Thank you for this wonderfully smooth feature - I think quite a few people who have attempted this so far struggled with the bit you mentioned in your closing remarks, but you sailed through it very nicely indeed! I didn't put too much thought into the title, only that it should relate to the TOroidAL nature of the grid... There'a a bit of a funny story behind the publication of this one. I was watching Scojo's Impostor stream and my pair of puzzles (one by me, one by my impostor) was about to come up, when @patrickgass787 aka ViKingPrime (one of the kindest and funniest members of the community) playfully mocked the complexity of my rulesets by predicting that they would include ludicrous nonsense such as toroidal little killers... I had this puzzle ready to publish the following morning, but after his comment, I published it there and then and sent him the link. He really does know me well!! Thanks so much to those who recommended the puzzle, I'm feeling very loved by the sudoku community at the moment! I'll hopefully see as many of you as possible in Stratford next month!! :)
@patrickgass787
24 күн бұрын
I've never experienced a bigger mic drop in my entire life, well played, that one
@myrtinyrtti
24 күн бұрын
you’re a genius, lovely puzzle once again!
@gordonglenn2089
24 күн бұрын
Ah, toirodALTOroidal...
@perigin3
24 күн бұрын
Could I request an edit to the wording of the rules on svens website if that's possible? To me, the current writing of the rules specifying that there must be a "continuous" run of "cellS" makes me think that you could alternate colours along a diagonal until a certain point, and only start counting once you have two or more of the same colour in a row.
@timotab
24 күн бұрын
You've gone and done it! Ever since my first Yin Yang construction, I'd vaguely had the idea of Yin Yang on a torus, precisely because it messes with the checkerboard and border lemmas. I just hadn't taken it any further than just a thought. Bravo!
@derekswager
24 күн бұрын
There's no 3 in the corner in this puzzle because a torus has no corners
@alanclarke4646
24 күн бұрын
But it can't be a torus: top meets bottom AND left meets right. There's no hole. It also can't be spherical, because: say we start with left meeting right, then the only way to seal the ends would be top to top, bottom to bottom. It's probably a shape that can't exist in a 3 dimensional space. I think it's most probably a 4d hyper-torus.
@HamishWHC
24 күн бұрын
Actually that is how a torus works. Imagine rolling this grid into a cylinder, with the top connected to the bottom, then connecting the ends of the cylinder into a torus, connecting the left side to the right.
@hummakavula3750
24 күн бұрын
@@alanclarke4646Woah. If it hadn't lost its religion already... 🤯
@MV-gr9xw
24 күн бұрын
@@alanclarke4646 Top meeting bottom and left meeting right simultaneously is what makes a shape toroidal.
@mathman0569
24 күн бұрын
@@alanclarke4646 No, there is no hole in a torus's surface, you're on the torus, not looking at it
@martysears
24 күн бұрын
Absolutely stunning little puzzle from the marvelous mind of the PedallingPianist. I'm afraid the 3 in the corner song must be rescinded though - there are no corners on a torus 😜
@falloutfan2502
24 күн бұрын
The confetti has spoken. There can be no doubt.
@neil2796
24 күн бұрын
The sudden realization that he needs to avoid a 2X2 across the torus boundary felt nice.
@Tahgtahv
24 күн бұрын
While that is true, I don't remember it ever coming up in the solve?
@RichSmith77
24 күн бұрын
@@TahgtahvI don't remember him using it either, and I was waiting for him to use it to colour r5c6 for 10 minutes from around 18:35.
@TheKtuno
24 күн бұрын
It came up in my solve path rows 1 and 6 columns 4 and 5 somehow I picked up on it right away.
@neil2796
24 күн бұрын
@@Tahgtahv Simon, as usual, found another way to get the same result. He never used what I realized.
@GuardOfGaia
24 күн бұрын
@@Tahgtahv it did for mine though - I had 3 of the corners in one colour and realized that meant the 4th one had to be the other colour as they form a 2x2
@makerpat
24 күн бұрын
I found it helpful to color the squares outside the grid to keep track of what colors were virtually next to the edges due to the toroidal. Then it was easier to spot potential islands and 4x4s, particularly at the corners.
