ViKingPrime checking in here - I believe Marty is currently travelling, so I'll chime in with a little bit about this puzzle. I'll start by proudly stating my small role in its creation, which was to pass along the squares layout Marty ultimately used. This puzzle is part of a series of puzzles between multiple setters, essentially a sudoku setting chain-letter, where one setter creates with a disjoint set and then provides a new setter with a new set-up to continue the chain (my original puzzle was based on Orion's belt, whereas the layout of the blue squares here was my best approximation of Cassiopeia). That was my one small part in all this; what I did not expect - though I should have, given it's Marty - was what a phenomenally great puzzle he would make with it. Marty has always been a genius setter but over these last few months he's completely levelled up. Every single one of his puzzles, without exception, has been beautifully set, with elegant logical steps, breathtaking aesthetics and absolutely dripping with flavour. I don't think it's controversial to say he may very well be the best setter out there - not creating the most difficult puzzles necessarily, but always making the best possible puzzle with the logic involved. He's tapped Heliopolix to be next in line for the sudoku-chain-setting; I'm very much looking forward to seeing the result, and I'm confident it will be every bit as brilliant as what Marty has done here.

- Vid over an hour long - Unique game board - Wall of text rules Me: Oh yeah! This is some serious gourmet shit!

Simon using some elaborate logic to figure out a castle couldn't be a 1 instead of using the fact that he already had a castle with a 1 in it...

Greetings from Lyon, France! This feature was a lovely end to my holiday, thanks so much for choosing to feature it, as I know that beginning section can be a bit tricky to grapple with. I hope it was fun also though, as that task of finding a kingdom with only one border was my initial concept for this puzzle, as I really enjoy that kind of geometric nonsense. In the end Simon pointed out all my main bits of logic that disprove other options for the 1 kingdom and leave you with just the one shape that can work. As he realised after a little while, one shape IS possible in the top right corner, but is ruled out because a 1 would need to go in its blue square, putting a 2nd 1 in that row. Bottom left corner is simple to rule out because of the bridge there, and it doesn't take too much playing about to see that the bottom right corner is impossible because even keeping the 1 kingdom as compact as possible, the bounding kingdom would need to pick up a blue square, and in doing so would become too large. Once the top left corner is known to be the location of the 1 kingdom, there was one small thing that Simon missed (at around 36:34)... the red region can never take row 3 column 1, because then the bounding pink region would have two blue squares in it. I think if he'd spotted that he would have felt a lot more comfortable about the configuration he found being the only option. But I agree it is a bit of a 'have a play around' kind of opening which will be better suited to some people than others. It is definitely possible to prove the layout of the 1 kingdom being unique, but it does depend on spotting the right things and asking the right questions. The whole puzzle, in fact, is a good example of a puzzle that is not strictly linear, but each solver is likely to have their own unique experience depending on how their brain works, which questions they ask, and in which order. I guess most chaos constructions will be a bit like that. The order of deductions affects the precise nature of deductions that come after it. But broadly speaking Simon's journey through discovering the 9 kingdoms was the same as my intended path. I was particularly pleased that he used the fact that the yellow region couldn't pick up the 5 castle (as it would paradoxically give it a score of at least 6) to force the path of yellow, and also the fact that green needed to touch a 4th colour so as to not have a 3 in its blue square, which would match orange's score. In both cases there are probably other ways to reach the same conclusions, but these were the ones I had in mind, and I found them satisfying. Sometimes when I'm setting I realise there will likely be multiple routes through, but my philosophy is, I don't mind what exact deductions a solver finds, if they are likely to be broadly similar to the ones I found myself, and probably just as fun / satisfying overall. As VikingPrime commented below, this was actually my response to a challenge from him, to create a puzzle from a blank grid he gave to me with 9 cells marked, which had to contain a complete set of the digits 1-9. I then had to make the puzzle around that, and these marked cells became the blue squares. This was certainly a challenge, and several times it would have been realllly useful if I could have moved one of the squares, but I was very pleased to have successfully completed his challenge with a puzzle I was very happy with. Thanks VikingPrime for this great challenge idea, because that limitation really sent me down a creative path which i would never have gone down otherwise. Also thanks for testing V1 of this puzzle and immediately finding a big shortcut that I had foolishly overlooked 😂I know you felt bad about that, and I admit I was initially gutted to have to unpick the intricate setup I had put together, but it was totally worth it in the end. And thanks again Simon for a very entertaining feature and for your thorough explanations as always. Lord of The Rings references always welcome too 😀🏰

