Can Your Brain See This Simple Trick?

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** TODAY'S PUZZLE **
Yet another extraordinary sudoku today, this time from the devious brain of Sumanta Mukherjee. At first glance, this puzzle seems utterly impossible and yet there is a simple trick that cracks it.
You can try it at the link below:
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Rules:
Normal sudoku rules apply. The marked diagonal contains 9 different digits in ascending or descending order. Along the thermometer, digits must increase from the bulb end. The sum of the digits in every possible straight triomino (orthogonal or diagonal) is divisible by 3.
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[@rikarddesilva3226]

Sumanta has created one of the most approachable puzzles I have ever seen, with no digits and such a minimal ruleset. Phenomenal!

[@n122333]

00:27:54 This is the first 0 digit sudoku I've solved on my own, before watching the video, now to see how much faster he came to the conclusions than me... EDIT: wow, we didn't get to this the same way at all, there's more than one pathway to the same solution! How cool!

[@nwdreamer]

Agreed! The middle 5 was easy, then it was just a matter of coloring everything with diagonal patterns. The thermometer simply told you which way the diagonal goes! 14:52 here.

[@G4M1L]

@@n122333 Interesting, I also just solved it (and I think my first solve ever using less time than the video length) before watching, and now I'm curious about Simon's approach. I basically did a full colouring on mod3-values, then did the thermo with the given colours and the additional rule about the diagonal being 1-9 in ascending or descending order, and then filled in all the vallue triples, colour by colour. Felt a lot like the recent modular/unimodular puzzle. P.S.:Yes, I also saw that the central cell had to be 5 but did not really bother, because I felt that this was only relevant for the disambiguation to come.

[@psiphiorg]

I got it in 3:56! The trick is super elegant and really causes the puzzle to collapse. Knowing that the negative diagonal had to be a modular line by its very nature of consecutive digits, I knew that the positive diagonal had to be unimodular (to use the term from the other puzzle). That allowed me to color the entire grid with positive-diagonal lines. The thermo disambiguated which color was which modularity, which filled in the negative diagonal. That gave me the 147, 258, and 369 throughout the grid, and everything just fell apart.

[@missingdeck9999]

Really nice deduction based on prior knowledge:-)

[@raswartz]

Nice comparison.

[@adamkamp8929]

Yeah, once you have the one trick, the puzzle really disintegrates. Or, put another way, Simon spots the trick to the puzzle and completely ruins it in about 30 seconds.

[@missingdeck9999]

Interesting! The local mod 3 constraints will lead to the global mod 3 constraints we had a couple of days ago --- should probably be much easier to prove that the striping will result! Nice to see mod 3 constraints being featured:-)

[@Coldheart322]

I doubt many global mod-3 puzzles will be made, as it restricts the board to this stripped pattern, and once you know that the entire grid becomes restricted. You then need enough clues within each set to resolve the rest. The 7/8/9 length diagonal restriction used in the previous puzzle would almost enforce the same pattern, but in box 2, 4, 6, and 8 the 'outer edge' would not be forced to follow the pattern as it could shift 1.

[@inspiringsand123]

Rules: 01:14 Let's Get Cracking: 05:11 Simon's time: 18m58s Puzzle Solved: 24:09 And how about this video's Simarkisms?! By Sudoku: 5x (10:37, 22:28, 23:12, 23:15, 23:48) In Fact: 4x (00:33, 01:11, 10:01, 16:47) Wow: 4x (24:11, 24:12, 24:12, 24:12) Brilliant: 3x (03:36, 03:40, 24:53) Ah: 3x (01:21, 10:20, 19:50) Beautiful: 2x (13:08, 23:32) Obviously: 2x (14:13, 18:26) Aplomb: 1x (23:24) What on Earth: 1x (13:43) Goodness: 1x (23:05) Sorry: 1x (18:58) The Answer is: 1x (07:00) Clever: 1x (23:39) Going Mad: 1x (13:14) Take a Bow: 1x (24:48) Approachable: 1x (04:05) Hang On: 1x (15:15) Pregnant pause: 1x (21:25) Panache: 1x (23:32) Cake!: 1x (03:44) Most popular number(>9), digit and colour this video: Ten, Thirteen (4 mentions) Three (83 mentions) Yellow (20 mentions) Antithesis Battles: Column (2) - Row (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!

[@JohnSmith-wx6rw]

Great keeping of stats, but one stat you have missed is how times Simon has to retype a solved digit.

[@samhurst7658]

@@JohnSmith-wx6rw yes I need to see that

[@kslingsby]

Wow! First time ever I've solved a puzzle in less than the video length!

