Can You Colour? Yes You Can!

[@alarictaqiarentza9451]

Hi Simon! Thank you very much for featuring another of my puzzle and for the kind comment! I'm very happy to see this one on the channel. Excellent solve! The stripe pattern is forced because of the puzzle symmetry, but there are one other pattern that technically can be form by the ruleset, one example: A B C B C A A B C Thank you very much for everyone that have recommend this puzzle, I hope everyone enjoy the puzzle too! :)

[@natalias.1561]

What a fantastic puzzle!

[@someguy-k2h]

This was the most fun puzzle I have done this year. It made me think, but then once I got the meaning of the colors, I was able to solve it quickly. You did a fantastic job.

Great puzzle.

[@jonathanallan5007]

Just stunning!

[@averagesongcontestan]

I'm not usually one to persevere through the hurdles of a puzzle that is featured on this channel, but this one was quite different to all the others in that regard. I had some blockades at the beginning, which was when I watched a little of Simon's solve, but what he did at the time I had already done, but a little something he said made me think of something else, go back to trying myself, and I can't believe that I made it all the way through without drawing false conclusions in between like I usually do. The satisfaction of having done this mostly on my own is a great feeling. Thank you for your puzzle!

[@f.b.jeffers0n]

These videos of you just painting the grid to then fill it in in only a few minutes are a special kind of beautiful...

[@PvPSteve]

It makes me happy that Simon takes so much care with regards to colour blind viewers. I'm not personally colour blind, but the thought for inclusion is lovely!!!

[@matt5075]

Same! I just wish Sven added some extra coloring options to the app.

[@TempuraFriedJoystick]

Absolutely. It would be so easy to not even think about it, and not many people would notice. But he makes a point to put the effort in every single time, because he knows these kinds of puzzles can already be kind of alienating to people and he wants them to be as inclusive to as many people as possible. It warms my heart every time to see the pure love Simon has for these puzzles and sharing them with people. :)

[@chesshead]

The more obvious break-in was to note that A numbers pertained to Andre Agassi (1 Olympic gold, 5 syllables in name, 8 Grand Slams), B to Bill Bryson (3 syllables in name, 4 children, 9 letters in birthplace (Des Moines)), and C to Christopher Columbus (2 children, 6 syllables in name, 7 letters in resting place (Seville)). Your break-in was also good.

[@benbrown7092]

I'm so happy to see someone else found this nugget of logic hidden in the puzzle. The really amazing part of how it tied into the Huey, Dewey, and Louie logic. If you don't know what I'm talking about, pause the comment and see if you can figure it out. I love this channel. I love this community. So many amazing people here.

[@pixllo]

Obvious indeed 😆

[@shellmichael9665]

Lmao

[@joethornton5321]

That's how I did it. Kind of disappointed in Simon, to be honest.

[@pouletbelette]

@@joethornton5321 Classic Simon! Always chooses the scenery route when there's a much simpler, quicker and easier way. What can you do?

[@blahfasel2000]

@23:45 One tip for cases where you need a second layer of colouring: Use coloured circles from the pen tool for the second layer. This way there's no confusion which color belongs to which layer.

[@zetamathdoespuzzles]

This was an absurdly beautiful puzzle, and I'm delighted to see it here!

[@alarictaqiarentza9451]

Thank you for streaming the puzzle on your channel!

[@inspiringsand123]

Rules: 05:49 Let's Get Cracking: 07:21 Simon's time: 40m55s Puzzle Solved: 48:16 What about this video's Top Tier Simarkisms?! Diddly Squat: 2x (24:34, 24:47) Phistomefel: 1x (02:52) Nori Nori: 1x (18:10) And how about this video's Simarkisms?! Symmetry: 11x (07:36, 07:49, 08:06, 08:13, 09:56, 15:29, 17:25, 22:12, 44:20, 48:32, 48:44) Beautiful: 9x (13:54, 32:39, 41:25, 41:26, 41:48, 48:12, 48:30, 48:35, 48:48) In Fact: 8x (07:25, 07:52, 26:52, 34:32, 38:37, 46:45, 46:56, 47:14) Sorry: 5x (02:02, 12:05, 12:07, 24:47, 46:40) By Sudoku: 5x (17:37, 25:23, 26:56, 44:12, 44:20) The Answer is: 4x (08:51, 14:00, 17:13, 41:33) Hang On: 4x (11:36, 23:00, 35:35, 46:38) Stunning: 4x (16:42, 16:48, 48:12, 49:11) Ah: 4x (13:42, 20:30, 29:47, 34:36) Nature: 4x (14:05, 15:44, 17:11, 17:44) Pencil Mark/mark: 4x (22:19, 22:31, 25:58, 46:54) Lovely: 3x (03:42, 17:07, 25:49) Magnificent: 3x (05:28, 16:19, 16:21) Chromatic: 3x (00:49, 00:58, 23:39) Goodness: 2x (36:01, 41:21) Clever: 2x (13:57, 41:21) Brilliant: 2x (02:50, 04:06) I've Got It!: 2x (13:45, 13:45) Wow: 2x (41:25, 41:25) What on Earth: 1x (22:53) What a Puzzle: 1x (02:18) Naughty: 1x (27:36) Surely: 1x (21:31) Think Harder: 1x (24:52) Obviously: 1x (40:30) Marries Up: 1x (22:01) Losing my Army: 1x (14:22) What Does This Mean?: 1x (34:03) Cake!: 1x (03:47) Most popular number(>9), digit and colour this video: Thirteen, Seventeen (2 mentions) Two (77 mentions) Blue (90 mentions) Antithesis Battles: High (2) - Low (0) Even (4) - Odd (0) Column (18) - Row (12) 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!