That stretch around the hour mark when Simon thought orange could have two blue squares in it and two castles could both have a 1 was a hard watch! I think his struggle at the beginning muddied the part of his brain which was holding the rules.

The mathematical term you were looking for at about 8'55": splitting an integer into a sum of smaller integers, as in 13 = 7+6, 6+4+3, ... 5+4+3+1, is called "partitioning".

Haven't been tuning in often enough lately. Love ya Simom, your soothing enthusiasm (ensoothiasm) is a huge help in getting through challenging days. Appreciate ya buddy!!

i solved this differently by getting the numbers of the castles much earlier. Once the topleft 2 regions were known, there could not be 6 castles with the number 6 in them (because 2 of them were now in the same kingdom) so the castles had the 1345 numbers on them. The number 5 can never be next to a bridge, which now puts them all in. This actually also helped with the shape of the regions to the right (since the 3 and 4 were already used in that row, the blue number had to be a 2, forcing the s-shaped snake region) Loved this puzzle!

This puzzle makes me think of the calculus of variations from graduate physics. Once Simon finds one 9-cell region (red) that is surrounded by one 9-cell region (purple) that has no castles thus is valued at 1, any variation on red breaks purple and thus that solution is "stable" with respect to variations. The only hope at that point is to find a very different ("unrelated") solution which had been futile up until that point, mainly because of the first placed digit ruling out the one other viable location. Amazing.

Who thinks Simon is the goat

Rules: 01:31 Let's Get Cracking: 07:44 Simon's time: 1h26m27s Puzzle Solved: 1:34:11 What about this video's Top Tier Simarkisms?! Bobbins: 1x (1:15:50) Three In the Corner: 1x (1:29:02) ​Scooby-Doo: 1x (52:45) And how about this video's Simarkisms?! Sorry: 9x (05:20, 11:59, 18:00, 24:22, 45:25, 1:00:58, 1:01:20, 1:17:42, 1:33:10) Hang On: 9x (10:15, 17:45, 33:07, 43:59, 1:10:53, 1:10:53, 1:10:55, 1:10:55, 1:16:58) In Fact: 8x (07:23, 09:28, 32:25, 36:01, 40:58, 42:44, 1:08:58, 1:16:52) What Does This Mean?: 8x (15:59, 40:38, 48:10, 1:03:45, 1:04:29, 1:07:24, 1:17:29, 1:21:10) By Sudoku: 6x (1:09:29, 1:09:39, 1:12:59, 1:24:37, 1:25:18, 1:33:33) Wow: 6x (33:46, 48:57, 52:54, 59:17, 59:17, 1:34:14) Ah: 5x (04:32, 33:34, 1:00:01, 1:08:00, 1:09:36) Pencil Mark/mark: 5x (16:05, 16:20, 49:45, 1:25:38, 1:28:42) What on Earth: 4x (42:23, 58:30, 59:17, 1:13:11) Brilliant: 4x (03:27, 1:17:50, 1:34:14, 1:34:17) Cake!: 4x (02:50, 02:59, 03:27, 03:30) Unique: 4x (05:50, 11:01, 25:16, 37:53) Good Grief: 3x (06:54, 1:30:15, 1:34:01) Stuck: 3x (02:22, 12:08, 51:42) The Answer is: 2x (47:45, 52:32) Clever: 2x (1:23:21, 1:23:24) Fascinating: 2x (01:14, 1:17:48) Shouting: 2x (02:46, 02:58) Weird: 2x (1:01:07, 1:01:10) Goodness: 1x (1:24:08) Bother: 1x (1:27:07) Naked Single: 1x (1:31:15) Nonsense: 1x (23:35) In the Spotlight: 1x (1:29:05) First Digit: 1x (15:45) Proof: 1x (37:15) Obviously: 1x (1:34:33) Progress: 1x (42:46) Chromatic: 1x (1:04:03) Phone is Going Nuts: 1x (40:38) That's Huge: 1x (1:09:36) Most popular number(>9), digit and colour this video: Ten (9 mentions) One (165 mentions) Blue (92 mentions) Antithesis Battles: Even (11) - Odd (0) Black (5) - White (0) Column (26) - Row (15) 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!