@pairot01
24 күн бұрын
Yeah, I think that was the author's intent
@Orenotter
24 күн бұрын
I thought I would give this a go. A toroid- no corners to show. And when 3 came along I launched into the song And sang "That's 3 in the... OH NO!"
@thaumaTurtles
14 күн бұрын
i love these limericks :D
@Anon-f8z
24 күн бұрын
I think Simon would have found this a lot easier if he just coloured the squares outside of the Sudoku, so that he can see the pattern more easily.
@alanclarke4646
24 күн бұрын
What I did
@TomatoFarmer8
24 күн бұрын
Surely that’s the reason for making them fillable “cells”. Was completely obvious to me…
@Mephistahpheles
24 күн бұрын
True that. Simon's "bipolarish" explanations and solves: he goes into extreme detail with the rules, and seems to have troubles understanding/explaining simple things....but regularly spots & solves extremely difficult logic. Slow to accelerate...but hard to keep up with him once he gets going.
@leestoddart7014
24 күн бұрын
Exactly - it amazes me how that simplification can be invisible to Simon when the most tricky logic just springs out to him as obvious.
@SophiiLuca
21 күн бұрын
@@leestoddart7014 That’s true, his brain most likely sees patterns differently than someone like I see them. I especially thank that if someone only really does very difficult puzzles, they get used to having to see more out of the box patterns instead of the usual easy ones. In that way, one no longer notices the simple patterns and solutions. Of course, this is only speculation, but I think it makes sense.
@SvenBeh
24 күн бұрын
I think there is some form of checker-board avoidance on a toroidal grid: namely there can be at most two checkerboard 2x2s (which may be overlapping as in this puzzle). Proving that requires a bit of topology: In this proof I will use the colors red and blue. Suppose to the contrary there was a grid with at least 3 checkerboard 2x2s. Then choose one such 2x2 and consider the orthogonal paths connecting the diagonal squares. Cutting the torus along those paths, one obtains (up to homeomorphism) a disk, whose boundary has two opposing stretches of red and two opposing stretches of blue. Now in the interior of this disk, there are 2 more checkerboards. For each of these checkerboards, the red square have to connect. But they cannot connect to one-another, as that would isolate the blues (as in non-toroidal ying yang). Hence, they all connect to the boundary. But whichever way one does this, it will create isolated regions of blue, which yields a contradiction. Hence, there can be at most two checkerboard 2x2s.
@BTGTB
24 күн бұрын
That's a very interesting point and proof, definitely use it for next time, thank you!
@garrettsmith9788
24 күн бұрын
My immediate thought was that there would be only one checkerboard, but that was proven wrong by this puzzle. In fact, Simon colored a valid toroidal with no checkerboards. Thank you for the thoughts on three!
@Kaepsele337
20 күн бұрын
Can there be exactly one checkerboard or does it have to pair up?
@SvenBeh
20 күн бұрын
@@Kaepsele337 Yes, there certainly can be. Imagine one Checkerboard in the middle of the grid, where the two blue cells are connected by a straight path around the edge, while the remaining cells are all filled red.
@uigrad
19 күн бұрын
@@SvenBeh I expected that a single checkerboard would also be allowed for a tube board, but it seems that even a tube prevents it. Going from a tube to a toroid allows you to go from zero checkerboards to two!
@HonkIfYouLoveBeer
24 күн бұрын
Thank you thank you THANK YOU for the colorable external squares! Would love to have this ability in most puzzles with outside-the-grid clues
@jonathanross6260
24 күн бұрын
Wow, just wow. This is an incredible puzzle. Thanks so much for setting it, Peddling Pianist!
@angec9908
24 күн бұрын
I love ♾️. That’s hilarious.
@adipy8912
24 күн бұрын
The infinity is new. You've solved two other sudokus that uses the torus rule: 1. Poisoned Bagel by Bismuth 4 years ago 2. Mozzarella by Perladel almost 2 years ago
@pairot01
24 күн бұрын
Did you pull those from memory?
