There’s a small extension to the Windoku trick explained around 10:15. If you mark off the 4 sets made by the windows, the two sets made by the columns (Simon highlights them in purple), and the two sets made by the rows (Simon highlights them in blue), you’re left with the final set as all the cells the corners of the windows point to, i.e., r1c1,5,9, r5c1,5,9, and r9c1,5,9. None of those cells can hold the same digit. Not sure if it would have helped with this puzzle, but it’s a good trick to keep in the back of your mind for other Windoku puzzles!
Yes, having opened the puzzle and glimpsed the words "antiknight" out of the corner of my eye as I did so, I then had to re-read the rules several times to be sure that it _wasn't_ part of the rules, thought I must be going mad and imagining things, and only quite some time later realised it was the setter's name!
Love hearing the children in the background having fun. Definitely put a smile on my face even before Simon mentioned it! And what a puzzle. What a wonderful windoku in the fog. The six in the middle was beautiful.
If I am not mistaken. the corollary of what you said about windowku is that R1C159, R5C159 and R9C159 are also a set of digits 1-9. Thanks for the daily video, it is a very good exercise for aging brain.
I can't ever see the logic. . . but my enjoyment of the videos comes purely from watching Simon get so much pleasure from working it out. His joy and delight is infectious!
I was kind of looking for a comment that gave a hint to the first clue. I don’t normally look for hints, but I’ve literally spent forever on this puzzle. I got it in 30 seconds after this comment.
I think this is the first time I've spotted the first digit before Simon, which has surely earned me some chocolate cake (or at least a slice thereof!)
I love how this puzzle tricks you into thinking all those digits are 1's then finally finding the first digit makes you realize it was all a red herring all along, very sneaky.
I really like how you wait a little bit as you realize something profound about the puzzle. And it's usually when I'm stuck on some bit of hard logic, so watching you pause, then be "it's the five or seven at the top" is just the trigger I needed for me to push through and solve the endgame! It happened two other times in the beginning too, which really nudges me in the right direction. So thank you for that! (Made it in 80m48s, with three nudges. I'm happy about that!) Amazing puzzle.
It took me 10 hours to solve this and now I can watch Simon solve it in less than a 10th of the time. How he does these without getting stuck is incredible!
I totally loved the break in! and very nice how the solving path (I presume there aren't too many up to that point) leaves the last bits of fog over the last few clues. Funnily, Simon goes about explaining set theory with a nice example, but somehow doesn't apply it to get the center digit 😉I think this was much easier that way, it took me a minute once the arrows were pencil-marked (took me much longer to write it down here!): so, keep the four green cages (four sets of 1 to 9...) then color four other sets purple: r4, r6, c4 and c6 (careful! corners in box 5 are counted twice). Remove common cells with both colors, and you're left, among other things, with purple donut in box 5. Given that green does not contain any 6, neither does the donut, hence the center digit.
U can get the 6 on another way. if u use all arrow cells in box 1,3,7 and 9. u can form the outer Phistomofel ring. then u have R1 C159, R5 C159 R9C159 as set from windoku. the 8 outer cells are all in the phistomefel ring, without a 6, and this six can only go in R5C5.
The windoku trick Simon demonstrated goes further -- if you count the sets Simon laid out there are four of them, which combined with the four 3x3 boxes makes 8 non-overlapping sets of the digits 1-9 -- since a Sudoku is made up of 9 sets, you also get one more set in the remaining cells (namely all the cells where rows and columns 1, 5 and 9 cross)
This was how I found the break-in. After pencilling the arrows we're left with 6s around the edges in boxes 1, 3, 7 & 9, which obviously can't use the corners without breaking the loop, leaving only the centre square in the "windoku pseudo region 9" you describe for the opening digit. Very elegant though.
What a remarkably clever puzzle. I didn't think it was possible to find a FoW puzzle that difficult but this one proved me wrong. Took me a while to spot the beginning and then I needed a nudge from Simon to spot r2c5. Kudos to Antiknight.
That worked out really nice. That "6" in the middle did a lot (nice spot). That made a 9. Then I looked where 9 went in that 1window (it's in col3 in box2) And a "9" had to appear in window2 (the only place for it was in the circle). It was the 2s (in col1 and and the 2 in row9) that forced a 1&2 on that 9arrow with a 1 (so 125 in there). I think it was the 2 being forced onto that arrow in window1 that made that 124+1=8 (disambiguating them). After some more things (a 123 triple up col8 and a 123 triple up col7) then it was those "extra regions" Simon mentioned. Cool stuff the Setter put in here. Nice.
Thanks to the CTC channel I know that when I've been solving for almost half an hour and I don't get anywhere I have to remember SET. The logic that led me to the 6 in the center was to take R4, R6, C4, and C6 as the orange group (r4c4, r4c6, r6c4, and r6c6 count double), and the four cages as the blue group: The groups are equivalent even if we remove their intersections (r4c4, r4c6, r6c4 and r6c6 remain in the orange group because they counted double). Therefore, 4 2x2 squares remain blue (those with cells illuminated at the beginning) and among other cells, all the cells of box5 except the central one are from the orange group. Therefore the only digit that cannot be in the blue squares is the center (6) and also all the other digits appear in the blue squares (so I immediately knew that there was a 5 in the arrows, which added to 9). Reaching the state of min 38:00 as there are two 8s and two 3s in the blue group, in the orange group r1c6 and r9c4 must be a 3 and 8 pair. Great puzzle with amazing logic, and excellent video as always.
For those who were wondering why you can't put a pencil mark of any kind into r4c6, it's because it's a given. I wonder if Simon knew that, which is why he used colours?
That's an astounding break-in (which I totally failed to find). After some study it's not hard to guess _where_ the first digit will go, but who would ever guess it was _that_ digit?
I finished in 144 minutes. I had spent about 55 minutes, desperately trying to find the break-in. I had thought it had to do with the limitation of low digits combined with windoku logic. However, that is when I saw that 6's couldn't go anywhere but the outside, so I put them in not expecting much. Then, I noticed that there had to be four 6's, so the centers couldn't have any. I moved on, until I haphazardly saw the 6's again and was blasted with the break-in. The 6 in the center box was forced. That was so amazing to see. It feels easy in hindsight, but that felt quite hard before I saw it. It was like one of those illusions that require you to focus on the shadows or empty space to see an image. I was so happy finding that. The rest was still not easy. I think my favorite part was labeling the 38's around the grid and disambiguating them after fully labeling them in box 2, which unwinds everything. I really liked this one. It had crazy logic. Great Puzzle!