[@wariolandgoldpiramid]

wow, got was super fast today

[@Wecoc1]

For some reason, today all the times are around 5 seconds late 🤔

[@CuddlyPuddles]

Would you ever be willing to share resources or do a tutorial on how to program this?

[@Allenonymous]

TL;DR from my last comment… The hardest combos in your pallet for me are; 1. Blue and Purple 2. Orange and Red 3. Yellow and Green I have have Anomalous Trichromacy with sever Protanopia and Deuteranopia, and mild Tritanopia.

[@Allenonymous]

Everyone’s colorblindness is different. So everyone is going to have trouble with different sets of colors. There are 3 primary types of colorblindness. 1: Monochromatic, which means you can only see in black and white. 2: Dichromatic, which means you can only see two of the following three, red, blue, or green. That means there’s three separate kinds of Dichromatic colorblindness. 3: Anomalous Trichromatic, which you can see all three (blue, red, green) but you have poor light sensitivity in one or all three. This means you can technically see all colors, but you can see way less hues than most people. There’s a nearly infinite number of Anomalous Trichromatic types. Personally, I have Anomalous Trichromatic, with severe color blindness is red and green, and mild in blue. I see way too much red light and way too little green light, and a little less blue than most people. That means that colors strong in red overpower greens for me by a lot. Unfortunately, there’s no really a way for y’all to ever fully have “colorblind friendly” colors cus everyone’s colorblindness is different. For me personally, you blue and purple are almost impossible for me to distinguish. Your red and green are actually easy for me to distinguish. Your Orange is hard to tell from green and yellow. But if you choose something like red blue and green on your pallet, I’ll be able to see all three distinctly. Or red blue and yellow.

[@th.nd.r]

Thank you for taking the time to write such an insightful and informative comment. If you were to recommend the statistically safest set of three or four colors such that it works for most colorblind people, do you have a gauge on what that might be?

[@felipevasconcelos6736]

@@th.nd.r black, dark gray, and light gray are the most colorblind-friendly, since they’re not affected by colorblindness at all. It might not be the best color scheme for people with a different vision impairment.

[@Allenonymous]

@@th.nd.r Well, something like 80% of all color blind people are mainly red/green color blind. So I would recommend Superman colors. lol Blue, Yellow, Red, and add a mid-tone gray to cater to the majority of colorblind people without having to go fully monochrome. But if you wanted to cater to all color blind people including the ultra rare monochromatic, you’d need to just go with shades of gray like the guy above said.

[@th.nd.r]

@@Allenonymous cool, thank you very much!!

[@Allenonymous]

@@th.nd.r A good trick to test if the colors are monochromatic friendly is legit to put the colors in the grid side by side then put a black and white filter on the image. It’ll show what they see. If you can distinguish the colors then they could.

[@KrisCadwell]

26:04 Simon finally admits that he overcomplicates things simply because he likes to. 😜

[@Vhoxzz]

I found the whole 89 thing overcomplicated as well tbh. No need to count to 13 xD. Once the arrows can't have a 2 you know where 6789 go in that box.

[@RichSmith77]

When he says "some people, myself included", I wondered how small the set of "some people" was. 😂

[@olivier2553]

What is funny is that in all the others videos of Simon that I have watched, he would always ask the question "where does 2 goes in column 7?" I have not seen him mentioning he would rather think of boxes before.

[@pattyboone4451]

Came looking for this comment- lol 😂

[@duane9433]

Simon's logic simply became completely ob-two's .. but I loved every second of it.. 😉😎

[@rookie3k]

I love watching you solve puzzles like this where you have to color the whole grid to start and then it just fills in at the end. Its so satisfying.

