors explaining "how they did it" :)

[@martinwj]

Huge congratulations Emre - really a work of genius.

[@Jellow2202]

What an amazing puzzle! Such an intuitive ruleset. This is the first time ever that I was able to solve a CTC featured 45min+ puzzle faster than Simon. Usually it takes me at least double the video length to solve those monsters.

[@e7diablo]

Rarely talked about sudoku-ism I love: - "Everything is fitting together nicely" = "How annoying!" - "And that breaks" = "How wonderful!"

[@SjorsHoukes]

46:20 “This is huge. This is huge! Well, when I say huge, I mean modestly interesting.” 53:38 “everything seems to be order, doesn’t it? That’s very annoying.” Oh Simon, you always give me a good chuckle. 😄

[@bluerizlagirl]

The arithmomaniacs among you might care to know that out of the 362880 possible different Sudoku rows/columns, there are 4772 which have equal X-sum and sandwich sums; and among those, just 24 have equal X-sums from both ends and sandwich sums. Also, the sight of nine nested for() loops is truly an accursed one, and I am going to have nightmares about this. But still - _it's for Sudoku_ .....

[@sammiddleton7663]

It seems that you've double-counted the rows with equal X-sums from both ends by considering the reverse order of a row to be distinct (e.g. 3, 4, 1, 8, 9, 7, 6, 5, 2 is just 2, 6, 5, 7, 9, 8, 1, 4, 3 backwards). It's also really easy to do in Python with permutations() from the itertools package: from itertools import permutations # functions for getting the sums def left_xsum(row): return sum(row[:row[0]]) def right_xsum(row): return sum(row[-row[-1]:]) def sandwich_sum(row): i1, i9 = row.index(1), row.index(9) il, ir = sorted((i1, i9)) return sum(row[il+1:ir]) # list comprehensions make things really easy xSandwiches_one_side = [row for row in permutations(range(1,10)) if left_xsum(row) == sandwich_sum(row)] xSandwiches_two_side = [row for row in xSandwiches_one_side if (left_xsum(row) == right_xsum(row)) and (row[0] < row[-1])]

[@bluerizlagirl]

@@sammiddleton7663 You have to treat them as distinct; because once you have used a combo one way round, it forces the direction of the others.

[@sammiddleton7663]

@@bluerizlagirl then why don't you claim that there are 9520 rows where at least one x-sum is equal to the sandwich sum?

[@Playmaker6174]

As a "decent" setter, I was at one point thinking about some ideas for a puzzle with the same "double duty clues" concept, and when I saw this puzzle on LMG I was totally bedazzled because not only it looks so minimal but also it's all ambiguous clues (!). I kept shaking my head throughout the solve and when I finished it, I talked to myself "man oh man, what if Simon was actually thinking about giving this one a go as well, he would be so shocked just like I was here". I'll say this again: take a bow Emre, wonderful and staggering construction with juicy logics all over the place 🙇

[@user-oj2xx1rk7d]

"15 sandwiches, I think they grow on trees" another one for the Simon Out Of Context compilation

[@crashtextdummie]

I am frequently in awe with setters featured on this channel, but rarely as much as this. An absolute masterpiece. An a pleasure to watch Simon solve it.

[@SnowTheJamMan]

I thought this was an April fools joke puzzle when i saw it on LMD... wow i'm very excited to watch this

[@Sam_on_YouTube]

That may be the smallest amount of information I've ever seen on a puzzle with a unique solution.

[@spitgorge2021]

well, there was the totally empty grid!

[@Sam_on_YouTube]

@@spitgorge2021 The totally empty grid had a LOT of information in the instructions.

[@afrayedknot81]

An easier way to see the break-in (imo) is to figure out that 8 cannot be on a ‘?’-adjacent cell (min x sum is 36 when x=8), and therefore there’s a 189 triple in row 1. Since it must be a non zero sum, 8 must be in the middle

[@roybatterham5002]

That was my starting point also, to recognize that the three numbers that couldn’t be adjacent to a question mark were 1, 8 and 9

[@sanabas1]

Same for me. At least after the initial 'wtf?!?!' moment upon opening the puzzle. The rest is also a little easier if you figure out that 1 & 9 can not both be in the same x-sum, as that would make the sandwich clue at least 10 less than the x-sum clue, rather than equal. So @22:30, the minimum for c8 is 689 + 234 = 32, with a sum of 3 outside the sandwich, and there's already a 6 outside. Fantastic puzzle.