@36:50 Interestingly, another way to discern r8c2 is 9 is to ask where 5 goes on the arrows, because if 5 is absent from ALL 4 arrows, it would need to be a Shroedinger Cell with 6 in the middle. At the point 8 is settled in r8c8, this also applies to 9 needing to be on an arrow. That Windoku Logic pulls a lot of weight as you narrow those digits down.
Once Simon eliminated the 5s from the arrows in boxes 1,3, and 9, then the arrow in box 7 _had_ to have a 5 on it. Otherwise, it's the 6 issue all over again, and you can't also put a 5 into the centre cell.
I noticed that, too. And thought after explaining that 1 couldn't be in R9C6 with that 6 in the middle, it's quite astonishing he doesn't use that logic on the 5s
@@janiswehner4071 Despite my pointing it out, it still amazes me that Simon and Mark solve these all in real time. When I watch afterward (and I solve a lot more of these on my own now), I generally see places where Simon figured out bits faster than I. It's a little nice, actually, that I sometimes see bits faster than he. :)
Hey Simon, wonderful and most interesting way to follow as usual. By the way, there IS a 3 in the corner in the third windoko, so the song would have been valid 🙂
Lovely puzzle, I love it when theres a million places to look. There are a lot of differences between my solve and Simons solve and that is just wonderful. Something weird and frustrating happened to me with this puzzle. I had a different start to the puzzle, I was quickly able to figure out that r3c2 had to be a 2 and from there it became obvious what the white dot had to be. After watching the video I tried to remember what exactly led me to these conclusions to try and share my story, but I couldn't do it. I was able to eliminate 4 from r3c2 again, because that breaks the arrow in box 3, but not more than that. Now I'm wondering if I had some faulty logic and got (un)lucky, or maybe I realized something special at the time and now it slipped my mind. I'd rather be sure that I had a legit solve of the puzzle than whatever weird feeling I'm currently having. Long story short while this probably made the puzzle a bit easier at some point, it didn't get me anywhere directly, so my next digit was also the 6 in the middle box. If anybody finds a logical way to start with these digits I'd love to hear how you got there :)
..enjoyed watching you solve this.Loved the rules about (you didn't use them) the cells in c3,4,5, r 1,5,9 being a set of 1-9. Also the corner cells, middle cells of each outside row/column, and central c5r5 cell also form a 1-9 set..
I got the first 6 in the grid I got completely stuck and i never worked out the 5 in box 2 (I should say 7 but the logic was all about 5s). Thank you Simon it was driving me up the wall and i would never have seen it!!!
From 29:00 onwards, it's possible to get the arrow-sum for the bottom-left arrow in one step. There's a 9 in what I call "the left remainder" (i.e. the cells Simon coloured purple at 10:52). So in box 1, 9 must be in column 1. Using that and left remainder, the 9 in box 7 has to be on the green cells, and it's obvious which one it has to be on.
11:16 there is actually one more trick to this SET theory! After highlighting the cage sets and then the virtual sets in the rows and columns, this leaves nine cells leftover in the corners and between the cages which are also one final set of the digits 1-9 with no repeats.
The logic leading to the 6 was that it was missing from all four 2x2 boxes we defined early on. Since any digit missing from those boxes had to appear in the center, and that could only be the 6, that meant all other digits had to be represented somewhere in those four boxes. Consequently there had to be a 5 in the lower left box, as there could be no 5 in any of the other boxes. That then unlocked a number of clues that helped move the puzzle along.
👉 Simon, it would be nice for me to find the puzzle description and link *consistently* at the beginning of the video description section (which is where I am always *guaranteed* to find them in Mark's videos). Just to make it simpler for me to locate the puzzle link, when I am in a hurry [Edit: or whenever my brain is *tired* and spontaneously switches to "automatic click" mode]. I suppose others would appreciate this as well.
i understand what you want, but it will take like 5-10 seconds longer to find the link by viewing the full description and find the correct link. im pretty sure you not in that kind of hurry.
@@FluffSWE Even though I am a CTC patron, I hate when I click the Patreon link by mistake. And it does happen. I sometimes do not pay attention, even when I am not in a hurry.
22: 44 I usually take 2x Simon's time, if not longer (if I finish at all, which is far from a given). This is my first time ever to solve a puzzle faster than Simon, so it's peculiar that the margin is so large. I thought the break-in was beautiful but not difficult to see, and the rest of the puzzle was quite easy. I'll have to watch Simon's video later to see what he struggled with.
The 2*2 blocks in the corner cells (the circle and the three cells on the arrow) can be used in a variant of the Phistomefel ring. Doesn't help with the break-in, but gives a little leverage later in the solve.
It took me a minute or so to deduce the first digit, but I really struggled after that, and was unable to spot the crucial logic on r2c5 without Simon's help.
Got the same first digit, but different logic path. I started with the expanded phistomophel ring. Then I used the Windoku sets on both columns and rows to get the 9th set of the 4 corners, 4 side-middles, and center cell. That last set has all the digits, but the phistomophel ring marks 8 of them as unable to hold the value that can't appear on the arrow or as a total.
25:45 Interesting, I saw the 6s but by a superficially different (if underlyingly similar) route - I looked at what happens if you did put a 6 in one of the green corner cells in box 5 -- if you do it limits the positions for 6 neighboring L-shaped regions such that they rule out any position for a 6 on the remaining L...
Interesting, I feel like I haven't noticed this in previous fog puzzles seems like probably the software is suddenly having problems with marks in ~~~SPOILER SPOILER SPOILER~~~ ~~~ ~~~ ~~~ fog cells with an underlying given, of which that's the only one in this puzzle? *edit* Might just be that we haven't seen this unexpected behavior because we haven't had a previous fog puzzle on CTC that's had givens in the fog? Took a peek at a bunch of them just scrolling down the feed to see if this same thing happens and thus far haven't found one that used them-everything I've looked at either had no given digits or treated any givens like placed digits and so had fog cleared around them from the start...
44:07 finish. I missed how the logic of how Simon got 6 in the middle; I went a different way. Using Window logic, the corners, the center of each edge, and the center cell form a set of 1-9. Using modified Phistomafel logic, it shows that 6 can't be in any of the aforementioned set except for the center cell. But definitely a fun puzzle!