[@alieutier]

First time solving one of these on my own! So proud :) I made the central arrows do a lot of work, which meant I actually didn't need the arrows in boxes 3 and 7 to complete the puzzle in the end. Basically I thought - how could all three digits on the central arrows be of the same color? Even with possible repetitions, they would have to be two sets of digits that don't contain two that still sum up to 9 or less.. and that's not possible. So I knew the central arrows had to be sharing digits, more specifically they had to be sharing the digits 1 and 3. From there my whole grid got littered in pairs, and then the arrow in box one helped disambiguate.

[@BaldorfBreakdowns]

This is basically what I did too!

[@muhilan8540]

So you basically did the same as Simon, if I’m understanding you correctly?

[@Raven-Creations]

Pedant's corner: if you rotated the grid about that axis, cells on the axis wouldn't move, and R1C5 would flip to R5C9, not R9C5 like you imagined. If you rotate a plane within a plane (which is what you were trying to describe), you are rotating about an axis which comes out of the screen, and passes through the centre of rotation in R5C5. For colouring, use red, yellow, and blue (they are about as far apart on the spectrum as you can get three colours to be, and almost everyone can distinguish them easily). Then, to identify versions 1, 2, and 3 of each colour, use light grey, dark grey, and black. Because the flashing colours are numerically lower than the hues, they always appear in the bottom right of a flashed cell, which makes scanning so much easier than picking a colour at random, where the flash may appear on top or below. You may think green and orange are distinct, but they have very similar values (as in the V of the HSV colour model), so although I _can_ tell them apart, they aren't exactly distinct, especially because colours can appear very different depending on which other colours they are near (even for normal sighted folk). E.g. you may have seen the optical illusion of a fire engine which is grey/green, but appears red, because of the context of the rest of the image. I sometimes have to stare at orange and green to be sure I've got it right. Unless they are next to each other, red with an orange flash can easily be confused for orange with a green flash. What a beautiful puzzle. The colouring was fun, then deducing which was which was also fun. It's nice to be able to fill nine cells at once with a single click. Your maths wasn't necessary. To get started resolving the colours into digits, observe that there are two orange/green arrows with two blues on them. They have to be the same two blues, so the third blue in each box is the same flavour of blue. You can work this around the grid in the same way you can with the 2s. You have the same situation with greys on an orange/red arrow, so you can propagate the third grey around the grid. Once you've flashed everything, you can easily tell from the arrows which cells are which, highlight all of the cells of that colour/flash, and click the digit. In case you're tempted in a future video to assume you always have a diagonal in a box, you don't. You could arrange the rows ABC/CAB/ABC, and both diagonals are AAC. You do get doubles of each colour in the columns though, so it might not work in a 9x9. I think I can see an arrangement that would work (by permuting the columns as you work down the grid), but I've not tried it out to be certain. I suspect that once you have one box with a diagonal, you do need a diagonal in every box, and vice versa.

[@pjbrady47]

It's a great puzzle. Wish I could have solved it! :) I spent 2 hours getting the coloring and completely failed to work the arrows to get the other digits. I'm glad I tried it, and Simon is right, the logic to color it is really nice.

[@77kaczka77]

Rotation symmetry axis is in the third dimension i.e. orthogonal to the grid, placed in the middle, and therefore seen as a point, not a line. But never mind. I love your logic show very much.

[@Aliessil]

41:36 for me - it amazes me how fast that collapsed once everything was coloured, I expected the actual numbers to require a lot more work!

[@Waggles1123]

Just to chime in, you can actually define each digit in the grid without getting into the math of the arrows. if you define the blue digits in box 2 as some X/Y/Z in some order, and the grey digits in box 8 as some J/K/L in some order, you can unwind the two into filling in the whole grid with X/Y/Z and J/K/L (on top of the 2s, the orange-greens and the orange-reds) before getting into what size any of the digits are.

[@AcanthaRayneOakMoon]

I spent more time than I care to admit, working out that there are 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 possible permutations of a sudoku grid, that's 6,670,903,752,021,072,936,960 in numbers. Thought some people might like to know.

[@Gusquoise]

This puzzle had me really amazed, took me 80 minutes of joy Your way of thinking of these puzzles is wonderful, it's really nice to see you solving them (I had to pencilmark the entire grid to see how to desambiguate the "grays")

[@emilywilliams3237]

Fantastic video, solve, and puzzle. Such a pleasure to watch this, Simon. I am very glad that you chose to use colors rather than using the letter tool, because colors are much easier to see at a glance when watching the video. It is much easier to see a blue cell than a cell with some standard pencil marks along with a letter, but no colors. So thanks for being Simon and choosing that option! I also have a new favorite word that I have heard you use a couple of times in the past week or so, and it is the word 'otiose." It is fun to say and has a special quality of people imagining that it might mean something that it does not, so it could be kind of fun to drop into a conversation without much context and see who gets bamboozled (another favorite word that you use from time to time). But in order for my comment to not become otiose, I shall close now with my thanks!