[@thefallenarm589]

Found another easy way to demonstrate it : the two X-sum clues must be 2 and 3 (because a 4 would lead to a 2-digit number in the sandwich), so the X-sums on row 1 include 5 digits. The minimum sum for 5 digits on a row is 15, so the only available digits for that sandwich is 8.

[@jdyerjdyer]

Don't know if he spots it later in the video, but after 35 minutes he hasn't seen a key piece of logic I used. The X-Sums cannot "eat" an entire sandwich sum. If it did, then the sandwich sum and x-sum wouldn't add up to the same total as it would be at minimum 1 more in the X-Sum. This helps rule down the Xs many times and in a few instances forces the placements of 1s and 9s.

[@mxspokes]

@@jdyerjdyer He does figure it out later on in the video

[@ShakalDraconis]

The idea of 'using up clues' is actually really useful in puzzles like this, where you're trying to figure out where you should be looking next. It would be useful in the software if you could click on a clue and mark it somehow, so you can more easily see what clues still might have logic to give and which you no longer need to keep looking back at.

[@robert-skibelo]

I suggested that six months ago but suggestions made here for improving the software don't ever seem to get read.

[@Clocksmith-s9w]

@@robert-skibelo Nah, they get read. It's just hard for Sven to code that in without breaking the checking feature.

[@celestia7411]

every now and then a puzzle comes along that completely challenges everything that I thought could be possible in a sudoku; this is definitely one of those puzzles. what an incredible construction

[@ChrisRemo]

I laughed out loud when I loaded this puzzle. Are you kidding!? Looking forward to this one.

[@markbennet9058]

This is yet another insanely elegant discovery - no digits and nine question-marks sets a challenge to constructors ... and the constraints here actually work interestingly together. The next miracle may well be truly brutal.

[@JayBea]

I solved this in just over 2 hours, which is *amazing* for me. By far the puzzle with the longest "Simon Solve" which I was able to do on my own without reference to the video. I loved it, thank you.

[@cluso9985]

Amazingly complicated. Simon, I am amazed you solved this. Emre, thanks for an fantastic puzzle. I couldn’t believe this could be solvable. I watched Simon solving r1 and c6 first. Then I had a go at c7, c6 and c2 but I got a different solution as I skipped forward to check what Simon had. After correcting my solution, and watching a little further in, I was then able to complete the puzzle. Extremely enjoyable. Long, yes, but we’ll worth the watch and my attempts.

[@wazzzuuupkiwi]

Great solve, jsut in case you ever need this technique again, i found it easier to think like this: take an X-sum digit, colour the corresponding number of cells in the row/column; If the sandwich overlaps with the Xsum then the Xsum digit plus one of the 'crusts' of the sandwich, plus any digits in between, their sum needs to be matched by uncoloured cells in that row/column and still surrounded by the other 'crust'. for example the Xsum of 7 you colour 7 cells, 2 left, one is crust so one uncouloured cell to match the sum of at least 7 and a curst digit. the only way to do this is 7+1=8. for Xsum 6 you have 2 cells to match 6+?+1 or 6+?+9, and the max for 2 cells w/ no 9 is 15... In this puzzle I used this on the 7 xsum and even though this is ambiguous which column it is, it still limits the 6 column to not have a 9 in the bottom row or a 1 higher than the 3rd row, and 6+1+anytthing is at least 9 and so requires 2 cells and would push the crust 9 to the bottom row where the 7 column already has it, so the only option is 6+9=7+8, placing an 8 in box 9 and forcing column 6 to be the 7xsum. That said, this logic was essentially all I managed before getting stuck and watching a pro like you solve it :P EDIT/ I went back after watching you do what I had done so far, and before the video caught up I spotted a pencilmark that could be excluded and that meant that one of the sandwiched was bumped into a larger cell size minimum, that then led basicallto the entire puzzle, this is truely the hardest puzzle from this channel I've ever solved! and all on my own, jippie! 134mins well spent :D

[@ascensionblade]

I derived the same logic. It's much easier to think about the logic of this puzzle as "the X numbers up to the first crust = the numbers after the Xth up to and excluding the second crust" (as you say)

[@kana2112]

Simon: "Do Have a go." Me: "uh, no." Lol.

[@pandorah_]

This puzzle is absolutely brilliant. One of my very favourites ever featured. Thanks so much for bringing it to our attention!