Imagine you are a first time watcher and you skip the video to half way. You would never understand how Simon has only put down 2 digits but he has solved half the puzzle 😂
The Werefrog got to the 6 in box 5 after about 10 minutes, but then it slowed down. The Werefrog found a bunch of 1-2 pairs going around, but then the 7 in box 2, that was hard. The Werefrog actually mapped out all the places 3 and 8 could go around the grid first, then noticed the 7 in box 2 was limited to 2 places, and if it was in the other one, that required 8 to go to the wrong spot. Great puzzle to fill a few hours.
the 125 triple for the 9 arrow could've been realized sooner, the moment 5 couldn't go into lower 8 arrow, no other place had 5, and one of the arrows had to have 5, otherwise it would've happened the same that happened to 6, and there's no such thing as a Schrodinger cell (5 and 6 in the center), but the impact is not very large overall thanks for sharing! amazing solve as always Simon!
At the end, Simon was saying he’d never seen logic like the 5 before, but it’s the same logic used on the 6 in the break-in. 😂 (Love you, Simon, never change.)
I found this to be quite hard, but i also didn't know the windoku tricks. Edit: My solve path was incredible different from yours as i missed the math logic on the top 2 arrows. After the break-in with the 6 in the middle and the 9 arrow i pencil marked the 9 in the top-left cage which gave me the 9 in the bottom left cage and 78 in all other cages. because of the same logic as with the 6, there must be a 5 on one of the arrows to avoid a conflict in the middle cell. That now forces a 2 on all the arrows.
I assume (and therefore everyone else has) the "do not overlap" rule means the heads of the arrows cannot share a cell? Cause otherwise how do you know each arrow arm passes through the fog at the start of the puzzle rather than two heads meeting and 'touching'? To begin with I assumed the rule meant just arms couldn't cross over each other, rather than no part of the arrow (including bulb and head) can share a cell with another arrow.
I found this unclear. So had to look at the beginning of the solve where Simon neither considers nor mentions that possibility. It makes no sense to me that the circle is part of the arrow, but I will have to accept that assumption to get on with the solve. Unfortunately it has already somwhat spoiled the solve for me, having skimmed through the comments, and also watched part of Simon's solve.
Had to watch to 47:46 to solve, but I seemed to get stuck on the exact same things that Simon did, so I don't feel too bad about that. Not as much direction from a fog of war puzzle than I'm used to, but that's not necessarily a bad thing. Still an excellent puzzle, had much fun solving it :D
Why don't you consider putting a circle in the R2C2 at the very beginning? One line segment could be an arrow connected to the circle while another could be an arrow pointing to that circle. There is no overlapping arrows and no circle with more than one connected arrows.
Rules: 05:24 Let's Get Cracking: 09:35 What about this video's Top Tier Simarkisms?! Three In the Corner: 2x (55:35, 55:47) Bobbins: 1x (32:10) Diddly Squat: 1x (31:45) And how about this video's Simarkisms?! Hang On: 6x (05:45, 25:10, 28:01, 34:49, 48:55, 49:54) Ah: 6x (24:53, 24:55, 34:49, 36:10, 47:40, 55:19) Pencil Mark/mark: 6x (18:04, 18:10, 18:17, 43:01, 50:14, 55:00) In Fact: 5x (07:15, 20:41, 20:59, 24:38, 40:19) Wow: 5x (41:35, 47:44, 59:40, 59:44, 59:44) Beautiful: 4x (28:21, 30:15, 30:59, 1:00:10) Obviously: 4x (10:03, 10:30, 26:46, 31:38) Goodness: 3x (23:13, 35:09, 40:59) Sorry: 3x (20:34, 23:20, 38:15) Missing Something: 3x (22:53, 44:46) By Sudoku: 3x (10:05, 26:23, 59:07) What Does This Mean?: 3x (31:56, 49:40, 52:05) Cake!: 3x (03:33, 03:37, 04:06) Symmetry: 3x (15:49, 15:52, 15:55) Clever: 2x (50:06, 53:27) Stuck: 2x (01:40, 1:00:07) Lovely: 2x (03:00, 49:13) Shouting: 2x (03:12, 03:29) Plonk: 2x (08:06, 57:55) Thingy Thing: 2x (29:05, 41:12) What on Earth: 1x (30:47) Bother: 1x (40:02) Out of Nowhere: 1x (51:10) I Have no Clue: 1x (23:20) Brilliant: 1x (03:18) Incredible: 1x (48:08) Our old Friend Sudoku: 1x (29:23) Of All Things: 1x (37:25) Surely: 1x (36:15) I've Got It!: 1x (19:10) Pregnant pause: 1x (30:59) That's Huge: 1x (35:28) Most popular number(>9), digit and colour this video: Ten (10 mentions) One (127 mentions) White (19 mentions) Antithesis Battles: High (4) - Low (1) Even (7) - Odd (4) White (19) - Black (6) Row (24) - Column (22) 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!
Wow that was brutal! 165:12 was my time. I needed a hint to get me past the logic to knock 5 out of r2c5. After that the rest of the puzzle resolved without much issue. I really didn't expect it to take me that long because I actually placed that 6 in the middle in a reasonable amount of time (and I agree that it was an extraordinary first digit!).
Probably the intended break in: The four cages are 4 sets of digits 1-9. Then rows 4, 6 and columns 4, 6 are 4 sets of digits 1-9. After, you'll notice entire box 5 is highlighted except for the middle cell. Since a 6 cannot go on the opposite highlighted cells, a 6 must go there.
Did you ever notice your thought at 23:00 was actually correct? I figured that out in one of those newspapers sudokus you mentioned in the beginning as well. I'm fairly certain I even had proof for it. I was certain you would use that to solve this puzzle but instead you did some genius 6 in the middle reasoning.
I had an idiocy brilliancy in finding the center 6. From set theory I deduced that r1c1,r1c5,r1c9, r5c1, r5c5, r5c9, r9c1, r9c5, and r9c9 were a set of digits 1-9. When considering where the sixes were in the four 3x3 boxes I was able to eliminate the six from all of the of members of that set other than r5c5, when captain obvious would simply note simple sudoku does the trick.
I'm aware of a couple other sets. After you get those sets you mentioned, the remaining are also a set. The other is that the digits on the outside of day the to left square that are not in the window, and the same as the digits on the window which are not in the siding sudoku square. That's all I know though.
The way I broke in feels like it was more work for the same idea. I ended up using set theory with r4+r6+c4+c6= the 4 windoku boxes. You end up with 8/9 cells in the center box in one of the sets and they all can't have a 6 because of the arrows in the other set. Unfortunately I never saw the logic for that 57 cell, but at least, as always, I got to enjoy Simon's solve.