haven't started yet, but thematically, this would have been such a great puzzle for Fog of War!

There needs to be more castles & kingdoms sudokus. So far my favorite new sudoku variation.

Having seen Simon's solve now there are a couple of points that might help (semi-spoilers below) ... ... The castle in column 2 has three bridges limiting its options which allows quick resolution of the castle numbers which in turn adds some extra blocking when building the regions. Trying to find a region with no castles and only one border can be simplified a little: The enclosed region can be seen as existing within a rectangle of x times y (must be at least 9 of course) and the bounding region will then need at least x plus y plus 1 cells to surround it, plus any additional cells for indentations in the shape. e.g. the 3x3 square needs 3+3+1=7 cells to surround it. This quickly cuts down the optipnsnfornthe shape. Note that if three sides are left free it becomes 2x plus y plus 2; with no aid from the puzzle edge it would be 2x plus 2y plus 3; all clearly impossible. I'll leave out how they resolve to not entirely spoiler this work of beauty. Hope that helps.

@11:10 Well one way of looking at Circle Clues might be to establish the total, mininums, and maximums like killer cage logic. There are 13 castles, and the largest bunch that see each other together are 4 in a row or column, so there are a minimum of 4 unique digits in castles. But the maximum number of unique digits in a sudoku which can total 13 is 4 digits. So there are exactly 4 digits distributed amongst the castles: One 1 since a 13 killer requires a 1, and three other digits totaling to 12. 7 was ruled out by column/row logic, so it's either 1345 or 1246, since 1237 is unavailable. I know you get to similar logic soon after, but I think getting one's head in "killer cage" mode is a solid perspective to approach the logic from.

For the red/purple region I sort of imagine the most efficient shape for 18 cells is 3x6 - and then the "bite" purple has to eat from red to make them both 9 is forced by the blue square

I eventually got the 1-point region the same way Simon did but then coloured in all the other regions pretty rapidly without adding any more digits, just based on "obvious" assumptions about most of the bridges with a bit of help from the knowledge you'd have to have one of each score. That lays out the three right-hand kingdoms very quickly as you need a. 2-,3- and 4-neighbour kingdom each with no castles

Just to chime in to Simon's query at the end, I solved in just under an hour but my derivation of kingdom 1 was no more rigorous than Simon's. I spent more time on kingdom 2 earlier than he did, which got the 2 in row 4 which disambiguated the castle values, probably accounted for the faster solve time (besides the fact I am not explaining everything as I go!)

Realizing that finding the weakest kingdom, and then rigorously proving where it had to be, was very impressive, Simon. I appreciate that you always seek to really prove, not just go with your gut, every logical deduction. Once that initial weakest kingdom was placed the puzzle became much easier in most ways, I thought. I see some comments below that suggest irritation that you did not see certain things sooner, or seemed to have forgotten certain things that you had figured out earlier. Yes, I did notice a couple of things like this, but really, which of us has not had exactly the same thing happen in a longer, more difficult solve? The number of times I have to rehearse the different ways 22 can be made up in four digits makes me very humble about watching your videos, because you are so much smarter and have so much more of a grasp of things that you decide and discover than I do. I love your videos, Simon - thank you!