[@ralfrussel1950]

25:44 The little Mark inside Simon got him 😃

[@pii-chan8804]

I love it when you focus so hard on the Logic (tm) that you not only miss doing sudoku but are slightly miffed when you finish WITH sudoku :P Keep it Simon, as entertaining as always!

[@Swisswavey]

I have no idea how to start this one but let's give it a go. I'm gonna get cracking!...

[@Jonas.Nilsson]

How did it go? 😁

[@Swisswavey]

@@Jonas.Nilsson I got the top row (mostly) pretty quickly, the rest is proving more problematic! And the football is getting in the way a bit

[@Swisswavey]

@@Jonas.Nilsson you'll be happy to know I finished it. Stupidly I paused the timer to watch the footy and forgot to restart it. The timer said 40 minutes but you can probably triple that.

[@Jonas.Nilsson]

@@Swisswavey good job!!

[@JPgreekgaming]

Usually no matter how hard a puzzle seems ill have a go at it first and then watch the solve... this is the first time that i look at a grid and im like "nope" lol, better get some crisps, sit back and enjoy the show!

[@sjm6280]

After some time watching this channel, I feared new puzzles may at some point become "more of the same", but so many brilliant ideas keep appearing This one was amazing and it seems care was taken to have every possible digit next to a ? clue appearing somewhere in the perfectly interwoven finished solution Simon proceeded sometimes slowly (for instance, with column 8) but always steadily towards the end: fenomenal setters and fenomenal solver, what else may you ask for?

[@Coyotek4]

There is simply no limit to the brilliancy at this site, is there? This is a simply astounding puzzle ... and I'm astounded that I was able to get through this one in under an hour (52:20 in total). I absolutely LOVED solving this one!

[@Kinada]

This took me quite a while but I'm not unhappy with spending a few hours on it while watching videos about music. Great puzzle.

[@DirkieB]

Simon 1:03:00 : "One of these *is* true" Also Simon: Marks them with red, the universal colour for truth

[@Raven-Creations]

This was insane. I'm glad Emre sets puzzles, because otherwise he'd be a serial killer for sure. One can only speculate what rage against humanity triggered the creation of this puzzle. It was really tough, and unlike other miracles, it didn't get much easier as the solve progressed. Nevertheless, I was thoroughly gripped by it. I could have thrown in the towel a couple of times, but having got so far, there was no way I was going to let it beat me. There was some very nice logic built into it, the discovery of which helped top up the dopamine, and kept my interest alive. Your deliberations at the start could have been quicker had you considered the 8th triangular number, and compared that with the maximum sandwich sum. This rules 8 out of any question-marked cell and gave me a quick digit, which pleased me greatly, considering how inauspicious the initial grid looked. R1 then almost solved itself, but any thoughts that it might turn out to be easy were quickly dispelled. You'd have seen things easier in C7 if you'd removed 2 & 5 from R3C8 after resolving R1, and corner-marked 2 & 5 into box 6 C8. That would have made you realise that there couldn't be a 2 in the 5 x-sum, which simplified a lot of the logic. In choosing where to look next, I think you were unlucky and opted for the wrong clues, which meant your path was harder. After C7, I worked on box 7, and where you switched to the top, I worked on R9C1, which was restricted to just 4 or 5 (it couldn't be 6 or 7, as you discovered), and was relatively easy to resolve. This made the C2 clue somewhat easier. I'm glad you spotted the logic on R6 ruling out the contiguous runs; I particularly liked that. You missed that 3 in C6 had to be in box 5, which would have meant you could place the 3 once you had the aligning 23 pair in box 4 and the 39 pair in box 6. I know, I know, you'd have had to do sudoku for that, and you don't do sudoku these days.

[@DubbleBluff]

That was the funniest “do have a go” since the OG miracle sudoku 😅

[@EmilyGamerGirl]

28:12 Importantly, you've just put the entire 4-cell sandwich INSIDE the 6-cell X-sums! That implies that the 4 cells add to X, and those 4 cells plus 2 more cells ALSO adds to X, thus requiring you place two 0's in the grid! That works not only to eliminate 9 (as the 1 clash does), but ALSO eliminate 1. Also that requires none of the logic done on the 7 column, and could have been done the instant you got the 6.

[@gombospatrik]

I've done a miracle Sudoku. Thanks Simon and Mark for teaching, this is a result of a progress that is pretty much fun for me, thanks to you.