90 minutes for me. Seems like there were several breakins to get to the end. Including a y-wing or 2. Would the first break be classified as a power-wing or a ghost-wing
So glad Simon got stuck at the same place I did (albeit not so badly) Odd that he didn't keep going on windoku to get 9 complete sets (once you have the gaps vertically and horizontally you have 9 diagonal-to-the-windokus left)
While the arrows are quite clear, as well as some of the consequences (I had a feeling that the high digits will be somewhat crowded in rows and columns 4 and 6), I was stuck here. Thanks to Simon's "what I know about Windoku", I got the first (and then immediately the second [non-given]) digit, it is really quite extraordinary. (By the way, an immediate corollary of the additional sets of 9 is that there is a last, quite spread, set of 9 digits, made up of the cells r159c159. This helped me near the end a bit.) I got stuck again for quite a while, until I figured out that *both* of the upper arrows needed to end in a 1. Total time was 204:02 (solve couner 5926).
I figured out the extraordinary digit fast enough, but it was still a long grind until I understood i had to switch my mentality to windoku. Solved in 1h48m47s.
39:01, but I had to watch the video to see that a 6 had to be in r5c5 and then again disambiguate r2c5 (neat trick!). Skipping through, I feel like I figured out the digits on the four "given" arrows pretty quickly, that took me about 7 minutes.
To my mind, "arrows don't overlap" translates as no cell may be occupied by two arrows, and that includes every part of the arrow (including circle and tip).
@@RichSmith77 That's probably the correct interpretation, but to me the "circle contains the sum of digits on the arrow". So if the circle is part of the arrow, it contributes to itself, which I think requires math skills well beyond the average solvers capabilities. Certainly mine. In my opinion a ruleset shouldn't be open to interpretation or assumptions.
@@joethornton5321 They do usually (and in this case) say digits *along* the arrow, rather than simply on the arrow. This may also be open to interpretation, but I can get behind the idea of "along" meaning along the shaft and tip of the arrow. Alternatively, it could be argued "arrow" as a word has two frequent meanings, even in the context of an "arrow" sudoku. They're rarely described as "arrow and circle" puzzles. The arrow in an "arrow type puzzle" stands in for the entirety of the tip, shaft and circle. They all make up the arrow, in that sense. Yet also, it's common to refer to the number of arrows coming from each circle, in which context "arrow" just refers to the shaft and tip. Which meaning the word "arrow" has, is often dependent on the context in which it is used. Having said all that, yes, I guess it is open to interpretation, and that's not ideal.
Hi there and hey diddle diddle. I'll give you a cute little riddle. Nine digits you enter, With one at the center, Four corners and every side's middle.
Brilliant puzzle, one of my favourite FoW puzzles so far. @ 18:05 - Shame on you for Pencil Marking ;) None of the 2x2s can contain 6, so ask where the 6 goes in each cage, and you get a Catherine-wheel effect, which places 6 in the centre. @ 28:31 - "I'm now worried that I should have appreciated that far more quickly" - you could have got it ten minutes earlier, but I wouldn't say you should have. It's not obvious until you ask the right question. The next question you need to be asking is where do all the 1s and 2s go. You didn't do this, but if you had, you'd have found there were 12 pairs all over the place. I was surprised you didn't consider the expanded Phistomefel Theorem, which seemed fairly blatantly set up from the start. This came into its own once the 12 pairs were placed.
I actually managed to find a set theory pattern that proved to me that every digit in row 5 were digits that were on one of the arrows except the middle digit and that's how I found the 6 (and as a bonus it told me that the arrows contained every sudoku digits except 6 at least once)
(more specifically, if you make a set of the 4 cages aswell as a set containing both box 4 and 6 and column 4 and 6 you can clearly see that the only digits left are on an arrow and the only digit unacounted for in row 5 is the middle digit and it has to be a 6 since that's the only digit that couldn't appear on the arrows)
Didn’t expect this one, so thanks for the ones who’ve recommend it. This will be a really nice treat for the night 🥳🙏.
More phenomenalness from you!! Loved it. Always a joy to see your "powers" in setting be at full force. 🙂
@@davidrattner9 Thanks David! I’m happy it was to your liking 😁
@@davidrattner9👍🏻
Thank you for showcasing the Windoku version of my theorem
Brilliant construction! Was a very nice way for me to spend 2.75 hours
Simon is officially a celebrity to me at this point. If I’m ever in England, I’d love to buy him a pint.
Agreed.
Just gotta find one of those parties we're not supposed to want to talk to him at!
I live in England, and I'd love to buy Simon a pint. A CtC social would be a great idea!
You wish you could get within spitting distance
Follow maverick. You’ll be sure to find Simon
There’s a small extension to the Windoku trick explained around 10:15. If you mark off the 4 sets made by the windows, the two sets made by the columns (Simon highlights them in purple), and the two sets made by the rows (Simon highlights them in blue), you’re left with the final set as all the cells the corners of the windows point to, i.e., r1c1,5,9, r5c1,5,9, and r9c1,5,9. None of those cells can hold the same digit. Not sure if it would have helped with this puzzle, but it’s a good trick to keep in the back of your mind for other Windoku puzzles!
..spotted this too..
I realised that during the watch and feel smart about myself now. thank you :)
This puzzle was an absolute joy, especially after recognizing the setter was a name and not a restriction in the rule set. 99:21
Yes, having opened the puzzle and glimpsed the words "antiknight" out of the corner of my eye as I did so, I then had to re-read the rules several times to be sure that it _wasn't_ part of the rules, thought I must be going mad and imagining things, and only quite some time later realised it was the setter's name!
Love hearing the children in the background having fun. Definitely put a smile on my face even before Simon mentioned it!
And what a puzzle. What a wonderful windoku in the fog. The six in the middle was beautiful.
If I am not mistaken. the corollary of what you said about windowku is that R1C159, R5C159 and R9C159 are also a set of digits 1-9.
Thanks for the daily video, it is a very good exercise for aging brain.
Yep. And i totally colored those extra ”windoku sets” and used them in my solve 😋
I can't ever see the logic. . . but my enjoyment of the videos comes purely from watching Simon get so much pleasure from working it out. His joy and delight is infectious!
That first 6 may be my favourite break-in of all time!
I was kind of looking for a comment that gave a hint to the first clue. I don’t normally look for hints, but I’ve literally spent forever on this puzzle. I got it in 30 seconds after this comment.
Oh wow, that was helpful!
I think this is the first time I've spotted the first digit before Simon, which has surely earned me some chocolate cake (or at least a slice thereof!)