It's kind of insane to me how fast Simon forgets that each region can only have one blue square at the start of this video

1:00:59 Simon Highlights r6c2 asking why it can't be a 1... Well Simon, how many castles containing 1 can there be in this puzzle when the number in the castle indicates how many castles contain that number? Having a blue castle containing 1 at that point (the first digit in the grid) , how can any other castle contain a 1?

A Genius Puzzle, Set by a Genius Creative Setter, input into Genius Software made by a Genius Programmer, Solved by a Genius Solver and enjoyed by everyone - that is a Genius combination! Thank you guys.

Puzzles like this hoover up my time in an ultimately unsatisfying way. I spent 100 minutes solving this, then had to skip through the video to see if Simon had a simpler/more rigorous explanation for the top left region (spoiler: he didn't). There's no doubt lots of nice deductions in this puzzle, but getting that first region, even if I did intuitively find it by exploring the possibilities, left me feeling similarly uncertain as Simon, as to whether I had legitimately narrowed it down to the single valid option. With a different mindset perhaps bodging my way through would be rewarding, but with my mind as it is I end up staring at a grid looking for clarity that never really comes, and my success feels like a false crown.

I am sure there exists another universe where *sudoku* constructors write: _"Regions are formed by side-by-side connected cells"_ or _"The snake moves non-diagonally"_ or _"The loop does not side-touch itself, but it may corner-touch itself"_ and where *chess textbooks* explain that: _"both _*_bishops_*_ and _*_rooks_*_ move orthogonally,"_ meaning they can only move in two orthogonal directions, (e.g. the bishop moves only along the positive- and negative-slope diagonal), while the *queen* can freely move in four different directions (horizontal, vertical, positive-diagonal and negative-diagonal). And a third universe in which their *René Decartes* used the term *vertizontal* to describe an orthogonal reference frame with a vertical axis, and this term was also later adopted by chess masters and kusodu constructors... (weirdly, in that universe, *sudoku* is called *kusodu* and Phistomefel is called Multiphemes, after *Multiphemes Smeik,* a multilingual maggot described in a German book).

I took one look at the rules and thought I will just let Simon solve this one lol very difficult to get started for my limited brain, well done!

I, too, started by trying to locate the 1 strength kingdom. At first, I thought the only possibility was the shape in the top right, shown at 33:33, that took the blue square in r4c9. I hadn't placed a 1 in a castle yet, but I saw this put a minimum of 2,3,4,5 in the castles in that row. This sent me on a merry hunt for the 14th castle I was convinced must exist and, for some reason, I wasn't seeing. It took several recounts before I was confident there were, truly, only 13 castles. Therefore there had to be another possibility for the 1 kingdom. I found it eventually. 😂

Can’t quite believe that a matter of days after I submitted my Enclosure puzzle, this puzzle comes up with similar region logic - I know it’s coincidence, but just so hard to believe!

I would love to see a more methodical proof that other blue squares could not be 1. That's where I actually spent the most of my time for this puzzle. Three options are eliminated immediately by the castle 1, but others are actually provable to be unable to be encircled by a single 9-cell region. The constraint "cant include castle and can't touch more than one blue square" turned out to be pretty powerful and for most squares you do not even need to look how to encircle them, because there is just no way to fit 9 adjacent cells adhering to the constraint.

I loved this puzzle, and its visual presentation! It would be great for other puzzles to have a presentation like this, appealing and readable at the same time

Something funny I think you didn't consider (probably because it's not necessary) is that the total sum of kingdom scores is 45 due to *the secret*. Thirteen of the score points come from castles, leaving 32. Each border counts as 2 points (one in each kingdom), meaning 16 total borders, and that is the number of bridges presented in the grid :)

This is the type of sudoku I'd love to see more of. A theme, visually pleasing, interesting combination of rules.