[@emilywilliams3237]

You wanted to know whether we solved the puzzle - NO. Did I have a go? NO. Did I enjoy the video? YES. Thanks - your "Bobbins, bobbins, Bobbins!" along sometime around my second serving of popcorn made me laugh out loud, as well as your chortle of joy when you finished the solve. So fun and entertaining.

[@josephsugarmann6765]

Phistomephel is definitely making a hard-mode version of this puzzle

[@nedb147]

One of the most beautiful break-ins, infinitely satisfying

[@David_K_Booth]

What an extraordinary puzzle! Emre Kolotoglu, my congratulations. And plaudits too for Simon for his solve.

[@keithlewis7205]

Fascinating! Forget the length, the puzzle could not have been more enjoyable!

[@lioneljdmello1601]

One of the most gratifying puzzles on CTC. Simon (and I) had to work very hard for each deduction.

[@HunterJE]

5:20 "The upper boundary for every question mark clue is 35" If you think about the interactions of the two clue types a clue cannot ever be 35 - a 35 sandwich puts a 1 or a 9 in the X position for its row or column, which would result in an X-sums clue of either 1 (a 1 counting only itself) or 45 (a 9 counting all 9 digits)

[@bluerizlagirl]

Yes, indeed. You can never have more than 7 digits in the X-sum, otherwise it would necessarily include 1 or 9; and then there would be no way it could possibly match the sandwich sum. This makes the maximum dual sum 28; the 7 as "X" and the 1 crust of the sandwich are balanced by an 8 in the sandwich but not the X-sum, and the 9 is not contributing to either total. There are 240 ways to make this, consisting of 7-1-(23456 all possible ways)-8-9 and all their mirror images.

[@a09nton]

It took 78 minutes for me to solve this brilliant puzzle exactly the same way as Simon!

[@inspiringsand123]

Rules: 02:39 Let's Get Cracking: 04:22 Simon's time: 1h21m41s Puzzle Solved: 1:26:03 What about this video's Top Tier Simarkisms?! The Secret: 5x (01:17, 04:50, 04:52, 04:57, 09:17) Bobbins: 3x (44:09, 44:09, 44:09) And how about this video's Simarkisms?! Hang On: 11x (11:01, 16:51, 19:36, 48:14, 51:45, 55:21, 55:21, 55:21, 55:21, 1:12:19, 1:12:32) In Fact: 11x (00:31, 06:55, 08:30, 19:25, 20:16, 20:16, 22:00, 32:19, 54:08, 1:04:45, 1:19:47) Wow: 11x (26:45, 33:31, 33:31, 33:31, 38:43, 40:47, 40:49, 49:49, 1:04:12, 1:15:36, 1:18:12) Ah: 11x (07:41, 08:36, 10:34, 16:47, 18:13, 47:03, 51:45, 56:15, 56:23, 1:16:13, 1:20:30) Sorry: 6x (12:37, 16:33, 19:48, 30:39, 39:30, 1:13:00) By Sudoku: 6x (48:18, 48:24, 50:35, 57:25, 1:18:02, 1:24:10) Beautiful: 5x (10:23, 17:11, 35:00, 51:31, 1:21:04) Obviously: 5x (05:05, 07:49, 12:24, 32:52, 1:22:36) Ridiculous: 4x (04:10, 33:12, 1:26:20, 1:26:20) Good Grief: 3x (23:06, 33:31, 1:20:14) The Answer is: 3x (09:31, 14:58, 15:16) Clever: 3x (16:37, 23:06, 1:27:07) I Have no Clue: 3x (04:26, 51:45, 1:26:41) First Digit: 3x (02:51, 06:26, 11:28) Nonsense: 2x (12:35, 1:08:26) Bingo: 2x (1:20:12, 1:20:12) Break the Puzzle: 2x (24:35, 34:36) Going Mad: 2x (30:30, 1:14:31) I've Got It!: 2x (1:04:31, 1:04:31) What Does This Mean?: 2x (13:44, 15:57) That's Huge: 2x (46:20, 46:20) Missing Something: 1x (1:19:40) Brilliant: 1x (34:54) Incredible: 1x (1:27:00) Extraordinary: 1x (02:36) Take a Bow: 1x (1:26:37) Shouting: 1x (01:26) Of All Things: 1x (57:25) Surely: 1x (30:22) Disappointing: 1x (20:30) QED: 1x (33:11) Whoopsie: 1x (1:04:59) Progress: 1x (25:49) Have a Think: 1x (36:12) Thingy Thing: 1x (05:43) Nature: 1x (1:17:34) Pencil Mark/mark: 1x (1:16:53) Most popular number(>9), digit and colour this video: Ten (18 mentions) Nine (193 mentions) Yellow (7 mentions) Antithesis Battles: High (8) - Low (5) Even (3) - Odd (1) Higher (5) - Lower (3) Outside (10) - Inside (0) FAQ: Q1: You missed something! A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn! Q2: Can you do this for another channel? A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!