I love how this puzzle tricks you into thinking all those digits are 1's then finally finding the first digit makes you realize it was all a red herring all along, very sneaky.
I'm a bit addicted to this channel 😊, very entertaining for me. Thank you CTC 👍👍👍
I really like how you wait a little bit as you realize something profound about the puzzle. And it's usually when I'm stuck on some bit of hard logic, so watching you pause, then be "it's the five or seven at the top" is just the trigger I needed for me to push through and solve the endgame! It happened two other times in the beginning too, which really nudges me in the right direction. So thank you for that! (Made it in 80m48s, with three nudges. I'm happy about that!) Amazing puzzle.
That was pretty hard, and that break with the 57 in R2C5 was otherworldly
It took me 10 hours to solve this and now I can watch Simon solve it in less than a 10th of the time. How he does these without getting stuck is incredible!
Enjoyed watching that. Simon made it feel almost as if I could actually do it. I couldn’t of course but lovely to feel that I could.
I feel that way a lot! 🤔
I totally loved the break in! and very nice how the solving path (I presume there aren't too many up to that point) leaves the last bits of fog over the last few clues.
Funnily, Simon goes about explaining set theory with a nice example, but somehow doesn't apply it to get the center digit 😉I think this was much easier that way, it took me a minute once the arrows were pencil-marked (took me much longer to write it down here!): so, keep the four green cages (four sets of 1 to 9...) then color four other sets purple: r4, r6, c4 and c6 (careful! corners in box 5 are counted twice). Remove common cells with both colors, and you're left, among other things, with purple donut in box 5. Given that green does not contain any 6, neither does the donut, hence the center digit.
At 54:14 you could have used the 1234 quadruple in r2 to place 8 in r2c6 and disambiguate the 78 pair in the circles
U can get the 6 on another way.
if u use all arrow cells in box 1,3,7 and 9. u can form the outer Phistomofel ring. then u have R1 C159, R5 C159 R9C159 as set from windoku. the 8 outer cells are all in the phistomefel ring, without a 6, and this six can only go in R5C5.
The windoku trick Simon demonstrated goes further -- if you count the sets Simon laid out there are four of them, which combined with the four 3x3 boxes makes 8 non-overlapping sets of the digits 1-9 -- since a Sudoku is made up of 9 sets, you also get one more set in the remaining cells (namely all the cells where rows and columns 1, 5 and 9 cross)
This was how I found the break-in.
After pencilling the arrows we're left with 6s around the edges in boxes 1, 3, 7 & 9, which obviously can't use the corners without breaking the loop, leaving only the centre square in the "windoku pseudo region 9" you describe for the opening digit.
Very elegant though.
🤯
I noticed that too and wanted to comment.
What a remarkably clever puzzle. I didn't think it was possible to find a FoW puzzle that difficult but this one proved me wrong. Took me a while to spot the beginning and then I needed a nudge from Simon to spot r2c5. Kudos to Antiknight.
That 6 was awesome! I kept begging Simon to look at 9s but he just backed into them anyways
That worked out really nice.
That "6" in the middle did a lot (nice spot).
That made a 9.
Then I looked where 9 went in that 1window (it's in col3 in box2)
And a "9" had to appear in window2 (the only place for it was in the circle).
It was the 2s (in col1 and and the 2 in row9) that forced a 1&2 on that 9arrow with a 1 (so 125 in there).
I think it was the 2 being forced onto that arrow in window1 that made that 124+1=8 (disambiguating them).
After some more things (a 123 triple up col8 and a 123 triple up col7) then it was those "extra regions" Simon mentioned.
Cool stuff the Setter put in here.
Nice.
Happy sounds of children and Simon having fun! That’s why I tune in daily…..😊
Thanks to the CTC channel I know that when I've been solving for almost half an hour and I don't get anywhere I have to remember SET.
The logic that led me to the 6 in the center was to take R4, R6, C4, and C6 as the orange group (r4c4, r4c6, r6c4, and r6c6 count double), and the four cages as the blue group: The groups are equivalent even if we remove their intersections (r4c4, r4c6, r6c4 and r6c6 remain in the orange group because they counted double). Therefore, 4 2x2 squares remain blue (those with cells illuminated at the beginning) and among other cells, all the cells of box5 except the central one are from the orange group. Therefore the only digit that cannot be in the blue squares is the center (6) and also all the other digits appear in the blue squares (so I immediately knew that there was a 5 in the arrows, which added to 9). Reaching the state of min 38:00 as there are two 8s and two 3s in the blue group, in the orange group r1c6 and r9c4 must be a 3 and 8 pair.
Great puzzle with amazing logic, and excellent video as always.
Each time I watch Simon complete a fog of war puzzle, Simon convinces me that fog of war puzzles are my favorite as well.
For those who were wondering why you can't put a pencil mark of any kind into r4c6, it's because it's a given. I wonder if Simon knew that, which is why he used colours?
That's an astounding break-in (which I totally failed to find). After some study it's not hard to guess _where_ the first digit will go, but who would ever guess it was _that_ digit?
I finished in 144 minutes. I had spent about 55 minutes, desperately trying to find the break-in. I had thought it had to do with the limitation of low digits combined with windoku logic. However, that is when I saw that 6's couldn't go anywhere but the outside, so I put them in not expecting much. Then, I noticed that there had to be four 6's, so the centers couldn't have any. I moved on, until I haphazardly saw the 6's again and was blasted with the break-in. The 6 in the center box was forced. That was so amazing to see. It feels easy in hindsight, but that felt quite hard before I saw it. It was like one of those illusions that require you to focus on the shadows or empty space to see an image. I was so happy finding that. The rest was still not easy. I think my favorite part was labeling the 38's around the grid and disambiguating them after fully labeling them in box 2, which unwinds everything. I really liked this one. It had crazy logic. Great Puzzle!
@36:50 Interestingly, another way to discern r8c2 is 9 is to ask where 5 goes on the arrows, because if 5 is absent from ALL 4 arrows, it would need to be a Shroedinger Cell with 6 in the middle. At the point 8 is settled in r8c8, this also applies to 9 needing to be on an arrow. That Windoku Logic pulls a lot of weight as you narrow those digits down.
Once Simon eliminated the 5s from the arrows in boxes 1,3, and 9, then the arrow in box 7 _had_ to have a 5 on it. Otherwise, it's the 6 issue all over again, and you can't also put a 5 into the centre cell.