[@MisterM2402]

Back in the day, if Simon opened a puzzle like this live on camera he'd be dumbfounded and incredulous. Now amazing constructions like this are so par for the course it's more just a quick "haha anyway, let's get on and solve it".

[@riluna3695]

Funny to look back on that. "Okay Mark is 100% trolling me, I'm gonna do this for a second, get stuck, then go give him a stern phone call." Solves the entire thing and dubs it the Miracle Sudoku. Though at the same time I do wonder how many times Mark and Simon have _actually_ trolled each other with unsolvable or joke Sudokus, that we never see the recordings of. That would make a hilarious compilation video of its own if they kept any of them.

[@Alex_Meadows]

I sometimes imagine setters carefully excavating sudokus like this one out of the grid, a bit at a time, painstakingly revealing the clues. Well done Sumanta, it's an extraordinary puzzle! If we were in a golden age of sudoku a year or so ago we're surely in a diamond age now. And given that the explosion of astonishing puzzles coincides so neatly with the success of this channel, we surely have to give some of the credit to Mark and Simon, alongside the increasingly brilliant setters.

[@57thorns]

What we have seen is a whole lot of sudokus that are challenging without being brutally hard. Where the break in is actually manageable, without being obvious.

[@VJ-xc8ci]

The "all triominos divisible by 3" rule simply means that all rows and columns are "modular lines" (the cyclic coloring), the 1 to 9 negative diagonal tells that negative diagonals are modular lines as well with cyclic coloring (that is the positive diagonals are "unimodular lines" i.e. they have the same color). The 5 in the middle and the r4c6 must have the same modulo(color) so the latter is 8 on the thermo, followed by 9 on the thermo in r4c5, and this already defines which color is which modulo, this defines the direction of numbers on the negative diagonal. The rest is just clicking-typing exercise.... 1 minute fun (thinking), 1 minute coloring, 5:30 typing, 7:30 solve time here, it was a GAS :)

[@chitraagarwal8259]

Did it exactly this way.. but i took around 15 mins coz i took my time with the coloring :)

[@gregporter8325]

Fascinating puzzle. Also fascinating that you can use different variations on the logic and still solve the puzzle. I never saw the quasi-disjointed sets that Simon saw, but did quickly realize that digits of the same modulus could never be orthogonally connected (if 2 orthogonally connected cells were of the same modulus, all cells in that row or column would have to be of that same modulus which of course won't work), which quickly led to the striping.

[@AWanderingSwordsman]

Taking it one step further, the middle 5 is surrounded by 8 numbers. 6 of those numbers will be alternating to form 3 triominos with the 5 in the center and two will be repeating forming one triomino with 5 in the center. The horizontal and vertical lines can't repeat so it has to be one of the two diagonals and the puzzle tells us immediately that top left to bottom right is an alternating triomino instead of repeating leaving top right to bottom left to be the repeating line. Because horizontal and vertical alternate, all top right to bottom left diagonals must be repeating. That lets you very quickly solve the thermo and then the puzzle.

[@jkid1134]

@@AWanderingSwordsman a brilliant step further! the 3 6 and 9 must go opposite the 1 4 and 7 and then the 2 and 8 must be paired on the diagonal. very powerful. (Simon's disjoint grids immediately give 28 pairs which alongside the 46 pair from the diagonal also place the 28 pair on this diagonal quite willingly, even if he didn't see it, so I guess the diagonal is meant to be discovered, really)

[@jwolfe01234]

12:58 for me. I Goodliffed the thermo and the diagonals and then things just collapsed from there. It's basically the same logic as the puzzle the other day, which made it easier. I started coloring the puzzle, but then ended up with only 3 cells singled-colored and 2 cells multi-colored. Once you have a digit, you can just go boom, boom, boom, three away in any direction to get a digit from the same "group" (147,258,369). Instead of modulus, I thought in terms of -1, 0, +1, but it's the same thing.

[@willemm9356]

If you happen to know a bit of maths trivia, it all falls into place very easily: If three numbers sum to a multiple of three, they're either all different mod 3, or all the same mod 3. (So in any direction, you either get a repeating cycle of all remainders, or just one single remainder repeating)

[@darreljones8645]

One consequence of the "multiple of 3" rule is that any set of three digits in a line must either be all the same or all different modulus 3 - you CANNOT make it work if two are the same and the third one is different.