@prodigis.
24 күн бұрын
@pairot01 haha they probably checked the video index (link in the description) but I'd be impressed if someone just liked the toroidal rule enough to carry that in their back pocket
@adipy8912
24 күн бұрын
@@pairot01 I remember there were two videos before. The oldest one I remember the video were called "the 98% sudoku". The other one I search "cracking the cryptic peradel" and got the name of the other one.
@adipy8912
24 күн бұрын
@@prodigis. If something is really good you have a higher chance of remembering it
@davidchen8251
23 күн бұрын
Hi~ First time commenting here, hope it will help. This puzzle reminds me of the one I've solved a couple weeks ago called "Twin Galaxies in Curved Space". It has similar topology and yin-yang rules, with some insane setup that leads to a unique solution. More importantly, it's a 9x9 puzzle which brings more fun ;) It would be amazing to see you guys feature that if it's possible. It only has 14 solves right now, and I truly believe it deserves more.
@patrickgass787
24 күн бұрын
This is one of my all time favourite puzzles and really could only have been done by ThePedallingPianist (and that is a challenge to all you imposters out there!)
@A_CC_K
24 күн бұрын
What a brilliant puzzle! Another amazing puzzle from the The PedallingPianist.
@davidhughes7174
24 күн бұрын
Astonishing again, just beautiful, the puzzle and the solve. Thank you
@tianyi05
24 күн бұрын
You can color the cells outside the grid to represent what the connected cell across the grid is it helps to see the regions.
@feldinho
24 күн бұрын
There could be a Klein bottle grid if the orientation was flipped in the perpendicular axis upon crossing an edge. I have no idea how to make this into a puzzle, but it is possible!
@jounik
24 күн бұрын
And a Moebius strip grid if that's only true for one pair of edges and the other pair consists of true edges.
@Nyarlah
24 күн бұрын
So many incredible 6x6 lately, with new ideas, smart difficulty, and incredible craftsmanship. The Sudoku scene is in very good health !
@johnpauladamovsky86
24 күн бұрын
25:07 - "TRIOMINOIC" - That's the word you're looking for.
@Coyotek4
22 күн бұрын
Took me over 40 minutes and over multiple sessions ... felt like sudoku's answer to non-Euclidian geometry Insane puzzle!
@kevinthurlow8055
24 күн бұрын
Your invented word "triominic" is not to be sneezed at (especially as it's an old drug used to to treat hay fever).
@johnpauladamovsky86
24 күн бұрын
The word he "wanted" to use was actually, "TRIOMINOIC"....!
@inspiringsand123
24 күн бұрын
Rules: 05:16 Let's Get Cracking: 09:47 Simon's time: 26m07s Puzzle Solved: 35:54 What about this video's Top Tier Simarkisms?! Maverick: 2x (08:03, 26:03) The Secret: 2x (12:22, 12:22) Three In the Corner: 1x (35:29) And how about this video's Simarkisms?! Weird: 7x (01:27, 08:35, 09:02, 15:46, 16:03, 16:07, 16:58) Hang On: 5x (09:13, 16:18, 19:40, 24:55, 34:26) Goodness: 4x (02:13, 10:32, 36:54, 36:57) Sorry: 4x (21:22, 21:51, 22:04, 29:48) By Sudoku: 3x (34:17, 34:46) Checkerboard: 3x (11:17, 12:16, 13:02) Lunacy: 3x (35:51, 35:59, 35:59) Ah: 3x (17:59, 26:20, 35:40) What on Earth: 2x (18:07, 36:14) Nonsense: 2x (17:24, 24:44) Lovely: 2x (36:45, 36:45) Ridiculous: 2x (30:17, 30:17) Cake!: 2x (05:01, 05:02) Useless: 1x (31:09) Clever: 1x (36:20) In the Spotlight: 1x (35:30) Beautiful: 1x (32:36) Brilliant: 1x (35:13) Bonkers: 1x (03:19) Approachable: 1x (01:52) Surely: 1x (09:51) Obviously: 1x (22:22) That's Huge: 1x (33:57) Most popular number(>9), digit and colour this video: Ten (13 mentions) One, Two (34 mentions) Green (55 mentions) Antithesis Battles: High (2) - Low (0) Even (5) - Odd (1) Outside (2) - Inside (0) Column (6) - Row (5) 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!