I noticed that, too. And thought after explaining that 1 couldn't be in R9C6 with that 6 in the middle, it's quite astonishing he doesn't use that logic on the 5s
@@janiswehner4071 Despite my pointing it out, it still amazes me that Simon and Mark solve these all in real time. When I watch afterward (and I solve a lot more of these on my own now), I generally see places where Simon figured out bits faster than I. It's a little nice, actually, that I sometimes see bits faster than he. :)
16:30 ALL I CAN THINK IS... TEENAGE MUTANT NINJA TURTLES....
16:30 simon inadvertently makes the ninja turtles
I thoroughly enjoyed watching Simon exorcise the fog. The power of sudoku compels you! Begone!
Hey Simon, wonderful and most interesting way to follow as usual. By the way, there IS a 3 in the corner in the third windoko, so the song would have been valid 🙂
Lovely puzzle, I love it when theres a million places to look. There are a lot of differences between my solve and Simons solve and that is just wonderful.
Something weird and frustrating happened to me with this puzzle.
I had a different start to the puzzle, I was quickly able to figure out that r3c2 had to be a 2 and from there it became obvious what the white dot had to be.
After watching the video I tried to remember what exactly led me to these conclusions to try and share my story, but I couldn't do it. I was able to eliminate 4 from r3c2 again, because that breaks the arrow in box 3, but not more than that. Now I'm wondering if I had some faulty logic and got (un)lucky, or maybe I realized something special at the time and now it slipped my mind. I'd rather be sure that I had a legit solve of the puzzle than whatever weird feeling I'm currently having.
Long story short while this probably made the puzzle a bit easier at some point, it didn't get me anywhere directly, so my next digit was also the 6 in the middle box.
If anybody finds a logical way to start with these digits I'd love to hear how you got there :)
..enjoyed watching you solve this.Loved the rules about (you didn't use them) the cells in c3,4,5, r 1,5,9 being a set of 1-9. Also the corner cells, middle cells of each outside row/column, and central c5r5 cell also form a 1-9 set..
I liked the 57 logic to get the 7 in r5c2 and then immediately forgetting about that when faced with the 45 in the cell below that.
I got the first 6 in the grid I got completely stuck and i never worked out the 5 in box 2 (I should say 7 but the logic was all about 5s). Thank you Simon it was driving me up the wall and i would never have seen it!!!
From 29:00 onwards, it's possible to get the arrow-sum for the bottom-left arrow in one step. There's a 9 in what I call "the left remainder" (i.e. the cells Simon coloured purple at 10:52). So in box 1, 9 must be in column 1. Using that and left remainder, the 9 in box 7 has to be on the green cells, and it's obvious which one it has to be on.
I'm loving Simon's Teenage Mutant Ninja Turtles fan art in this one.
11:16 there is actually one more trick to this SET theory! After highlighting the cage sets and then the virtual sets in the rows and columns, this leaves nine cells leftover in the corners and between the cages which are also one final set of the digits 1-9 with no repeats.
42:23 for me. I found the break-in pretty fast, but then got completely stuck. Nice puzzle anyway!
The logic leading to the 6 was that it was missing from all four 2x2 boxes we defined early on. Since any digit missing from those boxes had to appear in the center, and that could only be the 6, that meant all other digits had to be represented somewhere in those four boxes.
Consequently there had to be a 5 in the lower left box, as there could be no 5 in any of the other boxes. That then unlocked a number of clues that helped move the puzzle along.
👉 Simon, it would be nice for me to find the puzzle description and link *consistently* at the beginning of the video description section (which is where I am always *guaranteed* to find them in Mark's videos).
Just to make it simpler for me to locate the puzzle link, when I am in a hurry [Edit: or whenever my brain is *tired* and spontaneously switches to "automatic click" mode].
I suppose others would appreciate this as well.
Yes we would. Have asked for this before, but I think Simon thinks we will hit the Patreon link by mistake and sign up...er...no.
i understand what you want, but it will take like 5-10 seconds longer to find the link by viewing the full description and find the correct link. im pretty sure you not in that kind of hurry.
@@FluffSWE Even though I am a CTC patron, I hate when I click the Patreon link by mistake. And it does happen.
I sometimes do not pay attention, even when I am not in a hurry.
@@Paolo_De_Levafair enough
Yes, that bugs me too.
Finished in 24:50 with help from the video showing me the break-in.
22: 44
I usually take 2x Simon's time, if not longer (if I finish at all, which is far from a given). This is my first time ever to solve a puzzle faster than Simon, so it's peculiar that the margin is so large. I thought the break-in was beautiful but not difficult to see, and the rest of the puzzle was quite easy. I'll have to watch Simon's video later to see what he struggled with.
Ninja turtles coloring
My inner child very much appreciated that!
Came in here for this! Sweet username as well hoobaustank!
The 2*2 blocks in the corner cells (the circle and the three cells on the arrow) can be used in a variant of the Phistomefel ring. Doesn't help with the break-in, but gives a little leverage later in the solve.
7:50 you could draw boxes instead of coloring it green, if you want to.
The first digit is like 27-28 minutes in, if you are curious.
It took me a minute or so to deduce the first digit, but I really struggled after that, and was unable to spot the crucial logic on r2c5 without Simon's help.
Got the same first digit, but different logic path. I started with the expanded phistomophel ring. Then I used the Windoku sets on both columns and rows to get the 9th set of the 4 corners, 4 side-middles, and center cell. That last set has all the digits, but the phistomophel ring marks 8 of them as unable to hold the value that can't appear on the arrow or as a total.
That 6 ! 🙏
25:45 Interesting, I saw the 6s but by a superficially different (if underlyingly similar) route - I looked at what happens if you did put a 6 in one of the green corner cells in box 5 -- if you do it limits the positions for 6 neighboring L-shaped regions such that they rule out any position for a 6 on the remaining L...
the 9 in box 7 was available for a long time. by asking where 9 goes in windokubox 1, then asking where 9 goes in windokubox 3
great solve! good job Simon!!!!!!!!
There's a bug in the puzzle. r4c6 won't acept any input. All the other cells seem to work normally.
Interesting, I feel like I haven't noticed this in previous fog puzzles seems like probably the software is suddenly having problems with marks in
~~~SPOILER SPOILER SPOILER~~~
~~~
~~~
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fog cells with an underlying given, of which that's the only one in this puzzle?
*edit* Might just be that we haven't seen this unexpected behavior because we haven't had a previous fog puzzle on CTC that's had givens in the fog? Took a peek at a bunch of them just scrolling down the feed to see if this same thing happens and thus far haven't found one that used them-everything I've looked at either had no given digits or treated any givens like placed digits and so had fog cleared around them from the start...