[@KestrelQ]

I always love the reaction when you are asked to open a puzzle live on stream xD

[@thalax]

@14:00 Alternately, you could have looked where to place the 2/8 pair in box five. Which has to go in bottom-left and upper-right corners by Sudoku. Since 2 can't go in the upper-right corner, due to the Thermo, 8 has to go there. Placing 9 in the end of the Thermo

[@bobblebardsley]

Absolutely beautiful, this one completely deserves the 'miracle' in its name. No givens (if you don't count the 5), brief and simple rules, completely collapses as soon as you've placed the first 2-3 digits. Very, very good.

[@ildusiks]

It’s really miracle, because I chose exactly the same colors 😁

[@PepperKoi]

15:39 for me, I think the solve being so similar to the puzzle from the other day really helped, though getting the initial logic to get to that point was fun

[@tegxi]

This is an incredible puzzle, and it makes a great introduction into variant sudokus! I realized the secret and got the colors only a bit slower than simon, but I took twice as long just because I have very little sudoku experience. It was incredibly satisfying to do! (I can complete very few of the sudokus featured on this channel)

[@LixLorn]

Accidentally had the video play until "ooh, and this diagonal means we can place a digit!", immediately paused the video before you could say what it was. Then solved the puzzle in fifteen minutes! VERY proud of myself. I broke in by pencil marking the thermometer, eating away at possibilities, and then going "box 5 row 4 contains a four or six, r4c6, and X. box 5 column 6 contains a four or six, r4c6, and Y. because four and six are two apart, X and Y have to be two apart!" and the only thermometer possibilities left were 9/7, at which point I could propagate the modulo patterns in all directions and trivialise the sudoku. VERY proud of myself, great fun to play, and great fun to watch!

[@ludomine7746]

Insane how it's almost identical (in pattern) to the puzzle you mentioned at the beginning. Even the rules seemed to relate somehow

[@Coyotek4]

3:02 ... definite GAS, if you know how to attack the sudoku. This doesn't take away from the sheer beauty, though. Nice puzzle!

[@Fogmeister]

Got it in 27:49 about 5 minutes after I spotted the trick and then coloured in the grid and blasted through all the numbers. Nice puzzle and a good intro puzzle for spotting those sort of meta restrictions that are implied by the rules. Liked it 👍🏻

[@notnotandrew]

8:39 for me - I just played the modular/unimodular sudoku a couple days ago which primed me though. This was really more a question of how quickly I filled in the grid, and how much time I wasted wanting it to look pretty.

[@christinemenard1412]

9:01 for me! After that unimodular thing, this one was pretty straight foreward!

[@nickatty462]

@@christinemenard1412 I beat Simon for the first time too (and, who knows, perhaps the last), but I too had done the unimodular one a few days ago and that definitely helped. I ended up colouring the entire grid before I started working on the numbers - which made it even more fun.

[@faddy91]

Yes. That puzzle was essentially the same solution in general. One of each set of 147, 258 and 369 need to appear exactly once in each row or colum in a box. And every box replicates the same pattern of those sets.

[@janerobson2297]

For the very first time I did this without even looking at the video in 22:49! I know this is slow but even 2 months ago I don't think I'd have been able to start this without a hint. Thank you so much for helping me to get cleverer!

[@Prosim757]

28:21 As a beginner, I had no idea what modulus was. Solved it using pencil marks, addition/division on all orthogonal triominos.

[@dmb-zw8nn]

Me too, had to do math in the centre square and propagate the sums from there

[@nicolasgarland9872]

I'va done the Modular Miracle Sudoku earlier today, it's helped a lot. The logic is very similar.

[@davidalderson]

The pattern follows the same idea as the modular miracle sudoku from the other day, having watched that was able to solve it in 06:42.

[@drlabos]

Pre pandemic me could never have solved this puzzle. I love how this channel has grown and we’ve all grown with it.

[@markp7262]

7:19 finish. The way I broke in (after placing the 5 in the center square) was to consider that the 5 would touch every number. This meant that it would have to have 2-5-8 in a row somewhere in box 5. If it were to be an orthogonal triomino, the it would require the entire row to be 2-5-8s, which clearly would not work. This means that the 2-5-8 must be a diagonal. Since the diagonal line is 4-5-6, then 2-5-8 is the other diagonal. The 8 has to be on the thermo, placing the 9 at the end of it. The start of the thermo, opposite 9, needs to be 1-4--7 (can't be 4-7, so is a 1). Continue solving from there.

[@kayangelus1]

8:09 First time I beat Simon. Once I figured out that I could use the triomino rules to color the entire grid (and finish coloring), the entire thing was just rapid fill-in-the-blanks.