If you want to fit 6's in castles in six columns, then every column must have exactly one 6. Therefore there must be a 6 in r6c2, which excludes one castle in column 5, so there must be a 6 in r4c5, this exludes the rest of row 4, so we have 6 in r8c1. We are now left with plenty choices for columns 3 and 6, say r7c3 and r1c6. The final one is the lonely r3c4. Surprised me Simon didn't go about it analytically at the start, that's his stronger suit than sudoku :)

Oof, completed this entire puzzle (in 5 hours) forgetting the castle counting rule. It required a bit of visualizing what regions could reach what squares, (I recognized there were limited places to put a region of strength 1, and ruled all but one out) but I’m pretty sure the logic was sound, so doable without the castle size rule.

My first time screaming at the screen. The grey orange region was super obvious to me after the purple and red were made. Yay! I feel like watching has helped my logical intuition (if that makes sense)

this was my favorite video in a while [: ive been really busy so i had to watch it in chunks over the week. i always love coloring puzzles [:

Love how the strongest kingdom is protecting the weakest one from the enemies 😄

@ 11:24 - "I'm struggling here" - Do it logically, rather than picking random cells. There has to be a 6 in each column containing a castle, so start with the columns with only one castle. That eliminates one from C5, so you can select the remaining castle in that column. That in turn eliminates one of the two in C1, so select the other. You're then left with two choices in C3 and C6. Because of R4 and C3, there must be four different numbers in castles. If the largest is 6, those other numbers are 124, and if the largest is 5, the others have to be 134. If the largest is 6, there has to be a 4 in all of the remaining columns. For the 1 region, this was my logic: it can't be a 3x3 without picking up a castle or a second blue square, so it has to be a 2x5 in a corner, with a gap in the row which is not on the edge. The 2x5 must be surrounded by the second colour, which is eight cells, plus the gap cell making nine. The only corner that is not affected by bridges is the top-left and it has to be horizontal to avoid picking up another blue square. The gap has to be the blue square in R2. I don't know why you resisted considering the bridges in the top-right corner. It was obvious that these had to be three different regions and their paths were heavily constrained. The ones in R1 and R2 had to get out, which forced the paths they took, giving you a 2 region. The 2 in the box means the castles don't include 2 and must be 1345. The regions down the right side constrict where blue can go. If it doesn't take R4C4, that region would be forced to hit a second blue square in R6C5, so blue must take R4C4, and R4C3, which places the final green in R8C2. In R4, 5 can't go on a bridge, so R4C1 must be 5, with a 34 pair on the other castles. The same logic in C3 makes R8C3=5. You can now place all of the other 5s. @ 1:16:14 - "It's quite difficult for me to believe this isn't blue" - You could ask where blue gets its 5. It can't reach the one in R7, and it can't use the one in R6 because it's a blue square. The only option left is R8C3. When stuck, I question the efficacy of the strategy to assign Middle Earth kingdoms to the regions. This was a cracking puzzle, with a nice solution path. I think your avoidance of sudoku once again meant that you veered off the path and were missing some easy wins, which made some of the construction easier. You could have got the three regions in the last three columns very early on, and simplified a lot of the later logic. There was lots of irregular sudoku that could be done, which you never touched on.

As regards the 1-total region, you can start by placing it in one of the 4 corners as even on an edge, to cover 3 sides of the most constrained region would take 11 cells. You can then assess that any region 3×3 would take 7 cells, and to keep a shape even close to 3×3, the only alternative to keep a max 9-cell region that uses 3×4 is to place 432 out from the edge. A 1×9 is interrupted by a bridge on all sides. The last alternative is a 2×5 region with a gap in one of its inner sides. The problem with this in the top-right corner is that, for a single region to be surrounding it, you would need no interruptions which the bridges have caused. Therefore, it is clearly in the top-right, and due to having to avoid castles, bridges, and more than one blue square, the placement is simple.

During the break in I find it useful to work out the minimum number of different digits by looking at the maximum castles (circles) in one row or column. In this case we know there are at least 4 and that the total (13) cannot use more than 4 digits. Because 13 from 4 digits must use a 1 (2+3+4+5=14, too much), and there is a cross of row and column which both have 4 castles, the intersection must be a 1.