[@calluminglis7837]

Bobbins bobbins bobbins

[@PhaythGaming]

I really think Simon saying "ah, look here" Is worth recording.

[@shangaiguarisnaque9277]

@@calluminglis7837 I was really hoping to hear 3 bobbins

[@longwaytotipperary]

I'm going to need more popcorn...🍿🍿🍿🍿

[@primeweasel3977]

Such a spectacular solve! I always love to see what Simon did, having solved it myself a few days ago on LogicMasters.

[@akaEDL]

14:38 for me. I mean 14 minutes of watching at the grid without any decent ideas before deciding "Nah, i'll better just watch Simon this time"

[@TaranAttavar]

“Is the sandwich a big mac or hamburger?” 🤣

[@happy8318]

1 hour, 41 minutes and 56 seconds was what it took me to solve this 'Ultimate Miracle' sudoku... never in my life have i done a sudoku in this manner and i must say its incredibly refreshing! Lots of mental calculations from 1 - 9!! Thank you for sharing this brain teaser with us Simon!

[@andrewnelson2525]

I got the top row fairly quickly but it was a three hour slog after that. As usual with one of these difficult unique rule set puzzles, I kept thinking after getting two thirds of the way through that if I'd made some early erroneous assumption I was dead. It's hard to have confidence when all the logic is new. And every time Simon or Mark says "wow that was not easy to see," my response is always "you're telling me buster!"

[@oneofthenorth]

Absolutely jaw dropping. I genuinely thought this was the most insane thing I’ve ever seen, and then Simon solved it…… there is no way on earth I’d have been able to finish this one. Hats off to you, and to Emre for such clever setting! Would I be crazy suggesting Simon’s hero Phistomafel might even find this a brilliant puzzle?

[@andersosterholm2538]

Thank you Emre and Simon for making this video a reality. It was very enjoyable to watch. 😀

[@noahgolan603]

solved it in an hour and 42 minutes - such an amazing puzzle, it keeps feeling like we don't have enough information, and yet the 1s and the 9s push through. Also first time I'm even close to Simon in the really hard puzzles - so this is a proud moment

[@andykillsu]

Videos over an hour automatically get a thumbs up from me!

[@MarushiaDark316]

Well done, Simon. This was another amazing solve. I don't think I could have even started this one, much less finished.

[@markp7262]

1:03:19 finish. Very tricky, with some beautiful logic. I actually started by identifying the ranges for every first digit at the question marks. Once you hit 5, the upper bounds become constrained by the sandwich part of the clue. Fun! 2 (3-11) 3 (6-20) 4 (10-28) 5 (15-30) 6 (21-29) 7 (28)

[@AdventCloudStrife]

I'm not sure if Simon will realize it, but I'm typing it now just in case. Because of the rules of the puzzle, the x-sum CANNOT possibly include the entirety of the innards of the sandwich. It's pretty obvious why; the inside of the sandwich sums to the number outside the grid, and the x-sum cannot start with a 1 or 9. So, if our x-sum includes the entirety of the innards of the sandwich, then it will add up numbers that sum to the clue PLUS more, breaking the puzzle. Therefor, in column 8, once we know the sandwich innards must be 4 cells long, we know for sure that there must be a 1 or 9 in r8 or r9 in that column, because if it was any higher up the grid (i.e. r7 or below), then the x-sum of 6 would include the entirety of the innards. Now to see Simon to see that 5 seconds after clicking "comment"

[@HunterJE]

Started writing a comment to this effect then refreshed comments and saw yours and was glad I could delete mine because you'd put it so much more clearly than I was managing to XD

[@CaptianKatsura]

You're in luck, it took him an hour to see that, not the 5 seconds we expeccted.

[@KalOrtPor]

I'm surprised that wasn't spotted immediately also, a subset of a group is clearly going to be less than the group. A lot of eliminations I got right away was seeing when the sandwich clue couldn't ever be the cell immediately outside the x-sums. I also used the x-sums amounts outside the sandwich to figure how much needed to be "made up" in the sandwich.

[@spreekstem]

I always love popcorn episodes. 😁

[@ocaly]

these are the kind of videos I could fall asleep to. and I don't mean that negatively.