[@felix_irgendwas]

6:14 for me One of the easier break ins in recent times, and once you find a pattern, it basically solves itself :D

[@sanabas1]

Step 1: Colour box5 r5 in r/y/b, as Simon used. Step 2: What colour is r6c6? It's not blue, because each row and column cycles colours. It's not yellow, because it's 1 different to the yellow central digit. It must be red. Step 2: Because each row & column cycles colours, you can now colour the entire grid. Puzzle is now 90% done without entering a digit. Put 5 in the middle, pencil 46 in box 5, the remaining 2 reds are 17, 28 or 39, and 28 and 39 break the thermo. Step 3: So now red = 1 mod 3, yellow = 2 mod 3, blue = 0 mod 3, write in box 5 and the diagonal, and you're basically finished. Fun puzzle to gain confidence for anyone who finds minimalist grids and colouring intimidating, as it's also minimalist difficulty. BTW, the diagonal triomino rule automatically follows from the orthogonal trionimo rule, so is superfluous.

[@RichSmith77]

I mean, if you're going to call half your steps "step 2" then yes, it's easy to do it in very few steps. 😉

[@Syrange13]

I love this, because you can get to that colored grid from pure math without even looking at the puzzle, just from the divisibility rule. When 3 numbers sum to a multiple of 3, they either all have the same remainder or there's one of each. Nothing else works.

[@billbliss7407]

14:25 -- which is, I think, a personal best for me trying any puzzle (other than GAS) featured on this channel! Thanks for sharing, and thanks to the constructor for making this!

I got it in 13:15, my mind went straight to modular arithmetic, and I started to put the colouring straight away. The middle box gets very easy when you look at where 8 and 2 can go in the box. The rest follows.

[@RealCadde]

Another name for this puzzle could have been "/ 9-15-21 \ 12-18-24" because that's what the puzzle boils down to in the end. And once you figure out the direction of the red line, you can color all cells on the ' / ' diagonals in their respective mod 3 colors. They form straight diagonals of 369-147-258 possibilities. After that it's just hunting for what digits see what digits and the thermo and red line gives all you need to know to eliminate them all one after the other.

[@robynrox]

18m46s for me. Haven't seen Simon's solution yet, but I really enjoyed it. The logic is divine! Thank you, Sumanta!

[@srwapo]

15:44, I'm super happy I thought to do some coloring. Looks like my "try coloring one way and see if that works" wasn't as clever as the solution in the video, but it sure went fast!

[@klgan90]

So happy that it is one of the first time I solved faster than Simon. Want to share my method here. My method is to quickly establish the position of 1 and 9 in the center box. Because 4 and 6 is already taken in the center box, Anything opposite the 1 can only be 3 or 9. The thermometer quickly restrict the 1 to r6c5 as a result. Once 1 is in r6c5, r6c6 cannot be a 4 as both 1 and 4 give a remainder of 1 when divided by 3. If 4 is in r6c6, then r6c4, r6c7 and all cells in r6 are required to give a remainder of 1. Hence, 6 is in r6c6. Once we have 1 (remainder of 1) in r6c5 and 6 (remainder of 0) in r6c6, we can establish that r6c4 and r6c7 requires remainder of 2. From there, we are able to colour code all cells according to whether they have remainder of 0, 1 or 2. We are also able to complete the marked diagonal and solve all cells according to their colour code.

[@danielcamp789]

Amazing that this solves & once you spot the break-in it's actually relatively straightforward. Great puzzle.

[@Orenotter]

Everything just seemed to jive. The whole puzzle just came alive. The digits were ringing The universe singing And all of it thanks to a five.

[@HunterJE]

You can get to the fully shaded grid for the three mod-3 options right away without even looking at the thermo (though this method does not tell you which of the remaining mod 3 values relate to the two colors besides yellow). Just extend the logic Simon does on mod-2 (yellow) by asking what about the domino of yellow and one of its neighbors? If the neighbor is 1 mod 3, the two combined add to 0 mod 3 the next one down has to be 0 mod 3 to reach a total of 0 for the triomino, while if the neighbor is 0 the domino adds up to 2 mod 3 the next one has to be 1 to get to 0 for the triomino. (You might ask what about the neighbor being 2 mod 3, but it cannot be since you already have all three 2 mod 3 values in the relevant rows/columns). This propagates through r/c 2/5/8 the same way yellow did, and then can be propagated to the rest of the grid from those cells, quickly shading the whole grid with strictly alternating mod 3 values in the rows and columns and the following diagonal diagonal and unimodular stripes on the rising diagonal

[@AngelWedge]

Yeah. I started by colouring the diagonal, then did something like that starting in the corner to propagate and colour the whole grid. (Then note that the first two cells on the thermo are the same colour as the 4 or 6 in r4c4, and must therefore be either 1,7 or 3,9 … after which it's just filling in the digits)

[@nkorppi]

I also three-coloured the whole grid before starting.