I appreciate not all these rules are super intuitive but I'm sure Simon could have worked out you can't put 2 blue squares in the same kingdom if he thought about it for another 10 seconds at 36:15 You clearly can't ever take r3c1 with red - you have to take r4c1 as purple because it's a neighbour and now you have to take r4c2 too which is illegal because it's two blue boxes in the same kingdom

An easier line of argument about the starting regions is to look at how many ways you can arrange 18 cells of the "1" region and its boundary, having a single-region border. (It's still a handful but the additional constraints on the grid help narrow this down rapidly )

It's so much more fun to see then the usual sudokus Cause in effect all the rules are fairly normal variante rules, so the adding this kingdom idea it give it a extra touch 👍, love the idea

50:22 This was incredible from beginning to end. The use of the squares and bridges to pen in the shapes to force the regions was sublime.

This puzzle is truly a work of art. The rule set is brilliant, elegant and full of flavor, the initial visual, as well as the visual of the completed puzzle with all the kingdoms and bridges connecting them is beautiful and the solve (in terms of intention as well as how Simon did it) is amazing!

Finished in 74:36. Lovely logic to fill out the puzzle. Plus, I really like the castle and power scheme for the puzzle. Extremely fun puzzle!

I think the one one with 5 castles should be rivendell

There haven't been enough chaos constructions lately so this is a nice treat. Please do more chaos!

Thank you Simon for showing how to solve variant sudoku puzzles. I don’t think I will ever even reach a novice stage let alone the expert level that you clearly display to all of us.

I like this one way more than the yestarday one... Fun notes: Simon forgeting at the middle that no more castle can be 1; he don't pencilmark the blue squares at the end (I think he should). Thanks!:😊

What a puzzle… Had to restart it several times as I ran into a contradiction due to several wrong conclusions. After I finally managed to wrap my head around all the implications of kingdom power and castle numbers, the rest of the puzzle went as smoothly as an irregular sudoku will go (considering my skill, or better: the lack thereof). I finally clocked in a bit shy of two and a half hours - considering the length of the video, I take that as a win. Edit: After watching half of Simon‘s solve, I take it even more as a win. Granted, Simon solved the irregular sudoku much faster and he didn‘t have to reset (I messed up the regions on the eastern border once and drew a wrong conclusion on the green and blue regions on the western border of the grid, which cost me about 45 minutes in total to rectify). However, I feel I was more efficient and observant in my final attempt, especially in the region drawing phase - ignoring that Orange had to grow to r7c8, because it already got its blue score cell (r5c8), for instance. Also, which maybe wasn‘t completely legit as I might not have actively ruled out _every_ other configuration, I settled quite quickly for the score one (Red) and surrounding Purple kingdoms, including its score of 9. Again, what a nice puzzle. I often don‘t even attempt puzzles that take Simon 1.5 hours, but this one kinda caught me, and I had to power through it.

Yay I loved this one when it came out. Glad to see it featured.

I like this sudoku, as it is a new and fun approach to the setting. I feel like playing a medieval game and a puzzle game at the same time.

I started with the castles rather than regions, and came to the same conclusion that the valid solutions were 1246 and 1345, and where the 1 goes. I then looked at where could 2 go in order to satisfy the need for unique digits in castles in row 4 and columns 3 and 6. I couldn't make the 4's and 6's work after that. Then seeing that 5 had to go in the castles, and that 5 can never connect to a bridge, it narrowed down the positions of the 5's very quickly.

This was an absolutely beautiful puzzle with the break-in with the 1 kingdom strength region being both logically approachable as well as nearly jaw-dropping. 37:02 here but I suspect I was not as rigorous in logically proving where I felt like the lower strength kingdoms "had to go." It just seemed like there was only one way forward once the first one was in place. Bravo!