@sjm6280
24 күн бұрын
This puzzle has so original and fun logic!!!
@phoenixaki3458
24 күн бұрын
Very bizarrely unique combination of rules with this new toroidal idea! Worked so well together
@eytanz
24 күн бұрын
I had serious new ruleset struggles with this one - I never attempted a torodial yin/yang before - and I kept getting confused about whether edge cells could get out or not. Took me about 45 minutes.
@MarkBennet10001
24 күн бұрын
Had to give it a go - simply outstanding
@MarkBennet10001
24 күн бұрын
Lucky the "usual" Yin Yang example still works on the torus ...
@MarkBennet10001
24 күн бұрын
A mathematical way of approaching this (which I thought of but didn't quite use) is to relate the number of allowable checkerboard patterns to the Euler Characteristic of the surface. But here the logic is that you can't have more than two (there was another puzzle on the channel with a hole in the middle of a big grid where the same logic applied). It will help if someone creates a Klein Bottle puzzle, for example.
@Gonzalo_Garcia_
24 күн бұрын
22:34 for me. Wow that was confusing. Great puzzle anyways!!
@Tringard
24 күн бұрын
toroid yin yang was interesting. I appreciated being able to work with the outside grid, copying my colors over to the opposite side helped me keep track of successful connections.
@cameronbaydock5712
21 күн бұрын
“Do come along, we’d love to meet you.” Exactly what AI might say…
@dVTHoR
22 күн бұрын
I know I could never have solved this having no experience with Toroidal, would have for sure needed that thoroughly explained to me beforehand.
@markp7262
24 күн бұрын
23:17 finish. A fun puzzle, but definitely pushes you, having to picture the wraparound. An excellent offering!
@roccov3614
18 күн бұрын
Had a bit of trouble, mid-game, keeping track of how everything was connected but I got there. Nice one.
@rmjarvis
24 күн бұрын
19:16 for me. Very nice puzzle. Mostly a matter of not assuming too much. Eg about checker boards or how many cells can make up a 5 clue. Keep yourself grounded and it is fairly straightforward.
@wojciechpietrzak1981
24 күн бұрын
12:30 The other secret is still valid but void. The perimiter can still have only one change of colour but what use can you make of it when there is no such thing as perimiter?
@alexhawco2970
24 күн бұрын
I think there's a pretty important ambiguity in the rules: Simon solves this assuming that each of the diagonal clues also signal the 'start' of their colour strip. For example in the very first deduction he makes that proves that the infinity diagonal and 22 diagonal are different colours he uses the fact that then 10 diagonal needs at least 2 cells of the same colour, however that only follows if you assume that the second cell in the 10 diagonal needs to be r3c2. The rules don't explicitly rule out the possibility that the strip of r5c6 and r4 c1 is a valid possibility for that 10 clue. The rules only state that the clue applies to "the first continuous run on their diagonal" and if the clue sits in the middle of that run, so to speak, that would still be the first run the clue sees. If these kind of 'mid-run clues' are possible then I'm almost certain that the puzzle is impossible to solve so I think they do need to be said to be invalid within the rules text.
@frogsinpants
24 күн бұрын
I agree it would be better to remove the ambiguity. However, I don't think it's impossible to solve if you allow mid-run clues. Because the 22 shares a diagonal with one of the 5 clues, those clues cannot be mid-run clues. It takes some doing, but I've pretty well convinced myself that whichever color the 22 diagonal is, you can't make either the 10 or 24 a mid-run clue without the coloring breaking down with either a 2x2 block or an isolated group somewhere.
@themorebeer3072
23 күн бұрын
If the clue sits in the middle of a run, it can't possibly be the first continuous run on the diagonal. The first cell starts (and may end) the first continuous run on the diagonal!