[@G4M1L]

As far as described, this was also exactly my solce path. First colouring the grid per mod 3, ignoring which one was 1mod3 and which 0mod3, then disambiguating things with the help of thermo and diagonal.

[@zuphix1802]

20:04, absolutely beautiful. I also went with a colour strategy but discovered the 258 x-wings in box 3 and 7 much later. After colouring in the whole board you just solve the rest by sudoku. Really nice logical path through this one.

[@MattYDdraig]

3:38 The opening with the thermo to break it open is neatly done, but after that its just a fill-in with basic maths. Well presented.

[@killamoosdraree730]

So pleased that Simon chose to use the same color scheme that I did in my personal solve. This was quite fun, I loved the modular trick! Thanks!

[@PauxloE]

Nice. Here the new "check pencil marks" function really comes handy (after coloring, I've added three middle pencil marks in all squares of each color, then just filled in the ones which were not marked red).

[@mmmmmratner]

Long time viewer, first time solver! (A few times I have stopped to try puzzles and then given up.) This one I actually solved in my head. Not that I could keep the whole grid in my head, but I had the whole solve path in my head, and entered it in soduko pad in five minutes. (6:48 with my fumbling)

[@xnisfuzzy]

Sat for 15 minutes with 3 sets of digits in almost every square trying to figure out how to properly fill the cells. Had forgotten about the secondary constraint of ascending/descending cells on the diagonal. Finished in 32:09 after I came back to the video to see if I had missed something. Thanks Simon lol

[@nickroethel3326]

A MUCH more elegant way to slove it than what I had. I'm really glad I came back to watch this puzzle. I manged a few digits in the middle box. Then went full Mark and wrote down and eliminated possibilities until I got some momentum (or got lucky). I love this solve much more.

[@trudain]

Saw mod color approach thanks to an earlier puzzle and solved in 12 mins. Thanks!

[@gordonglenn2089]

I dawdled along, enjoyed coloring, and finished in 17:13 Now to watch Simon's approach to it!

[@Tabandija]

It took me 45 minutes to figure out the modulus. The remaining 15 minutes were spent painting and filling in the puzzle. Great one.

[@mipsuperk]

11:00 not too tricky after the doing modular lines pack, but it's always fun to see a miracle constraint squeeze out a solution out very few clues.

[@rewolff2]

Beat me by 1:07.... Still.... Proud to have solved the puzzle, proud to have beaten simon for the first time. :-)

[@chitraagarwal8259]

Beauty in simplicity... Its one of the hardest things to achieve...Sumanta has set some really good puzzles before, but this one ia my favorite thus far just for the minimalism and how approachable it is. Must include in whichever compilation of best puzzles of CTC is published next!

[@RichardDamon]

9:51, I saw the modulo trick right away.

[@nkorppi]

It’s immediately obvious that if a line has two adjacent cells of the same modulus, then the entire line is of the same modulus. This quickly gives a full three-colouring before even starting.

[@frankthompson9630]

I think other commenters have covered this already, but it's actually possible to entirely color the grid with mod 3 colors with no info except that the diagonal in the middle box has three different colors on it. It's pretty easy to see that you can never have two boxes of the same color orthogonally adjacent, because if you did you'd need to have an entire row/column all of the same color to fulfill the modulus condition. E.g if 1 and 4 (both equal to 1 mod 3) are orthogonally adjacent, then to satisfy the modulus requirement the next digit has to be 7. But if the next digit is 7, what comes after that? You need 4 + 7 + X to be a multiple of 3, and the only valid possibilities are 1, 4, and 7, all of which appear in the row/column already. So as soon as you know you have three different colors (each representing a different remainder) on the diagonal B _ _ _ Y _ _ _ R you know that the squares touching two different colors only have one possibility which you can immediately fill in: B R _ R Y B _ B R And once you've got two adjacent squares in any row/column, you can color the rest of that row/column. This lets you color in the entire grid very easily. And once you have the coloring with the middle box looking like this: B R Y R Y B Y B R You know that the low B and the high B are the first two items on the thermo (since the middle B is on the diagonal). Since there are two higher items on the thermo, the high B can only be 7, then the high Y can only be 8, and the high R can only be 9. Thus throughout the whole grid you have B = {1,4,7 } Y = {2,5,8} R = {3,6,9}. From here it's just straightforward sudoku-ing!