Very happy solving it in 37:37. I quickly homed in on the key starting points which sped things up quite a bit. I wasn't that rigorous in proving my solution was the only possible though, which no doubt would have added time.

Oh boy this looks tough! I’ll just watch today

i had a different break in not sure it was any easier than simons though. i was able to fill in a lot of the castles from the start. first i found out like simon that the castles had to either 1246 or 1345, which lets us place the 1 like simon did. if there are 2s in the castles, then they have to go in castles from row 4 and col 3, in particular not in r6c5 (remember that later) then i noted that it's really hard to place 6s in the castles AND in the blue squares, as most blue squares are not on castles, so i gave it a try. if there's a 6 in the castles, then each of the first 6 columns needs a 6 in a castle. column 2 and 4 only have 1 castle which gives us a pair of 6s. these give us more 6s in columns 5 then 1. those 4 6s see all blue squares except the one in column 8, so another 6 goes there. that gives us the rest of the 6s in castles (7 total). 6 can only go on a bridge with 3s and 4s, and so we get a 34 pair in column 5, and now the puzzle is broken since we can't fill the r6c5 castle. it has to be 1, 2, 4 or 6 since we have 6s in castles, but it sees 4 and 6 in the col, and we have the quota of 1s and 2s in other castles. You can then see simon's solve at 1:07:30 how many digits you get knowing the composition of the castles. i still had to find where to place the 1 region, but it was a bit easier

2 regions, 18 cells, box 1 and 2 of a normal soduku lol, simon is the best

Did anyone else realise Simon was singing 5-7-8-9 near the end to the tune of City Boy's 1978 hit 5-7-0-5? An absolute classic!

39:00 r3c1 cannot be red because your purple has to circle it, and it would force it into more than one blue box. This alone forces the shape of the power 1 kingdom

What an interesting puzzle idea!

This puzzle might be easier to visualize and perhaps solve if the castles were moats and the moats were castles. Then there is one castle in each region and the moats look like circles.

1:54:48 - Wow! Another incredible Marty Sears Puzzle. I’m really chiluffed to have worked out the hidden break in. PS - Simon - you left a blue cell in the red kingdom.

55:05 yes, the upper right corner IS where you should be looking ... because the low-power kingdoms (i.e. the no-castle kingdoms) are so difficult to make. the restrictions are maximized.

no way I was able to solve a 4/5 stars difficulty puzzle after almost giving up halfway through because of a false 1 that I had accidentally placed a while ago without realizing

Most enjoyable, thanks, even though I am always uneasy about not being able to rigorously rule out particular shapes to my own satisfaction.

whow, finished it in less than half the time! 41:32 instead of 94:53 , to be fair i probably lucked out on this, i almost immediately found the box 1 because it could only fit there to be touching a single other box and have no castle, then i expanded the box 2,3,4 on the right, looking how it fit perfectly, and then tried to make box shapes that would fit the count and restrictions and found the correct shapes quickly (except for 4 cases of box 5 and box 7, but with 7 ending in a castle, it wouldn't work, so i switched those 4 cases around so the 5 and 7 switched case and then it was all basically sudoku at this point

Simon doing a region building puzzle while avoiding building the regions on the right side of the grid...

around 55:00 we know that green kingdom has 3 castles which occupies 2 positions of sixes so the "1246" combination can no longer work (we have 6 columns that have castles but 2 of them are in the same kingdom) also 56:37 the castles in row 4 include the digit 4 so r4c9 can't be a 4... not helpful in any way though 😅

Holy cow! I legitimately solved this faster than Simon! A first!!

I usually love these puzzles with figuring out regions with colors, but found the logic a bit hard to trust myself with. I got to where Simon is at 1:30:00 in the video, I had some pencil marks that made the puzzle break in the 1 power kingdom leading to heartbreak, I think I had wrongly ruled out 8 from r2c3 or something. Slightly relieved when I checked the video to see my mistake was only being excessive and sloppy with my pencil marks.