[@olanmills64]

Holy crap, always a good feeling when you finish within a similar time to Simon! I like doing these puzzles where you have to use a lot of deduction basically color everything first and then the digits fallout within a few minutes of additional deduction after everything is colored

[@KANPAI666OPPAI]

Got it in 46:34 - ended up making an incorrect assumption about the r1c1 arrow and had to backtrack a couple times because it kept putting the last cell I'd get to in conflict as I was assigning values via Sudoku that tacked on like 10 minutes. Once I realized where I was wrong in my assumption, the puzzle was pretty much solved. Really clever setup and logic in solving!

[@KANPAI666OPPAI]

Watching Simon's solve, it's interesting how his solve path diverged from mine. After getting Box 5's 2, I was able to deduce that the box 2/8 circles are 8 and 9, and then figure out from there that C group's other numbers are 6,7, which put 1,3,4,5 for the remaining cells and from there I was able to figure out the relationship between them - one group is 159 and the other is 348. From there, it was breaking them up into 13, 45, and 89 pairs and penciling out locations based on Sudoku up until my mistake above where I assumed the non-2 digits on the box 1 arrow would be both 13s, when instead r1c2 could also contain a 4 as well (just not a 5) and that's when I was able to solve it.

[@th.nd.r]

Such a ridiculously good puzzle, and I honestly think it got better over the course of the solve. Well set and well solved!! Love a good coloring puzzle, and this is a TOP TIER coloring puzzle.

[@alarictaqiarentza9451]

Thank you very much for the kind comment Thunder Hart! :)

[@Scott2148]

Got it - 159 minutes, wow, I could see success, but I fluffed it and had to start again. Persistence paid off. Thanks again.

[@warren_r]

I needed just under an hour to finish this one. Quite a challenging puzzle until you figure out how to ask the right questions. Super cool.

[@jurjenvanderhoek316]

20:17 I think you should have noticed early on that in every box-row and box-column there should always be 3 colors (follows indirectly from the general rule). That would have given you grey in r4c1 here (and blue in r6c9 at 21:58).

[@RichSmith77]

"Follows indirectly from the general rule" - but why does it, though? It doesn't seem obvious to me. It's similar to when Simon was asking if there was a reason there had to be a diagonal stripe of one colour in each box. It seems to turn out to be the case, but I'm not sure what the proof is. It's certainly not forced by looking at a single box. The following would obey the rules within any one box, A B A C A C B C B

[@alarictaqiarentza9451]

The diagonal stripe is forced by the symmetry, but not necessarily by the ruleset. As Richard Smith point out, there are one other possible "box pattern" that can be made by the rules.

[@BeardlessWhelp]

44:23, though I did need the prompt to look for the center digit, and from there worked out the rest of the puzzle. I love painting puzzles!

[@renevillarreall.r.3503]

Brilliant as always Simon! Thanks for putting out these videos

[@林老師-i5d]

107:41 for me. I color the whole grid and use letters to identify the three different cells of the same color. Finally, I try to establish some math equations according to the arrows. It works but really slow. Simon's solving is brilliant.

[@crystalgehrt8861]

One feels one cannot fully praise this puzzle without the use of expletives. I hope to see many more features from this setter.

[@alarictaqiarentza9451]

Thank you for the very kind comment! I usually posted my puzzle on CTC discord & LMD if you're interested. :)

[@matthewcharlap7785]

Found the color of 2 very quickly (as simon did), but then stuck for a while. I eventually 9-colored the entire grid (thank so those ABC labels, I could keep track of the sets without keeping multi-coloring). Once I have the whole grid colored, took about 5 minutes to fill in the numbers. Don't know if that is how this was intended to be done, but there you have it.

[@averagesongcontestan]

That's how I did it as well. I struggled for the longest time to differentiate between the 3 blues, but once I got to it, everything came together in a matter of minutes!

[@ELStalky]

I solved this very differently at the end. It is possible to distinguish all different digits without filling in anything except the 2s. So I had the entire grid filled with colors and could use the "equations" provided by the arrows to figure out that in my case "black = blue + 2". From there I slowly reduced the possibilities until there was no wiggle room left.

[@chocolateboy300]

I finished in 60:06 minutes. This was a super fun coloring puzzle. It reminded me of some mean mini puzzles that were limited to 3x3 boxes. The pattern felt very similar with a diagonal of color always present. The ending was a bit tricky, but focusing on box 5 really sealed the deal. It is so cool that a puzzle like this can be created. It's just so cool. Great Puzzle!

[@Xehanort107]

once I saw you using more colors, I was able to solve the puzzle, but dang I enjoyed it. Everything was a double and nothing solved itself for me EXCEPT that top-left corner exposed a 4 in the arrow and everything unraveled. I wish I had the knowledge to design sudoku puzzles to make something like that, but the math involved would probably be beyond my level of understanding.