@alexhawco2970
23 күн бұрын
@@themorebeer3072 I don't think its obvious in any way that the first cell starts the run - after all the fact that its the first cell is just an artifact of how we've chosen to place the grid, which shouldn't matter since the grip is representing a torus which doesn't have any edges
@themorebeer3072
23 күн бұрын
@@alexhawco2970 I place an arrow pointing at a grid. What is the first cell along that arrow? Sure it's an artifact of how we place the grid. It's also an artifact of how we placed the arrow. That's still pretty obvious however.
@gabisalkin8881
23 күн бұрын
I agree, this threw me off. It's hard to define a single cell as "a continuous run".
@Ardalambdion
24 күн бұрын
We had at least one torus here before... Well done, both to the setter and the solver.
@Ardalambdion
24 күн бұрын
Besides, the 4 colour theorem doesn't work at a torus as you need 7.
@IdoN_Tlikethis
24 күн бұрын
i wish i would've tried this one myself before watching the video. this was brilliant
@SynVT_
24 күн бұрын
I saw a torus and I knew immediately it was PedallingPianist lmao
@ronjohnson6916
24 күн бұрын
Clever path building that collapses quickly (not a complaint -- I think the path building is the point) once you get the path.
@nakorbluerider
24 күн бұрын
I discovered this on Logic Masters a few days ago and in the process of solving it got really tied up on the topic about checker boards, so I took to a whiteboard and I *think* I've convinced myself that for a toroidal yin-yang puzzle there can be at most two checker boards in the grid. If you imagine an actual doughnut shape in 3D, one checker board would represent a green line going around the doughnut and a purple one looping through the hole, while the other checker board would be a point where a green line loops through the hole and a purple one wraps around the doughnut. You can do that much without green lines intersecting purple ones, but a third point on the torus with nontrivial loops of each colour cannot be placed. I didn't take the time to consider whether there's some issue taking that logic based on a continuous smooth surface and applying it to a grid of cells, but I think it holds. You can see at the end of Simon's solve for example, the purple cells form a loop horizontally across the centre of the grid, but also vertically along the left edge - two loops that the green cells can still manage to navigate. A third loop would be one too many though.
@marktherunner6334
24 күн бұрын
Absolutely brilliant. Loved it!!
@IRLtwigstan
24 күн бұрын
Another video with the amazing Simon!
@hummakavula3750
24 күн бұрын
That was a great new twist on an old rule set. I wish Simon had realized you can mirror the cells on the outside of the grid. That makes it easier to visualize.
@TheKtuno
24 күн бұрын
40:20 I'm definitely stoked I managed to solve this awesome puzzle!
@richbuckingham
24 күн бұрын
Brilliant puzzle, its not often that a completely new set of rules can produce a challenging but approachable puzzle for me. Took me 65 minutes but enjoyed the challenge.
@steveunderwood3683
24 күн бұрын
The numbers and the first half of the shading was straightforward, but I took a while to complete the shading
@DaveLeCompte
24 күн бұрын
I appreciate that the rules say to shade the grid in two colors, which is what Simon would do anyway.
@57thorns
24 күн бұрын
Stunning and funny simultaneously as a challenge (if not technically hard, still a challenge to wrap your head around it) and some hilariousness with the infinity diagonal. Took me about 22 minutes to solve.
@57thorns
24 күн бұрын
A small hint: copying the rows and columns outside the 6x6 help with seeing many colouring limitation.
@milliams
20 күн бұрын
If you'd have coloured in the borders with the colours from the opposite side,it would have made it much easier to keep track of the toroidal colouring.
@letMeSayThatInIrish
24 күн бұрын
According to Claude AI the Ramanujan sum of that infinite diagonal is -8 (the diagonal sums to 16, so it's -16/2).
@OlafDoschke
24 күн бұрын
Alto as is the musical term (in italian) for high, perhaps? Infinity is pretty high. Also, if you pick only one side for connecting the grid to a cylinder, it may represent a wax cylinder for a phonograph, if not a music-box cylinder.