57:24 with a peek at the video at one point (I marked 3 OR 4 regions around what ended up being region 3 using two colors and then forgot those two colors could be the same region and typed in a 4). I thought about the 1 region pretty early on and kinda figured it had to be in the upper left corner. I don't think I proved it to myself undeniably, but just didn't see what else could work. So, I'd say half lucky on that one.

39:25 the question of uniqueness at the very beginning is a tiny bit unresolved. however, there is NO OTHER WAY of doing it. i checked very carefully. a couple things can be set as principles: 1) the surrounding kingdom may not cover two of the four edges ... there is not enough "length". 2) you need to have a near-maximum area per length, so thin rectangles won't work. also, it will be very difficult to make the low-power kingdoms, which require NO castles, and FEW neighbours (leads to next several phases)

What a beautiful puzzle!

How do people input these kinds of non-standard grids into the software? The browser app seems to only be able to play puzzles, not edit them, as far as I've been able to find. And I picked up the Steam version and the puzzle creator there only supports standard rules. Can't even put domino dots or killer cages.

At the end of the puzzle, Simon's OCD didn't trigger when a red square was still left blue, but mine did!!

What a brilliant and fun puzzle!

Are we not going back to the DST upload time or is their spring ahead not for another couple of weeks?

I got to the same point Simon is at at 1:26:00 in about the same amount of time, but then Simon only takes 10 minutes, and I've been stuck for an hour trying to fix rickets. Guess my sudoku fundamentals are letting me down.

I missed the "it's not a regular sudoku with 3x3 grids being meaningful" part. The 4s toward the lower left corner were driving me nuts.

I'm troubled with the red and purple in the corner, as Simon was. Is there a way to more solidly explain why it must be that shape in that corner? In sketching things in I actually guessed the exact shape Simon settles on. But if even Simon can't pin the "why" down it's hopeless for me.

Not sure about rigor, but I spent some time drawing up possible contained kingdoms. I got a vid.

At 1:05:30 Simon does something I've never seen him do before, namely speculate his way to a final region division with anything other than logic. Doesn't seem very Simon to me. Did he send out the AI this evening to take his place?

Loved this one! 43:14 for me

54:50 if r4c4 is not the blue region, then we have two new regions at r4c4 and r4c5 which would clash in cell r5c6

43:19 for me. Very confusing puzzle. Quite interesting once you understand it, though.

Good job, Simon.

Am I missing the logical leap that said the shape in the upper left was better than the shape in the upper right? He found the upper right, started working on the left, played around with it, and then decided to go from there. @33:30 and @40:18

I got the starting part well before he did then just was so much slower at the actual sudoku I was probably done with the kingdoms by the time he was still working on finding some of the blue green edge and he still finished the rest before me... only by a minute or two but still

Dang I knew very early in my attempt that the 1 region was top left but kept making bad assumptions around the bounding of the 234 regions and getting conflicts for the castles and making some terrible mistakes.

50:09 For me, wonderful break-in in the corner, break-in in the spotli-

Now to get Albert to watch this video *Today* 😁🥰

amazingly, the lmg difficulty rating should only be 3. literally anyone can do this puzzle, although a lot of WORK is required. but only basic reasoning is needed, and no special sudoku knowledge. the approval rating of 199% (everyone likes it) is appropriate.

1:14:56 - 1:15:28 I don't really get why it's impossible for R7C3 to not be blue. We can have max 5 regions + 2 castles that are already in the blue region, so we just need at least one more castle, and it can be R7C6. Right? Edit: fixed typo

Great puzzle, and a wonderful solve, as always, Simon! Thank you. A word of caution, though Simon: It appears that Sudoku can be Hobbit forming.

Given the uniqueness of the initial area, what is the purpose of the bridge between r1c5 and r1c6? Doesn’t the castle already forbid entry in that direction?

Can we have a “castle” count? (The number of times Simon said “castle” in the video)

Castle became the new norri norri

Simon kept using the term “tricky” and I was hoping for him to change to “tricksy”.

Is this basically a Carcassone sudoku?