[@emilyr2836]

Interesting, I used letters rather than flashes of color and completely solved the puzzle with no digits but 2, but then I missed the 89 pair on the central arrows and instead had a very long and convoluted puzzle where I ruled out one digit at a time for each letter. On the plus side, I had everything worked out, so as soon as I got a digit, I could fill it in the entire puzzle at once!

[@joubess]

Simon, I figured out that the center box arrows had to come to 8 and 9 and that the possible digits were 1345 several minutes before you came to the same conclusion!!!! Only because you weren't looking at those that way yet. You were focused on coloring. That's my only excuse to get ahead of you on that one. You finished it way before I did, but it was good to be on the right track all by myself for once!!! I also figured out each color had to have a low, a middle, and a high digit! Once I figured those out it was much easier to complete the puzzle in under an hour. I'm finally seeing some learning paying off.

[@mse326]

Simon, love the videos. I don't know if it will help you, but it did me, instead of using a flash to distinguish members of the same color group use letters. If you are on the letter selection mode you can type in any letter (and number for that matter too). So even with the ABC maybe getting confusing you'd have 23 options to work with. That would allow you to distinguish within a color and even notate a cell as a group of A, B, or C and leave the double coloring for two cells that you are know are a pair of groups.

[@alarictaqiarentza9451]

Letters can definitely be very helpful indeed, I used letters too for this coloring-type puzzle. Especially since the app allows double-clicking to select all letters. :)

[@mikepictor]

42ish minutes - really fun. There is a really subtle pivot point to land the first couple of digits, and then it all unfolds in a flash

[@mikkelthomsen72]

Very nice solve, I got the 89 from the center arrows when we figured out that the digits on the arrows did not repeat and we knew that 2 was not one of the digits, meaning that the smallest sum we could make with three numbers was 8 and the other arrow had to be different. I found that logic easier to spot than the one you used, but the same result nonetheless.

[@annonamis]

Simon solved this in such a pretty way. I did the center logic early and brute forced the 1,3 double into flagging every cell besides the 2s. Amazing puzzle but doing it the right way meant that Simon didn't have that moment of panic from the important 7 not being a 6 like I thought it would whew

[@doug3512]

I quit this one and restarted a few times. When I finally committed to doing it, I was at 65 mins. Which, feels like a good time for me. The 89 pair was the piece that took me the longest. I also struggled with a coloring schema that didn't fall apart halfway through.

[@hyperactvehuman]

29:36 if Simon realized that in each box in each row or column a color can appear only once, he could solve it way faster.

[@joakimjohnsson6201]

How do you prove that?

[@hyperactvehuman]

@@joakimjohnsson6201 I didn't try to prove it. My solve path was a little different than Simon's. Simon did the slash coloring only for orange color (with red or green slash). I did that with all three colors. Eventually coloring without that lead to contradictions all the time. I also showed that R4C7=R5C4, and R6C3=R5C6 mid solve. I think that also helped. Simon realized this after he finished coloring.

[@hyperactvehuman]

@@joakimjohnsson6201 I wish I could post a picture. For example, at around 18:34 of the video, when I reached this state I worked on the Box 5 arrows to realize R4C7=R5C4 which eventually brought me to the conclusion of the comment I made.

[@carlscheuermann3684]

Simon, your handle on math concepts has always impressed me, but you erred today when you tried to explain the symmetry of the puzzle by rotating it about a line. As I'm sure you know, you can flip it or fold it across a line, but it is rotated about a point (or the central square, in Sudoku terms).

[@joelstevens5670]

Hi Simon, My name is Joel and I have been following the sudoku channel for a year and a half now. I’m not too great at communicating well/simply (it takes me ages just to write messages) but I just wanted you to know how much the channel has helped me with getting through a difficult period as well as allowing me to discover the beauty of sudoku variants. I know you are probably busy but I hope that you see this. I’ve also recently come up with a few cryptic clue attempts if you’re interested (I can email them over if you are). Thank you. 🙂

[@kathyjohnson2043]

It is wonderful to hear that the channel has helped. It has helped me too. I wish you the best

[@th.nd.r]

Hey Joel! I’m so glad you’ve found CTC and have been able to use it to help get you through tough times, and I hope you’re doing well 💙. As per the cryptic clues, are you in the CTC Discord by chance? If not, I highly recommend hopping in there and sharing your clues there!