@gibbbon
23 күн бұрын
you didn't use it, but in my playthrought, the fact that the cases right outside the 6x6 could be colored to continue the pattern really helped me a lot
@donaldsnyder1543
24 күн бұрын
How about a Dyson Sphere puzzle now? 😂 Also could someone please start counting the infinty diagonal now and let me know when your done 😜
@tBagley43
24 күн бұрын
23:41 would love to see more puzzles with this torus feature
@Apptelope
24 күн бұрын
I used that R5 C6 had to be green because of the 2x2 rule. Same for that corner. All corners can not be purple.
@penningmeestercgkdelft9159
24 күн бұрын
Simon and Mark, if you ever plan to do a performance during a festival in the Netherlands, probably a lot of people like me (who aren't going to make it to Stratford) will try to be first in the queue to buy a ticket ;-)
@BryanLu0
24 күн бұрын
16:06 had to restart a couple times, because I assumed maybe there was only 1 checkboard allowed. Instead I avoided using checkboard. Coloring the extra cells on the border helped with spotting potential 2x2s, but the connection issues were hard to spot
@shaunbrowne9870
24 күн бұрын
Building a Klein bottle in a sudoku would actually be quite easy. All you do is take a normal toroidal rule and "flip" one side upside down (so that r1c1 is "orthogonal" to r9c9, r2c1 to r8c9, r3c1 to r7c9, and so on). For a Mobius strip you do the same thing except instead of having a normal toroidal edge you have one edge that's, well, just an edge (reusing the prior example, r1c5 isn't adjacent to anything in column 9).
@davidclayton4712
24 күн бұрын
It is a Klein bottle. Isn't it?
@jonh6585
24 күн бұрын
30:23 Completely ridiculous but completely forced. hats off to PP
@titusadduxas
24 күн бұрын
52:17 - That was gorgeous, though the colouring took some working out. Once that was done, the rest was easy!
@LithmusEarth
24 күн бұрын
21:27 does the 2x2 rule extend through the Torus it must right? if so, column 6, row 5 is green, it can't be purple. Don't think it'll help much.
@srwapo
24 күн бұрын
30:51, was hard to see if I was in a dead end or not when the regions looped around and around and around and around. And not being able to use the "rule" that you couldn't have the two colors in the opposite corners of a 2x2 region.
@bobblebardsley
24 күн бұрын
One 'secret' of a toroidal yin-yang puzzle that I have just noticed (and no doubt other people have so sorry if I'm stating the obvious) is if all four corners were the same colour, they would form a 2x2 via the torus. So at least one corner must be different from the rest.
@Yttria
24 күн бұрын
Fantastic puzzle took a couple of tries to get it right. The successful solve took 33 minutes while being somewhat distracted. Those distractions are probably what caused the earlier attempt to fail.
@Rubrickety
24 күн бұрын
Next up, a Möbius puzzle. After you cross an edge, 6's become e's, with a value of ~2.718.
@yashmehta9299
24 күн бұрын
A bunch of new rules for me, very proud that I could complete it in 51:37
@jonotick
24 күн бұрын
Finished in about 20 minutes, only i hadnt as i stupidly msde the 5 diagonal only 2 cells long and then found a valid solution that worked. Then when i realised it wasnt the solution back-pedaled and then finished properly in 24 minutes :)
@dannstarrjp
23 күн бұрын
I found this puzzle extremely hard - or I should say, easy to make a mistake. I ended up in situation where there’s no solution that works and had to restart twice. With third attempt though it took me about 15min to color it and putting in digits was just a minute. It was a good one but I as much as I love ying yang, I prefer to look at a grid as a square 😅
@bait6652
24 күн бұрын
Nice concept... But think "grid is toroidal " should be the second thing stated behind sudoku... Trying to grasp orthogonally connected before noting toriodal reallly was a bugger. Who would have thought the easiest thing to grasp was the inf.