Hi, r4c6 already has a digit so that may be the reason 😁
Ahhh, so it was windoku. I gave this one a try last week and while I made a good deduction about there being several 1's, I couldn't get further.
44:07 finish. I missed how the logic of how Simon got 6 in the middle; I went a different way. Using Window logic, the corners, the center of each edge, and the center cell form a set of 1-9. Using modified Phistomafel logic, it shows that 6 can't be in any of the aforementioned set except for the center cell. But definitely a fun puzzle!
Imagine you are a first time watcher and you skip the video to half way. You would never understand how Simon has only put down 2 digits but he has solved half the puzzle 😂
At 54:30, the simpler way to look at it is to remember (and see) the 1234 quadruple in row 2, so R2C6 must be 8.
The Werefrog got to the 6 in box 5 after about 10 minutes, but then it slowed down. The Werefrog found a bunch of 1-2 pairs going around, but then the 7 in box 2, that was hard. The Werefrog actually mapped out all the places 3 and 8 could go around the grid first, then noticed the 7 in box 2 was limited to 2 places, and if it was in the other one, that required 8 to go to the wrong spot.
Great puzzle to fill a few hours.
the 125 triple for the 9 arrow could've been realized sooner, the moment 5 couldn't go into lower 8 arrow, no other place had 5, and one of the arrows had to have 5, otherwise it would've happened the same that happened to 6, and there's no such thing as a Schrodinger cell (5 and 6 in the center), but the impact is not very large overall
thanks for sharing! amazing solve as always Simon!
At the end, Simon was saying he’d never seen logic like the 5 before, but it’s the same logic used on the 6 in the break-in. 😂
(Love you, Simon, never change.)
I found this to be quite hard, but i also didn't know the windoku tricks.
Edit: My solve path was incredible different from yours as i missed the math logic on the top 2 arrows.
After the break-in with the 6 in the middle and the 9 arrow i pencil marked the 9 in the top-left cage which gave me the 9 in the bottom left cage and 78 in all other cages. because of the same logic as with the 6, there must be a 5 on one of the arrows to avoid a conflict in the middle cell. That now forces a 2 on all the arrows.
I assume (and therefore everyone else has) the "do not overlap" rule means the heads of the arrows cannot share a cell? Cause otherwise how do you know each arrow arm passes through the fog at the start of the puzzle rather than two heads meeting and 'touching'? To begin with I assumed the rule meant just arms couldn't cross over each other, rather than no part of the arrow (including bulb and head) can share a cell with another arrow.
I found this unclear. So had to look at the beginning of the solve where Simon neither considers nor mentions that possibility. It makes no sense to me that the circle is part of the arrow, but I will have to accept that assumption to get on with the solve. Unfortunately it has already somwhat spoiled the solve for me, having skimmed through the comments, and also watched part of Simon's solve.
Had to watch to 47:46 to solve, but I seemed to get stuck on the exact same things that Simon did, so I don't feel too bad about that. Not as much direction from a fog of war puzzle than I'm used to, but that's not necessarily a bad thing. Still an excellent puzzle, had much fun solving it :D
Why don't you consider putting a circle in the R2C2 at the very beginning? One line segment could be an arrow connected to the circle while another could be an arrow pointing to that circle. There is no overlapping arrows and no circle with more than one connected arrows.
Rules: 05:24
Let's Get Cracking: 09:35
What about this video's Top Tier Simarkisms?!
Three In the Corner: 2x (55:35, 55:47)
Bobbins: 1x (32:10)
Diddly Squat: 1x (31:45)
And how about this video's Simarkisms?!
Hang On: 6x (05:45, 25:10, 28:01, 34:49, 48:55, 49:54)
Ah: 6x (24:53, 24:55, 34:49, 36:10, 47:40, 55:19)
Pencil Mark/mark: 6x (18:04, 18:10, 18:17, 43:01, 50:14, 55:00)
In Fact: 5x (07:15, 20:41, 20:59, 24:38, 40:19)
Wow: 5x (41:35, 47:44, 59:40, 59:44, 59:44)
Beautiful: 4x (28:21, 30:15, 30:59, 1:00:10)
Obviously: 4x (10:03, 10:30, 26:46, 31:38)
Goodness: 3x (23:13, 35:09, 40:59)
Sorry: 3x (20:34, 23:20, 38:15)
Missing Something: 3x (22:53, 44:46)
By Sudoku: 3x (10:05, 26:23, 59:07)
What Does This Mean?: 3x (31:56, 49:40, 52:05)
Cake!: 3x (03:33, 03:37, 04:06)
Symmetry: 3x (15:49, 15:52, 15:55)
Clever: 2x (50:06, 53:27)
Stuck: 2x (01:40, 1:00:07)
Lovely: 2x (03:00, 49:13)
Shouting: 2x (03:12, 03:29)
Plonk: 2x (08:06, 57:55)
Thingy Thing: 2x (29:05, 41:12)
What on Earth: 1x (30:47)
Bother: 1x (40:02)
Out of Nowhere: 1x (51:10)
I Have no Clue: 1x (23:20)
Brilliant: 1x (03:18)
Incredible: 1x (48:08)
Our old Friend Sudoku: 1x (29:23)
Of All Things: 1x (37:25)
Surely: 1x (36:15)
I've Got It!: 1x (19:10)
Pregnant pause: 1x (30:59)
That's Huge: 1x (35:28)
Most popular number(>9), digit and colour this video:
Ten (10 mentions)
One (127 mentions)
White (19 mentions)
Antithesis Battles:
High (4) - Low (1)
Even (7) - Odd (4)
White (19) - Black (6)
Row (24) - Column (22)
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!
9:39 "Let's Get Cracking" again
I found the 6 in the middle pretty quickly and then spent ages noticing the logic in r2c5 😅
I solved this in testing. Nice to see it featured.
Wow that was brutal! 165:12 was my time. I needed a hint to get me past the logic to knock 5 out of r2c5. After that the rest of the puzzle resolved without much issue.
I really didn't expect it to take me that long because I actually placed that 6 in the middle in a reasonable amount of time (and I agree that it was an extraordinary first digit!).
100% same boat.
Probably the intended break in:
The four cages are 4 sets of digits 1-9. Then rows 4, 6 and columns 4, 6 are 4 sets of digits 1-9. After, you'll notice entire box 5 is highlighted except for the middle cell. Since a 6 cannot go on the opposite highlighted cells, a 6 must go there.