[@joelstevens5670]

@@kathyjohnson2043 Thanks, it is isn’t it (as seems to be the case for so many). I’ve really enjoyed the journey into the world of variant sudoku generally (it matches my Mathematical/logic based thinking) but Simon and Mark are also such lovely characters that the channel has that warming feel to it (not to mention them being brilliant at puzzle solving). Life is chaotic but a little kindness can make the world of difference. :)

[@joelstevens5670]

@@th.nd.r So am I, it’s nice to know I’m not the only one who enjoys this kind of thing! My life is still a bit disorganised (hence the timing of my replies) but I’m probably through the worst now. I’m not in the discord but part of me feels like I should be, I just haven’t found the courage to explore it yet (my Asperger’s means I can be easily overwhelmed). I seem to come up with cryptic clues/plays on words/creative logic for fun, it’s kind of the way I think (even if it’s not always useful)!! 🤣 So it would be nice to have a platform to share them (so others can enjoy the contributions). I’m also a budding setter so that is another reason (I do have a setting name but I’ll leave that for when I make it onto the discord)! ;) On another note, I know there are a few regular commenters like yourself (I would be more regular if I wasn’t so bad at timings and taking ages to comment) so thanks for that (and some of the puzzles really are ‘off the scale’ levels of clever). :)

[@th.nd.r]

@@joelstevens5670 I’m Autistic and I find the server generally easy to navigate, of course all of us are different so listen to what your mind and body tell you and act accordingly!! I will say it’s worth at least joining the Discord to look around and see, and if you find it doesn’t suit you, feel free to leave the Discord!

[@Coyotek4]

Took me nearly an hour (56:27), but I finally found my way through. Incredible puzzle!

[@randomstrategy7679]

Slight nitpick, but rotations don't have axes of symmetry: those are reflections. Rotations have a center around which everything rotates (in this case, the center is the middle of the grid). In the case of a 180¨° rotation, EVERY line through the center is preserved.

[@dicebar_]

I wound up flagging all 9 digits with letters and playing parity alphadoku. Ending with a bunch of formulae to disambiguate, like "M = Y + 2". But, as always, Simon was infinitely more elegant than me. A very nice solve indeed.

[@njuham]

123 minutes but I did figure out how the colours worked faster than Simon so there's always that LOL.

[@piarittersporn]

A very fantastic puzzle and not nearly as difficult as I initially thought.

[@jensstalberg8968]

Took me way too long, but I used more colours, som I'm happy. I gave every cell in the middle box different colours, and then it was pure colour mayhem. "Oh, this could be purple, yellow, blue, green or dark grey". Then a little bit of maths in the middle box pretty early, finding out that R6C6 and R7C4 had to be the same digit due to maths. The most important thing, I got there in the end and had a lovely time solving and watching the video. Thanks again to my favourite channel.

[@sarahgray1735]

Great puzzle and beautifully solved. Although I do think that’s green in the corner deserved a song!

[@bbgun061]

At 34:15, every 3x3 box must have one of each color in each of its columns/rows. You could have used that a several times in this puzzle.

[@sugarfrosted2005]

That stripe is false BCB ABA CAC is a counterexample arrangement. However, if you have a line that's 3 distinct you can show it. Though I'm curious how other boxes would effect this.

[@Anivacuum]

34 mins. Fun puzzle, straightforward, no super tricks required.

[@troyshrauger3576]

27:13 for me, I put values into the center box to tell me the nature of 2 “low” and 1 “high” values.

[@adagraves]

The coloring was fun in this one, finished in 00:40:57, those 2s are gorgeous.

[@nationandy]

spilled my morning coffee at the flashing line thanks lol

[@HunterJE]

The axis of rotational symmetry is not the line Simon marked, it is a line extending in the "Z" direction (towards/away from the viewer) through the middle of r5c5. A rotation around an axis on the 2d grid would just be a reflection...

[@sunriselg]

Or in other words: in 2 dimension there is no axis, only a central point.

[@Gonzalo_Garcia_]

22:22 for me. Very fun puzzle!!

[@someguy-k2h]

Anytime you solve a puzzle by Alaric, I'm going to have fun. Thanks, Simon.

[@alarictaqiarentza9451]

Thank you for the kind comment! :)

[@LavenderGooms]

A very cute puzzle. Love any excuse to color.

[@_aullik]

I used letters when you used double color boxes. It also allowed me to use pair of colors for pencil marking. It still took me far longer. sometimes my brain just stops and needs to restart.

[@bristolrovers27]

Excellent puzzle I worry about the solver sometimes, but he's entertaining to say the least !

[@KevFrost]

Massive applause for the solve

[@keithmower921]

Could you say that Simon earned his stripes in that solve? Great and elegant puzzle, great and elegant solve.

[@gatlygat]

There is a lovely other piece of embedded logic that wasn't picked up in this solve. As there are a couple of sets of replicated arrows (I.e. 2blues = orange(green) in Box 3 and in box 8/9). It means the placings for all the blues can be unpicked ( and obviously grey in symmetry)

[@srwapo]

64:55, it was fun coloring, a little bit of work in the middle, but it took me FOREVER to figure out the numbers. Just so many things relating to each other and difficult to scan. Been a while since I solved a hard one!