[@willdavis2053]

That was quite a puzzle to say the very least. Kudos Emre and great solve Simon!

[@hisham_hm]

"When I say huge I mean modestly interesting" - classic Simon

[@TheClawNinja]

13 seconds into the video, and I'm already ashamed at myself for doubting you could solve this puzzle. I've also already succumbed to the fact that I'm not even going to open it and try. Let's see how this monster goes down!

[@mathpesto]

I am absolutely blown away.

[@jmcginty96]

“Oh bobbins, bobbins, BOBbins!” Going to have to put a parental warning on this one! Every one of these 90 minutes is worth watching. Amazing work!!

[@carstenkruse8527]

That may be the greatest setting ever. Emre IS the greateast. Nice job Simon on solving it

[@davidhughes7174]

simply stunning, puzzle setting, solving. WOW. thank you Simon.

[@ericpraline1302]

What sort of a twisted genius is Emre Kolotoglu? I couldn't give up on this, even if I should have done to save my sanity. Some of the logic here is incredible. Simon's brilliant solve is so incisive that it made me wonder how I could have taken so long to spot various things.

[@NijiRanger]

What an absolutely extraordinary and bonkers puzzle. I showed the blank grid to my family and they just laughed at me.

[@SolinoOruki]

I'm a bit behind on watching these. But this is perhaps one of the (if not the) most elegant Sudoku I've seen. Wow. So satisfying to watch it being solved.

[@HeroOfRhyme]

This is one of my favourit puzzles you have ever done

[@tristan4530]

Got it in 52:15. Brilliant Puzzle and very tough. At First I wasn‘t sure if I am able to solve this masterpeace but I am glad I did!

[@ocaly]

did you enjoy it? because I wanna give this a go but seeing the video length, and the fact that I am as fast as simon if not slower than him, really makes me doubt if this puzzle is meant to be solved for people like me. was solving it worth it?

[@jeremylarson5152]

@@ocaly I'm usually about twice as slow as Simon or Mark and I managed this one in under an hour. It's chalk full of logic that I found somehow intuitive but hard to explain without writing out strings of numbers that span the grid (which is what I think slowed Simon down). Give it a go if you haven't already watched the video.

[@ocaly]

@@jeremylarson5152 Good to know, and no, I haven't watched the video and will try solving it because of what you said. thank you very much!

[@indigorune]

Well it took me about 1hr 30min spread out over two evenings, but I am proud to say I managed to logically solve this one! Very clever ruleset.

[@omarlabbad8799]

in the begging of the puzzle in minute 12, instead of trying 678 individually. you can see that 8 works the same as 9 in the first clue position as it takes 8 cells and the minimal sum for 8 cells is 45-9=36 which is higher than the maximum sum for a sandwich clue.

[@downvote-skribbl6932]

Beautiful puzzle, and well solved! I did not try, and I have concluded I would not have managed it all w/o help. But there were a few places I felt like a winner (when seeing something you ignored). Like: 1:15:15 - There is a 6 in R4C1 --> There is an 8 in R4C7. 1:25:15 - Writes in an 8 in R4C7 But all in all (as usual): Fun video and a good way to spend the evening!

[@4ty2]

Just solved it, that was a really fun ruleset with nice and unexpected interactions

[@shteevuk]

This puzzle is insane. What great design!!

[@lorettawhelpton3831]

Bravo! Emre and Simon, amazing puzzle and solve.

[@th.nd.r]

Brilliant setting and solving as always! Way too much for me to get my head around but the fact that this solves is incredible

[@anthonybailey5655]

So good. The "I will only tell you _where_ the clues are not _what_ they are" presentation reminded me of "Tapa (Unique Clues)" by Tapio Saakinen published at GM Puzzles on 16 Jan 2015 - a lovely pencil puzzle.

[@SilverKiMak]

Dear Simon, Pleeeeease Do Sudoku!! At least 5 times in this puzzle alone you just didn't and made life harder for you and shoutier-at-the-screen for us :-)

[@1a2s3d6a9s5d]

Great solve and fantastic setting!

[@selenasilverstep7981]

What an absolute miracle! Overlap math, non-overlap-sum-to-45 math, column 6/7/8 resolved by the top 3 digits, 4/5/6 triple in column 1, sandwich length tricks. Everything. Finished in just under an hour, probably because I was thinking in overlap mode from the start. Simon wasn't.