@aleksapupovac
7 күн бұрын
I quite dislike when setters don't disambiguate all of the puzzles that are combined. Here the yin yang isn't disambiguated, in the sense that you don't know which cells are shaded, because both layouts work; however, I can almost fully forgive it because of such ingenuity and I have to say I quite enjoyed this one. Also I found it quite interesting that you don't have to use 24 not being able to be 6 digits to solve the yin-yang; although it seems it might have been the intended path.
@RealCadde
23 күн бұрын
28:51 STOP! Once you made R5C4 green, you've now forced your 22 clue starting at R1C6. 6+6+6+4 = 22 6+5+6+5 = 22 Those are the only options you have. And if it's 6+6+6+4 then the only cell that can hold the 4 is in box 4. So R1C6 and R2C1 are from [56] and R3C2 / R4C3 are from [456] But remember the 10 clue? It can only be [46] And if R4C1 were a 6, all options for the 22 clue would be impossible. So now the 22 clue IS 6+5+6+5 and R3C2 is a 6 and R4C3 is a 5 and R4C1 is a 4. Then, as R2C1 and R1C6 are effectively a [56] pair looking at R1C3 and R2C4, which is along the 24 clue, and those cells can only be as high as a 4. And R4C5 will see a 6. So it can only be as high as a 5. The highest the first two cells on the 24 clue can be is double 4, adding to 8. The highest the 3 remaining cells on the 24 clue can be is 17 (5+6+5 in that exact order for sudoku reasons) so you only have one degree of freedom left on the 24 clue which at most could be 8 + 17 = 25.That degree of freedom can only exist in one of the first three cells as the last 2 would otherwise have one digit only as high as 3 and you would lose 2 degrees of freedom. Point is, the last two cells on the 24 clue are from [56] and the order is known and resolves all [56] pairs you have so far. I have no idea how i just intuitively knew that limiting the 22 clue to stop where it does would resolve a lot of the puzzle but that is what i was seeing.
@thecaneater
23 күн бұрын
I think it would have helped him to see the toroidal rule if he colored the 'ghost' squares outside the puzzle.
@bobblebardsley
24 күн бұрын
I would like to suggest 'dominoid', 'triominoid' etc for toroidal dominoes. Except triominoid could be shortened to 'trioid' and tetrominoid to 'tetroid' for absolutely no reason other than that I think it feels quite satisfying.
@reecec626
22 күн бұрын
That five die pattern is called a quincunx.
@LednacekZ
24 күн бұрын
25:18 for me. it took me too long to get used to to the connected cells rule.
@DarrenNakamura
24 күн бұрын
Finished in 29:47. It was weird doing a yin yang puzzle where checkerboards were allowed!
@ApesAmongUs
24 күн бұрын
The first thing I saw was the checkerboard with the 10 and infinity, so that floored me right off the bat.
@stephencolwill148
24 күн бұрын
The mathematical part of my mind is troubled by the designation of the grid as being a torus The rules of the puzzle are symmetric as to going off the top and coming back in at the bottom or going off the left and coming back in at the right and vice versa in each case. So the grid has a 4-fold symmetry with respect to these transitions. But a torus seen from the side only has a 2-fold symmetry. Going left-right entails going around the equator of the torus, whereas going top-bottom entails diving through the hole in the torus. To me, this clash of symmetries represents a horrid mental dissonance.
@gordonglenn2089
24 күн бұрын
ALTO (halt, in español) appears on many STOP signs in Central America. All but one of these diagonals must stop, to avoid having infinite sums.
@josephbentley1300
23 күн бұрын
30:21 for me, what an excellent puzzle
@madsli
23 күн бұрын
>Purple and green Thanks doc.
@b005t3r
24 күн бұрын
When Simon got stuck, wasn't it enough to notice that c5r5 has to be green, to connect both green regions?
@RichSmith77
23 күн бұрын
Not sure if I'm looking at the right point, but for a long time the green region occupying r5c2 could take r6c1 and loop round to r6c6 toroidally to connect to the other side.
@FryGuy1013
24 күн бұрын
This one hurt my brain, but i got it. Fun puzzle
@alexeynezhdanov2362
23 күн бұрын
One can argue, that the 3 is not in a corner, since it's on a torus.