[@khronosh4954]

I don't understand the logic at 19:15. You have three different digits, so grey could have been 1, 2, and 3. 3 would go in the circle with 1, 2 on the arrows. It worked in the 3 cell arrows because of geometry where the different numbers/colors were seeing each other.

[@HunterJE]

But then what would go in the third grey cell in box 2, which sees both the arrow cells in its box and the circle in its row?

[@bay8791]

At 19:08, he says that r3c3 "sees" r3c6. It also can't be r1c5 or r2c4, because those are on the arrow. Because those three cells are all different (in box 2), r3c3 can't be gray. Nor blue due to othogonality.

[@khronosh4954]

Thanks!! I totally missed that part. I'm a goofer

[@krypton9984]

I used the circles and squares instead of the twin colours - worked well. However, there was just one move I just couldn't get, and even now can't see how you get it. The Orange/red in the forth row, cell 2. I just can't see how you know that

[@adrianhead6272]

Completed in 24m06s - the rules make this very straightforward.

[@swingardium706]

It is actually possible to prove that every cell has a stripe! It's a little in-depth but I'll try to be as clear as possible: *This logic can be swapped to work with the other option we "discarded" if we apply it to the columns instead of the rows.

[@swingardium706]

Proof that our only options for filling a 3x3 box are the diagonal and non-diagonal patterns: Consider a 2x2 region within a box. There are two options for how to fill this: The chequerboard: AB BA Or the "triplet": AB CA Let's consider the chequerboard when filling the 3x3 box. It doesn't matter where in the box we put it because the logic will be symmetric, so let's just put it in the top-left: ABO BAO OOO Now we have to ask ourselves the question "where do the three C digits go?" You can try shuffling them around a little, but it should be fairly clear that they must go in the corners to avoid touching orthogonally: ABC BAO COC But now we have a problem. The only digit that it is possible to fill either of the remaining O cells with is B, which would give us four Bs in the box. This proves that any chequerboard pattern within a box is broken. Now, let's consider the triplet within the 3x3 box. There are two ways of slotting this one in: with the middle cell being a unique digit, or with it being a repeated digit. Let's start with the repeated digit: ABO CAO OOO Now, let's consider the bottom-right cell. It actually has three options: If the bottom-right cell is A, we get our familiar diagonal stripe: ABO CAO OOA The full pattern (on the right below) is now forced, as placing a C in the centre-right cell would place a fourth A in the grid: ABC CAB BCA If the bottom-right cell is B or C, it forces the entire pattern: ABA CAC BCB or ABC CAB ABC We can see, though, that these patterns are actually the same; one is a 90° rotation of the other (if we swap the labels B and C, which is perfectly valid). For this reason I'm only going to consider this a single option*, which I'm going to call non-diagonal. The other option is the non-repeated digit in the centre. BAO ACO OOO Let's try our options for the top-right cell. If it is a B, the pattern is forced into our old friend the non-diagonal option: BAB ACA CBC If the top-right cell is a C, we have to be careful to avoid making a chequerboard pattern via the centre-right cell: BAC ACB OOO There are two options for the bottom row. Labelling the bottom-left cell B will give us the non-diagonal option, and labelling it C will give us the diagonal option. Thus, we have proved that there are only two options for the filling of a 3x3 box: diagonal and non-diagonal.

[@wanderlustwarrior]

48:54 for me. I didn't think I'd need to color the whole grid, but I wound up doing so.

[@BaldorfBreakdowns]

It's interesting to me how long it took him to notice the middle math problem. I got stuck in there for a long time because I didn't see the solution to the middle digit. Once you know the middle number, you can figure out every other number quite fast.

[@myfyrmadocjones]

This puzzle would drive me quackers.

[@Sam_weiqi]

21:04. Fun fun

[@chipsounder4633]

Excellent again ❤️

[@spoilers9723]

The way he went out of his way to avoid the center arrow clues was fun. My break in was that once you have the 2's, you know they have to be 1345...

[@glum_hippo]

“Two brains are better than one” - but only if those brains are not pre-occupied with dunking on each other! 😅

[@lisan9517]

38:51 Would you perhaps say that's... Green in the corner, that's green in the spotlight?

[@ShabbaDabb]

You mentioned colourblindness. To start, I'm inclined to agree with your logic - blue grey green. However, orange and red (to me) are the MOST similar in colour. And red green colourblindness (which I am) is very common. Therefore I think red orange green is potentially the worst combination at least for my eyes

[@ShabbaDabb]

One thing also that I'm noticing is that red has priority over orange over green so they align in a manner most disturbing

[@Allenonymous]

For me it’s red and Orange, and then blue and purple. I just can’t tell those apart. Mostly everything else is fine.