[@pengchengwu447]

Incredbly elegant design!

[@HonkeyKongLive]

We know that the minimum number of digits in a classic sudoku for it to solve is 17, but now I'm wondering what the minimum number of clues and clue elements. Like what is the barest possible puzzle that still solves. This has to be near the limit.

[@HunterJE]

I mean it's tough because unless you want to close it off to an arbitrarily chosen set of existing variant types, "clues and clue elements" becomes hard to define in a useful way. Like for an ab absudum example, I could arbitrarily define a clue type the "fnord line," which is defined as "a line on which the digits 341897562783915461294387512476982563149342587982563985167452186736174932975436218 must occur in that order", then draw a fnord line starting from the top left and spiraling clockwise to the center of the grid, and voila! A trivial "one clue puzzle!" And while that's obviously not in the spirit of the question it'd be hard to draw a nonarbitrary line on what is...

[@z-beeblebrox]

​@@HunterJE We can ad absurdum one better. We can create a rule called the "Complete Solve" rule, wherein you must place all the digits in the grid in a specific order defined by the rule. With this rule, you can set a grid with zero clues, as the rule itself is the solution. Actually...that would make for a pretty decent April Fools puzzle. BUT! Ambiguous clues are a different thing. By some definition they are less than a normal clue, as you need at least one extra deductive step before using them. So assuming it's impossible(?) to have a zero clue ruleset that isn't trivial (ie the solution is imprinted into the rule, which I suspect is QED), we can probably still say there's a near endless continuum of ambiguous clues that are possible between zero and one, in increasing levels of ambiguity. So potentially, the answer to "How few clues can you have, given a sudoku with an unbounded set of non-trivial rules?" is an infinitesimally small fractional real number larger than zero. But we won't know that number (or at least its limit) unless the measure of ambiguity is well defined.

[@lucy101]

Yeah this is close. I made one with just three two-digit quad clues, but it also has global nonconsecutive and partial anti-ratio and anti-XV constraints

[@HunterJE]

@@z-beeblebrox Ooh this gives me an idea for pushing the possible bounds of what counts as "variant sudoku" - some completely non-sudoku mathematic puzzle that results in a numerical string as its result, which is then entered in the grid based on some method in the rules, and when that's done it's either a completed or trivially solvable sudoku

[@weissesauge]

A really brilliant puzzle. Congratulations to Simon for solving it!

[@DucciVinci]

Most fun puzzle I've solved so far together with that one about a year ago which had 26 cages and the only restriction that their sums have to all be different. :-) 66 minutes.

[@maurobraunstein9497]

I did solve it, and I thought it was not as hard as you did, apparently. But I spotted the overlap trick right away, which you took a while to get. I never really thought about the actual sum of the sandwiches or X-sums, since the only part that's relevant is the part that's non-overlapping. I did the puzzle in pretty much the same order as you did. I'm not sure what my time was, since I solved it over the course of the afternoon and evening rather than in one sitting, but I think it was actually comparable to yours as opposed to my usual range of around three times as long, which is why I think it wasn't as hard as you thought it was. Great puzzle as always, though, and it was a great solve to watch as well!

[@__-nj5oe]

Love your videos so much. Can you please create a playlist of your longest videos? Maybe all the videos that are 1 hour+? It's really difficult to find them.

[@CauchyIntegralFormula]

74'15". I almost wasn't gonna start this one, until I spotted a break-in along the top row

[@TheTruth-xp2of]

Very proud of my time. Went just over 30 minutes before accepting this was beyond me.

[@psyckwhoever4197]

It's such a relief to watch these videos, when you managed to do the puzzles before 😅

[@chitraagarwal8259]

Such a genius construction! And amazing solve....didnt even have the courage to try attempting this at the beginning so was watching and solving along but half way through i got the hang of it and finished before Simon The 6 in r4c1 could have disambiguated the x sum in row 6 much more quickly..