@gibsoand
20 күн бұрын
There are no corners where we're going
@PathOfShrines
24 күн бұрын
Really cool idea. 38:18
@biaberg3448
19 күн бұрын
Of course I’m still here. Nearly always am.
@toddbiesel4288
24 күн бұрын
What if you had an infinitely long diagonal, but all the numbers added to zero (such as using -4 to +4 in a 9×9)? What would the outside clue be then?
@caspianmaclean8122
24 күн бұрын
You could call it undefined or divergent, but you'd probably need to explain it in the rules (to distinguish from infinity and negative infinity, unless you want to allow the ambiguity). Also calling it undefined sounds a bit like you just aren't given it as a clue. Interesting idea, I had a quick look on the Wikipedia pages for divergent series and limits, but didn't find any better terminology.
@RichSmith77
23 күн бұрын
@@caspianmaclean8122I don't see why it wouldn't be zero, if one "lap" sums to zero. N x 0 is zero for all N, so surely in the limit, as N goes to infinity, the sum is still zero, no?
@caspianmaclean8122
23 күн бұрын
@@RichSmith77 that would only work for a whole number of laps. It might have a sum of 0 after 9N cells (a whole number of laps), but a sum of -4 after 9N+1 cells, if the first cell in each lap is a -4. If the sum keeps changing between 0 and -4 as you include more cells, the sum series generally wouldn't count as converging to a number. There's special series sum definitions you could use to get an answer anyway, but not necessarily 0.
@chrispowell1455
21 күн бұрын
Incredible hulk colouring!
@asktheraccoon
17 күн бұрын
"infinity" clue and Hulk color scheme... is this a lost footage from an Avengers movie ?
@stephencolwill148
24 күн бұрын
Perhaps a triomino on a toroid should be called a triominoid.
@QwDragon
24 күн бұрын
Was it possible to have more then 1 checkerboard pattern in the grid?
@expensivehat
24 күн бұрын
I was wondering if that's true in general, but I took it over to a 9x9 grid where there's a little more room to stretch, and it was pretty easy to make 2 checkerboards. However I do think 2 is probably the max. Something about how each color can connect across the north-south edge once, and they can also both connect across the east-west edge once, but then those connections prevent any further ones, so each color can only connect once each on each edge, which can then only accommodate circumventing the normal no-checkerboard rule twice. But.. that's hardly a proof. We'll have to wait for some insane person to make poor Simon prove it generally 🙃
@brianarsuaga5008
24 күн бұрын
This is, for me I think, the LEAST approachable sudoku I've attempted on this channel. It's pretty, but I had to be hand-held for pretty much the entire thing.
@CaptainSpock1701
23 күн бұрын
Sorry guys. The shape not a doughnut, it is clearly a coffee cup!
@nicocost33
24 күн бұрын
40.32 for me, but I had to watch the video for some help twice.
@chocolateboy300
20 күн бұрын
I finished in 29:59 minutes. This was an absolutely incredible puzzle. I thought I would struggle with the visualization of the toroidal, but it felt very natural in my mind. I was distraught at the fact that every single Yin Yang rule I learned on this channel was completely useless. The setting of this puzzle was mind bending and almost feels impossible to me. This has to be one of my favorites. Great Puzzle!
@stephenmccarthy1795
24 күн бұрын
I noticed that I could not avoid a checkerboard between the infinity and ten clues and gave up; this is why we watch, to learn.
@leefisher6366
24 күн бұрын
20:17 - It's a toroiomino?
@russellyowell6255
24 күн бұрын
Took almost twice as long but I got there in the end.
@artisanalfirewood8202
22 күн бұрын
so while working on this puzzle...a silly pointless thought crossed my head.... how many designers who are fans of this show start off their puzzles wth a 3 in the corner, just to get simon to sing
@seb3745
24 күн бұрын
Colour scheme today was lit! I would like to know the opinion of colour blind people, maybe this can become a new standard since orange and blue always give an odd/even vibe
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