[@kathyjohnson2043]

Thanks for the explanation. I would have guessed that gray would have been a bad choice because of the possibility that some colors would look gray.

[@Allenonymous]

Then yellow and green.

[@GregJonson]

So... I utterly misunderstood the rules. I thought that when it said "digits with the same letter must be in the same group," it meant "digits BEGINNING with the same letter" so I threw Two and Three in one group, Four and Five into the other, Six and Seven into the third, and then I was left with 1, 8 and 9 thinking I'm going to have to deduce which of the three groups those belong in. Of course, had the rules actually said this, the puzzle would be impossible to solve - which I found out 15 minutes in and decided to give up and just look at the video. Let's just say, I frequently feel stupid trying to solve the puzzles featured on the channel, but never have I felt dumber than right at that moment.

[@Larsvn]

Me too. I was just going through the comments to see if I was the only one.

[@MartinEB72]

Labelled the whole thing with Letters. Able to figure out all 1 2 and 3s. Just had a pairs of 45 to place. They added up to 7or8 on one letter and 8 or 9 on two other letters. Obviously meaning 7 goes in my letter g, which solved all the 45 pairs, and solved the 89 pairs.

[@richnewt]

One thing I've learnt from ctc is that in rotationally symmetrical grids, the numbers pair-off opposite each other, so immediately know there's a 2 in the middle because it pairs to itself. But does that count at meta-gaming?

[@acidhelm]

The step of min/maxing the box 5 arrows was really cool!

[@scottwestleysmith3196]

So, whenever I try to divide up numbers into three colored groups, I would think to divide them into warm colors (red, orange and yellow), cool colors (green, blue and purple) and neutrals (light grey, dark grey and black).

[@IronLucario2012]

That was a *much* more elegant way to figure out the maths after the colouring was done than I had, lol. I labelled every kind of box individually after separating them into colours, but then ended up doing simultaneous equations with them on a notepad based on which ones were on which other one's arrows, which seems to have been a much harder way of doing it than your logic here. Whoops!

[@joschi4306]

I'm not sure why he never metiones that but here in germany we have something called "Punktsymmetrie" translated in to english its basically "Pointsymmetry". Its where you just use a point not an axis to mirror the grid. Its the same thing as to rotate the grid by 180°. Sry if i have any grammatical relaxed mistakes.

[@joebogle3172]

I used some slightly different logic, I realised that the Grey in your case in R3C3 could not be a 9 becuase the arrow in R7C4 featured the same 2 digits plus another digit.

[@mandyvk90]

On a totally different note. Who else thought about the show friends, when Simon said: seven seven seven seven! 🤣

[@CrankyOtter]

Oh hey, I’m a bit stuck about 2/3 thru the tallcat puzzle so I’ll have to check the video

[@andrewenzor6418]

Thank you for wishing me happy birthday! Yes I was able to pause and solve the at minute 17. I’m very proud 😂

[@Ardalambdion]

I knew that none the two remaining digits could occupy downleft or upright corner as they had to touch each other on an earlier point than Simon showed us. Otherwise, well done to the constructor and our solver.

[@markbennet9058]

Nice to see that the sets are entropic, which was a bit unexpected - guess the setter was messing with entropic sets. Could this have been deduced from the Box 5 logic? It didn't jump to mind for me.

[@alarictaqiarentza9451]

Yes I'm exploring the idea of ambiguity sets. :)

[@ServantOfSatania]

Took me 72 minutes exactly with one mistake that made me backtrack quite a lot, but considering the mess I made overlaying shades of grey on every color in the grid I think it was for the better

[@ImpInaBox]

Took me a whole lot longer than Simon and I got a different tho apparently valid result: Blue: 1, 5 & 8, Grey: 3, 4 & 9 which made orange/red=7 and orange/green=6. Sven says it's all good!

[@cjktoo]

35:30 Me too, Simon, Me too.

[@bobblebardsley]

38:51 Shout-out to anyone who sang "that's green in the spotlight..."

[@KevFrost]

An hour of thinking about my orange 2, my dark orange and my light orange makes me crave a Terry's chocolate orange.

[@icepyrox]

82 minutes, but I ended up labeling literally everything DEFGHIUL (blue was LUE orange was D2F, gray GHI) I could do that because the arrows in the centers forced out the ones that would be big. Then I could see those had to be 89. From there I could work it down. Also, I got a tick before noticing one of the arrows didn't work out, so backed it up and redid the maths and got it right the second time. Since it was all labeled, it wasn't hard to sort out

[@Pablo360able]

My favorite part of this grid is realizing r1c2 can't be a 4, and suddenly everything falls into place at once.