[@TsieLeMoswang]

wow, a few question marks around the grid is all you need for a unique solve. Crazy

[@godfoca]

My reasoning for c8 was that 1 _or_ 9 has to go in box 9. If they were both in boxes 3/6, then the entire contents of the sandwich would be part of the x-sum, which cannot happen. Now, whatever space remains between the end of the x-sum and the bottom "bread" must sum to the same number than you get from r1c8 to the top "bread". That means the bottom bread cannot be on r7, since then the difference would be 0. So the bottom bread has to be in r8 or r9. If it's in r8, then the sum from r1c8 to the top bread has to add up to a single digit lower than 9 (because 9 is outside the sandwich), which cannot happen: * r2c8 cannot be 1 (because there's already a 1 in r2) * If r3c8 was a 1, then the lowest you could make that sum is 9 (with r2c8 being a 2), but that doesn't work because a) 2 is already placed in box 3, and b) the sum has to be lower than 9. So the sandwich's bottom bread has to be on r9c8, and since r9 already has a 9 in it, the bottom bread has to be a 1, and the top bread has to be a 9. But that means that the sum of r7c8 and r8c8 have to add up to 6 + 9 + whatever is between 6 and 9 in column 8. The only way to make that happen is if 9 is in r2c8, and r7r8c8 are 8 and 7 (so you get 6+9 = 15 = 8+7). And because there's an 8 in row 8, that places the 8 in r7c8 and the 7 in r8c8. One thing I love about this channel is that I started watching the videos about a month ago, and there's *no way* I would've been able to make this kind of reasonings back before I started watching Simon and Mark

[@masaakunokouchi]

The fact the Simon never seems to grasp that the sandwich filling can not be entirely in the x sum... had me yelling at my screen... constant

[@SjorsHoukes]

I got to 21:23 by myself this time, thanks to the lessons from Simon’s previous videos. Still takes a while for to be able to do a whole puzzle like this, but I’ll take it!

[@veggiet2009]

I was looking away for 30 seconds and then I looked at the grid with the question marks and I ... I .... I .......

[@joelstevens5670]

That was a remarkably efficient solve of a monstrously difficult puzzle Simon (I spotted just the one possible assumption but that was easily resolved so no harm done) and an equally clean looking grid at the end as well. Brilliantly done and unbelievable setting from Emre (the overlap logic was something else)! Thanks both and Emre I hope you will forgive my frustration with the lack of clues at the end (columns 1 and 2 had me going round in circles for ages, though I did get there eventually)!

[@Rubrickety]

"A zero sandwich clue is impossible, but a zero X-sum clue is _not_ possible." Ah, the subtle distinctions in British English... 😉

[@PathOfShrines]

What an idea! I loved solving this; such an original concept. 1:04:57 for me.

[@Gonzalo_Garcia_]

54:30 for me. I can’t believe I just solved this!! How does it even have a unique solution? How on earth do you build such a puzzle as this one?? I’m completely blown away by this puzzle, I don’t think I’ve ever seen anything quite like it.

[@antoniobarros-limon2637]

What an amazing solve and puzzle.

[@davidlefevre7]

Simon : sure come home, you're in invited ! Also Simon : let me disapear for 1h30 while i play sudoku.

[@gabrielbenamy5270]

The interesting thing about the 6 clue is that -- once you've solved that the 7 clue must have a 1 in row 2 and a 9 in row 9 -- lies in the exclusionary zones, which is digits that are in the X-Sum but not inside the sandwich, which must equal digits that are in the sandwich but not in the X-Sum. Since it's not possible for both breads to be inside the sandwich (as the sandwich sum would therefore be less than the X-Sum) and it's not possible for both breads to be outside the sandwich (as that would leave cell 8 being a 27 or higher), at least one piece of bread must be inside. Now, if it was a 1 inside, then the earliest it can be is in row 3, which means the exclusionary zone must sum to at least 10 (6 + [minimum of 3 to have no repeats in the box or column] + 1). It also means the exclusionary zone for the sandwich must be at least 10. But since 9 can't go in the bottom row (since that's where it goes for the 7 clue), putting a 9 in row 8 means that row 7 must contain a minimum of 10, which is impossible. Therefore, you know that the X-Sum must include a 9, rather than a 1. But where can the 9 go? Because the exclusionary zone within the X-Sum must now be a MINIMUM of 6 + 9, therefore the exclusionary zone within the sandwich must also be 15, in at most two cells (since the 1 must go outside the X-Sum), which can only be done with 7 + 8, which is also the sandwich EZ's maximum. Therefore, 9 is in row 2, 1 is in row 9, and you have a 78 pair outside the X-Sum, which forces R1C6 to be a 7, since you can't repeat the 8 in box 9. (Which, of course also resolves the placement of the 78 pair, since you have an 8 in row 8 already).

[@gregind01]

Wow, wow and wow!!! What an amazing solve Simon!

[@michaelhoffman2011]

Wow. I solved it. An amazing puzzled. Surprisingly I got the top row pretty quickly.. and the rest just took a very long time