Did you ever notice your thought at 23:00 was actually correct? I figured that out in one of those newspapers sudokus you mentioned in the beginning as well. I'm fairly certain I even had proof for it. I was certain you would use that to solve this puzzle but instead you did some genius 6 in the middle reasoning.
I had an idiocy brilliancy in finding the center 6. From set theory I deduced that r1c1,r1c5,r1c9, r5c1, r5c5, r5c9, r9c1, r9c5, and r9c9 were a set of digits 1-9. When considering where the sixes were in the four 3x3 boxes I was able to eliminate the six from all of the of members of that set other than r5c5, when captain obvious would simply note simple sudoku does the trick.
I'm aware of a couple other sets. After you get those sets you mentioned, the remaining are also a set. The other is that the digits on the outside of day the to left square that are not in the window, and the same as the digits on the window which are not in the siding sudoku square.
That's all I know though.
Take a drink every time Simon says windoku
Amazing puzzle though
The way I broke in feels like it was more work for the same idea. I ended up using set theory with r4+r6+c4+c6= the 4 windoku boxes. You end up with 8/9 cells in the center box in one of the sets and they all can't have a 6 because of the arrows in the other set. Unfortunately I never saw the logic for that 57 cell, but at least, as always, I got to enjoy Simon's solve.
Oh a nice longer puzzle for a relaxing Friday evening!
I feel the 1 hour is new normal for Simon.
@@LukeSumIpsePatremTe fair point
@50:30 if you noticed that you already had a 1234 quad in R2 then that eliminates 3 from R2C6, breaking it open.
90 minutes for me. Seems like there were several breakins to get to the end. Including a y-wing or 2. Would the first break be classified as a power-wing or a ghost-wing
So glad Simon got stuck at the same place I did (albeit not so badly)
Odd that he didn't keep going on windoku to get 9 complete sets (once you have the gaps vertically and horizontally you have 9 diagonal-to-the-windokus left)
An awesome puzzle and solve!
Apparently Fog of War sudoku is so mainstream now that the rules don't even have to mention it. ;-)
i figured out the 9 in box 7 by just seeing where 9s go elsewhere, it all led to that spot
I got stuck on the 5 as well. Grats on the solve.
23:51 What does Simon say to the digits when he starts a sudoku?
While the arrows are quite clear, as well as some of the consequences (I had a feeling that the high digits will be somewhat crowded in rows and columns 4 and 6), I was stuck here. Thanks to Simon's "what I know about Windoku", I got the first (and then immediately the second [non-given]) digit, it is really quite extraordinary.
(By the way, an immediate corollary of the additional sets of 9 is that there is a last, quite spread, set of 9 digits, made up of the cells r159c159. This helped me near the end a bit.)
I got stuck again for quite a while, until I figured out that *both* of the upper arrows needed to end in a 1.
Total time was 204:02 (solve couner 5926).
I figured out the extraordinary digit fast enough, but it was still a long grind until I understood i had to switch my mentality to windoku. Solved in 1h48m47s.
This one was really hard.
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I would never have found r2c5 without watching the video
I wanted that 3 in the corner to happen so bad...!
39:01, but I had to watch the video to see that a 6 had to be in r5c5 and then again disambiguate r2c5 (neat trick!). Skipping through, I feel like I figured out the digits on the four "given" arrows pretty quickly, that took me about 7 minutes.
Man, if this was live streamed, the amount of capital letters would be staggering
I know its hard, colors and lines and fog and all, but the 1234 quad in R2 really would have helped near the end...
Fun logic. Got stuck for quite a bit until I found the singleton 7. 67:23
What part of the ruleset excludes a cell from containing a circle and the point of an arrow? Is it just obvious to everyone else?
To my mind, "arrows don't overlap" translates as no cell may be occupied by two arrows, and that includes every part of the arrow (including circle and tip).
@@RichSmith77 That's probably the correct interpretation, but to me the "circle contains the sum of digits on the arrow". So if the circle is part of the arrow, it contributes to itself, which I think requires math skills well beyond the average solvers capabilities. Certainly mine. In my opinion a ruleset shouldn't be open to interpretation or assumptions.
@@joethornton5321 They do usually (and in this case) say digits *along* the arrow, rather than simply on the arrow. This may also be open to interpretation, but I can get behind the idea of "along" meaning along the shaft and tip of the arrow.
Alternatively, it could be argued "arrow" as a word has two frequent meanings, even in the context of an "arrow" sudoku. They're rarely described as "arrow and circle" puzzles. The arrow in an "arrow type puzzle" stands in for the entirety of the tip, shaft and circle. They all make up the arrow, in that sense. Yet also, it's common to refer to the number of arrows coming from each circle, in which context "arrow" just refers to the shaft and tip. Which meaning the word "arrow" has, is often dependent on the context in which it is used.
Having said all that, yes, I guess it is open to interpretation, and that's not ideal.
Me waiting ages for Simon to work on 9s and it doesn’t yield anything he hadn’t already deduced 🤣
Hi there and hey diddle diddle.
I'll give you a cute little riddle.
Nine digits you enter,
With one at the center,
Four corners and every side's middle.
Brilliant puzzle, one of my favourite FoW puzzles so far.
@ 18:05 - Shame on you for Pencil Marking ;) None of the 2x2s can contain 6, so ask where the 6 goes in each cage, and you get a Catherine-wheel effect, which places 6 in the centre.
@ 28:31 - "I'm now worried that I should have appreciated that far more quickly" - you could have got it ten minutes earlier, but I wouldn't say you should have. It's not obvious until you ask the right question. The next question you need to be asking is where do all the 1s and 2s go. You didn't do this, but if you had, you'd have found there were 12 pairs all over the place.
I was surprised you didn't consider the expanded Phistomefel Theorem, which seemed fairly blatantly set up from the start. This came into its own once the 12 pairs were placed.
I actually managed to find a set theory pattern that proved to me that every digit in row 5 were digits that were on one of the arrows except the middle digit and that's how I found the 6 (and as a bonus it told me that the arrows contained every sudoku digits except 6 at least once)
(more specifically, if you make a set of the 4 cages aswell as a set containing both box 4 and 6 and column 4 and 6 you can clearly see that the only digits left are on an arrow and the only digit unacounted for in row 5 is the middle digit and it has to be a 6 since that's the only digit that couldn't appear on the arrows)
It would be cool to see one of these types with a majic square, black dots, white dots, X's and Vs.