[@Grammulka]

06:32, proving the math is fairly easy. The first thing I did was to color main diagonal (not knowing yet which color is what mod 3) and then you prove same color can't be next to itself, and that colors all the grid

[@alexholker1309]

This is an interesting emergent property, though it's probably too restrictive to be used anywhere apart from this.

[@sarahnash7174]

What a beautiful puzzle! Loved it!

[@_-_-Sipita-_-_]

4:56 for me. i definely knew where was this going because of something that appeared like 3 days ago

[@kamallewis-gopie6956]

Took me an hr and 20 minutes today to do the first puzzle in the 500k subscriber pack. But I'm sure without watching your videos I'd never have done it 😁

[@MysteryWaffles]

8:51 for me. I saw the modulus logic and just started colouring from there, felt like just filling it in. Simon's comment about this setter's puzzles being tricky because his brain works differently makes me wonder if me being autistic plays a role in how easy I found it.

[@andrewcook8093]

Amazing. It looks impossible but once you figure out that in any row or column any three adjacent cells must contain 0,1 and 2 mod 3. Once you figure out the ends of the thermo, the diagonal orients the grid so you can colour the entire grid and, after figuring out what else must go on the thermo, you can just write in the all the other numbers.

[@harmonicaveronica]

Managed to get this without figuring out the modular logic. I focused on where the 9 goes in the middle box. That required a bit of trial and error, but after I got that I just used math and sudoku logic, eventually figuring out that there were groupings of 147, 258, and 369, and that I just had to look back 3 cells to find which of those sets it was in

[@shaneminer15]

9:15 pretty sure I spent half the time coloring the grid on mobile and the other half solving the puzzle. I really should start solving at my desk

[@attilakiss8585]

Actually, you can realize without colorint that the ortigonally adjacent cells are 0,1,2 (mod 3). They cannot be 1,1,1 because then the pattern keep going (1,1,1,1,1,1,1,1,1) and that is impossible.

[@gordonbos5447]

I did this completely different. For starters I entered the 4,5,6 triple in box 5, then entered the possibles for the thermo which were already pretty restricted and only then started looking how the mod-3 was supposed to work where I sort of instantly figured that the corner digits in box 5 all had to be even, which I discarded just about as fast. It did prompt me to investigate what would happen if I entered 8 in r4c5 and found something for which only at the end I realized there is a generic rule for it: if you enter two digits that are mod-3 apart (i.e. 1-4-7, 2-5-8, 3-6-9) next to each other then the next digit must be from that same mod-3 sequence and thus this can only happen on a diagonal. So my initial hunch was correct, but the reason was completely wrong.

[@jasonpatterson8091]

The way I did it was similar but simpler, I think. I looked for mod3 triples that could result in a multiple of 3 - it's got to be 0,0,0 1,1,1 2,2,2 or 0,1,2. Only 0,1,2 (in some order, of course) can be in rows or columns, a triple of mods would require that all digits in that column have the same mod in order for the triomino rule to work out. However, because 5 is a central digit it will have to pair with every other digit to form a triple including 2 and/or 8. The only way that those could be used in the central square is with all 3 digits (2, 5, and 8) along a diagonal since they're all equal to 2 in mod 3. That tells us that one of the diagonals is a 2,2,2 (mod3) set of digits, and we know it's not the 4,6 diagonal. The thermometer tells us the position of 8 and 2, then the neighboring 9. That gives us the pattern of mod3 values on the entire board and the stripes are immediately apparent. With the restrictions on the board and the mod values the rest of the puzzle is trivial.

[@l3zl13]

At the beginning I was wondering if the middle box was a magic square, but it turned out to be a Parker square instead.

[@Rach881101]

17:26 for me. Essentially a unimodular/modular puzzle. Great miracle sudoku!

[@spelldaddy5386]

I really did enjoy this. I stared for only a couple of minutes before realizing how it worked, and got there in 10 minutes and change. It always feels good to beat the video length, but to hit less than half is shocking. Time to see what Simon did

[@tianyi05]

First thing I did was mark the diagonal 1-9, 2-8,.... with the 5 in the middle. then solved the middle box with the thermometer. Pencil marked the ring around the middle box and saw that all the cells were modular. After that was a color fest. I actually beat Simon's time.

[@rungus24]

8:37. It's probably the first time I've come anywhere near the speed of you and Mark's times on a solve. I could see everything that needed to be done about the puzzle immediately, although it took me until the end of the puzzle to remember the word modulus.

[@marcopezzin3932]

"I'm not doing anything clever other than just filling in digits." Simon Anthony 2022

[@awilliams1701]

I always love it when you get a surprise from mark. They are the best videos. Also Sumanta is one of my favorites as well.

[@FlyingPichu]

My first sub 10 solve, and what an approachable and beautiful puzzle this was... Wow!

[@gdshoe5822]

I got 10:58... and I'm sure there will be plenty of people who will complete this far faster. I actually overlooked the 5 in the middle at first, and got the whole grid colored before proceeding (the red line alternates modularity; propagate; swordfish). Then, I observed the 456 in the middle, and the fact that the first two cells on the thermo share modularity. From there, box 5 surrenders quickly.

[@SirBradiator]

12:42 for me with the benefit of having watched/solved Wednesday's puzzle which is essentially the same logic

[@RoderickEtheria]

Very simple to figure out the trick. Just propogate along the diagonal, to get same modulus lines along the positive diagonals.

[@AngelWedge]

7:28 for me… now going to see how much of Simon's time is spent explaining rather than solving.

[@gdshoe5822]

My thought exactly. Wait... I finished in less than half the time of the video? He must have spent a lot of time explaining!

[@moersertrupp]

After getting the Initial yellow squares, we can also locate the positions of 2 and 8 in box 5 and with this resolve all yellow positions in the whole grid and their value, making it much faster

[@AvatarBowler]

An alternative explanation for the thermo having 1 and 9 on the ends is that there’s a 2/8 pair in r4c6 and r6c4. The 2 can’t be on the thermo since it’s the 3rd cell, so 8 goes there instead, which forces 9 on the tip.

[@craigthibodeau324]

Simon made this so much more complicated than it needed to be. With 4-5-6 on the middle diagonal, fill in the possibilities for the thermo and see it is extremely restricted. Then there's only one possibility for the thermo to work with every triomino divisible by three, then the whole puzzle falls into place very easily. No complex theorizing, no colouring, this one is easy with brute force. Should have been a GAS puzzle.

[@robertmale7413]

Another brilliant puzzle and solve - thank you! And the 500K free puzzles are superb too!

[@benjaminrealy5661]

12:25. Yay Christmas! LOL. Took about 5 minutes to figure out the pattern in middle square then realized the pattern had to repeat so started coloring and it took off super fast from there. Enjoyed the uncommon methodology but thankful how quick I surmised it. Seeing the ruleset and lack of clues, I didn't expect one of my fastest non GAS solves.

[@rudyderidder394]

Excellent puzzle. Needed 45' to solve but needed 20' to get a good start. Thanks

[@liborkundrat185]

12:33 One of the first sudokus I solved. Technically faster than Simon in the video, but then again, I didn't have to verbally explain the mechanics in an easily-understandable fashion to an audience for most of the time.

[@AWanderingSwordsman]

Did it in 16:55. You made this way harder than it needed to be. In any triomino theres only 2 ways to be divisible by 3. Either you have 1 of each mod 3 group or 3 of the same mod 3 group (the groups being 1,4,7/ 2,5,8/ 3,6,9). Around a single digit there must be 4 triominos that use that digit as the middle digit. So the 5 in the middle of the puzzle is also the middle of 4 triominos, being vertical, horizontal, and both diagonals. Since 5 is in the middle of the box, all 4 triominos must be contained within one box so there can be no repeats. That means 3 pairs of opposite mod 3 groups (1,4,7 and 3,6,9), and one pair of same mod 3 group (2,8). It's impossible for horizontal or vertical to be the same mod 3, because shifting one over, you'd need another from that group. So basically if you have a 1,4,7 triomino vertically, both above and below that would need to be another 1,4,7 which is impossible because of normal sudoku rules. This means that either top left to bottom right or top right to bottom left is the same group triomino. Fortunately, the puzzle gives us one diagonal (the top left to bottom right) and we know that it's opposite groups instead of same groups (around the 5 it must have 4 and 6 which are not in 5's group). Once you realize that, you realize that top right to bottom left diagonals will be same group and since horizontal and vertical have to be different groups, that same group for top right to bottom left will apply not only to the diagonal going through the middle but to all top right to bottom left diagonals. At that point the entire puzzle is all but solved. You simply then have to realize that the row 4 column 6 cell (which has to be in the 2,5,8 group cannot be 5 or 2). The whole puzzle is solved at that point despite you only placing 2 numbers.

[@Thurhame]

Solved it in 15:50; I can't believe I actually beat Simon's time on a Sudoku! I used the fact that every orthogonal triomino must contain all three colors (147, 258, 369) to solve the thermometer and the diagonal, then simply colored in the rest of the grid and the puzzle solved itself from there. (I feel really embarrassed that it took me several minutes to realize that an orthogonal triomino cannot contain three of a single color, since that would fill the whole row/column with that color) The diagonal triominos rule is superfluous; I solved the puzzle without ever using it.

[@maurobraunstein9497]

That was a fun little puzzle! Definitely on the very easy side. I personally think the harder miracle sudokus are a lot more fun, like I think the first one I saw on this channel where I think there was a king's move constraint and a restriction on consecutive digits (it might have been that consecutive digits can't be a king's move away? I don't remember). You had to go through each digit one at a time and methodically mark where each digit could be in each box, etc. That was really cool. This one at least didn't take very long!

[@mirkoschultz9347]

07:15 for me. My best time ever on this channel. 🙂

[@drawsgaming7094]

13:30 Could have done it faster. Glad I still did it sub-CTC.

[@veggiet2009]

the most interesting tidbit is that any 3 numbers with equal remainders when divided by three, will then even divide by three when summed together

[@Terrariagrossmeister]

I think on my solve I used a slightly easier and quicker method. First I looked at the diagonal. Each cell on the diagonal [with the exception of the middle) has exactly two options. After that I figured out that the we have 3 types of numbers used in triominos. 3x, 3x+1, and 3x+2 ( 3 6 and 9, 1 4 and 7, and 2 5 and 8). And with the same logic you used I figured out that each of the three options would be in the same cell of every box. So if I have 3x in R1C1 I can confidently say that it will be in R7C4 too for example. Knowing that I colored in all the cells in the middle of the boxes as 3x+2. Then I figured that r1c1 and r9c9 have to be different options. One of them is 3x and one is 3x+1, so I colored them and their corresponding cells in different colors. With that I had each cell on the diagonal colored, so I had to color the rest somehow. That's when I looked at the possibility of 2 cells in the same row of a box being the same color (for example r1c2 and r1c3) but since they would correspond to two other cells in the same row each that would be 6 cells with the same color sharing the same 3 digits. So I knew that if in a box there already was a color in a row I couldn't use it again, thus turning the box into a mini 3x3 Sudoku. With that I could easily figure out where each color was in every cell (e.g. r1c1 is red r2c2 is yellow, both see r2c1, so it can neither be red nor yellow so it's gotta be green. etc) With that I had each cell reduced to a maximum of 3 possible digits and only had to deduce which one goes where. The thermometer helped solve that and with that I solved it in about 10 minutes. Probably not an amazing time but as a beginner solver I'm proud of it

[@sampathkumar-ej7xl]

Sumanta Mukherjee I have seen you commenting on any of the puzzles here but sure hope you read the comments. Solving the puzzle itself was not hard but just the way that the grid has been put together was phenomenal. Look forward to more of your creations.

[@sumantamukherjee4631]

Hi Sampath Kumar, I hesitate to come in front in social websites but I do read the comments and feedbacks on my puzzle. I have seen you always enjoy solving my puzzles and give good feedbacks. Thank you for that.:)

[@sampathkumar-ej7xl]

@@sumantamukherjee4631 I fully understand keeping away from social media part. Your puzzles have been fantastic. Keep it up. I get so much joy out of solving some of these wonderful puzzles that I feel compelled out of gratitude, to at the very least, thank their creators.

[@fluscim]

Again, this feels more discovery than design? Very cool discovery. Is there a limited space for such discoveries? Or do they grow when more rules are designed?

[@rewolff2]

The trick to building this puzzle is to design the thermometer in the middle to disambiguate the order of two digits of the same color and to disambiguate the order of the diagonal. (This shape does exactly that. Place it (this shape) in any other box and the puzzle solves just like this one, with a possibly different solution!)

[@fluscim]

@@rewolff2 Wow. Hm. So yes, there was design too. Very curious about the different solutions. Thanks!

[@felixrohlfs8566]

What i really enjoy is not only the fantastic puzzles and their entertaining solve- The channel also adds to my vocabulary. Today I learned the word "perculate" :-)

[@alanclarke4646]

Such a great puzzle. It only took me about 8 minutes, which is about my best time for zero given digits!

[@chipsounder4633]

It is amazing how much little information can lead to the most creative and impressive sudokus ❤️