Brutal But Utterly Brilliant
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- เผยแพร่เมื่อ 21 ก.ย. 2024
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Today's sudoku is something of an enigma - it has a modest rating on Logic Masters Germany (85% or so) and yet this is one of the cleverest puzzles we've ever seen. It's called Brutalism (!) and it's by PulverizingPancake... you can play it at the link below:
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Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships.
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I wish I had words for the sheer heart-breaking beauty of this puzzle. I struggled and gave up. Then I watched Simon revealing the wonders of a true work of art. The interaction of the boxes is amazing - but more, much more, important is the joy on Simon's face and in his voice when he finds the logic path. That he left the 9 marks in box 3 unresolved when the NE-SW diagonal needed a 9 in that box, is just the usual manifestation of Simon's non-standard perception of the grid: his brain just sees a different grid than most of us do: different salient features, different dynamics, different everything.
I said it before and I say it again: I love that man.
Simon,, I have to say: you did a bundle. An absolute bundle has absolutely been done by you. You are the bee's knees, the wasp's nipples. You are, I would go so far as to say, the entire set of erogenous zones of every major flying insect of the Western world.
🤣🤣 This gave me my first really good belly laugh in a long time. Thanks Amos!
@@GotG113 You realise I shamelessly plagiarised all the humour from Douglas Adams's _So Long And Thanks For All The Fish_ , a work of enormous importance in the canon of nerdity. Simon is no doubt word-perfect and has no trouble detecting the true source. I did not think it necessary to make proper attribution. 😎
@@amoswittenbergsmusings I still attribute the hilarity of your comment to your cleverness in using Mr. Adam's work to further praise Simon's work. I enjoyed reading Douglas Adam's books but I am no good at retaining details and then using them in such a clever way. I think people who can are admirable.
@Godess of the Garden , I couldn’t agree more. I’ve been enjoying Amos Wittenberg’s humour for the past 17 months!
I like the "prove Phistomefel in a new tab" thing since it makes it very easy for those of us who have seen it to jog forward until you see numbers again to get past it...
Or they can make a video explaining it and just refer to that.
29:00 A year ago I knew mostly nothing about the wonders of sudoku and all its variants. Every time you explain the ring or set theory or anything else, we will not be impatient.
This! A million times this!
I'm pretty sure Simon just likes saying Phistomefel by now lol
There was an easier way to win the first digit. Once you get a green 89 in box 1 and box 9, you can look at where it goes in box 7. It can't go in the 8 cage, so it must go in the top row of box 7. Once you know that, you know that it has to be in the 15 cage in box 8 as well, which means it's a 9.
Just came to the comments looking for this!
I saw that as well, but just think: you wouldn't get that amazing 17 cage logic if you spot that because you get the 38 from the 4 in box 2. I argue that the video was better because he missed it!
@@PurpleSidewalk1 that may be true! And I couldn't solve it all by myself anyway, so while I get excited when I spot something he doesn't, I admire Simon's skills.
Simon got hung up on the Phistomofel ring instead of his other common obsession with the diagonals. They gave us more info. Leave it to Simon to teach us how to do these, then he sits on one theory and ignores the other tricks.
Spot on! Indeed a quicker win
This is definitely a great puzzle. I think the reason the cage without any numbers was there for symmetry. My thought is it was there and had a total but later shown that it was unnecessary for the solve but was kept for symmetry. Pulverizing Pancake is a great solver in his own right. He has graciously tested my puzzles many times on discord and has a truly gifted way of getting through them even though the ruleset is something new and never been seen before. This puzzle also proves that he is definitely a great puzzle setter.
Agreed. And I think also perhaps to make it even clearer to the solver that Phistomefel was going to be a prudent path to take at some stage. If that cage isn’t there, it looks like there might not be enough information to use Phistomefel, and so not bother and get stuck.
When solvers miss logic and then bifurcate to get a solution they may rate a puzzle low. I usually add a hidden comment that describes the logic to solve tricky spots that the solver might have missed to try and prevent this. After the solve, hidden comments become visible to all who solved the puzzle.
9:57
"We're using gray and I can hardly see gray. It's not the graytest thing in the world."
Simons doing a little word playing I see.
That wasn't intentional
Your sudoku engine programmer should add a couple more colors so that all 9 digits can have different, non-grey colors
Brown & Pink, perhaps? :)
One possible explanation for lower ratings on very good but difficult puzzles is that there may be a larger percentage of solvers who can’t find the intended path, and end up using a lot of chains/bifurcation to finish it.
I will NEVER get tired of Simon proving Phistomefel.
I'm REALLY over it. :(
I always love watching these profs.
And I really appreciate Simon making sure every video is approachable for a newcomer to the channel.
Simon proving Phistomefel is the symetric counterpart of Mark goodlifting every thermo sudoku, both do it every single time they can and they will never get tired of doing so
Simon, Thank you for taking the time to prove Phistomefel, that was the exact point I was stuck at in this puzzle and I hadn't seen it before. I had more markings so the puzzle really all fell apart from that point! - A stunning puzzle!
You can get the central 5 without needing the ring theory, because of the 5s in the 7 cage (top middle) and 12 cage (bottom middle). If the centre isn't a 5 then any 5 placed on a line in one corner would exclude a 5 from all the other corners, and therefore one of the lines would be missing a 5.
I didn't know you did Sudoku, Cyriak, only nightmare fuel. But I agree, sometimes Simon does complicate matters for himself.
Getting the 5 with Phistomefel was quite satisfying though
Didn't quite expect to see you here! The puzzle could've been solved with some extra Sudoku logic on box 9 as well. Would be interesting to see if the puzzle could be solved without the Phistomefel theorem.
A crossover from both of my favorite content creators, who would believe that.
With the addition of where 5s go in box 6, yes. Placing it on the line in box 1 doesn't exclude it from the line in box 7, and vice versa, but placing it on both of those would break over in box 6 or column 7.
@@davidcanchila4045 I certainly solved it without the theorem, though it took a while to spot the trick with the central 5. Nothing against using the theorem of course, but the logic without it is quite pleasing to discover, as you chase the imaginary fives around the outside of the puzzle
In the thumbnail... is that... a brutalisk? That will get my... uh, *our* research off to a flying start.
why do you need that Stettman?? *Stares*
Wow cool puzzle and great solve! Side note: I love how approachable these videos are. Yes, many of us have heard the Phistomefel logic explained, or set theory, or even the rule sets, and that's why TH-cam allows for time skipping. I never would have gotten into these videos if not for the random one the TH-cam algorithm gave me being a puzzle whose solver (Simon) was so good at making the logic understandable.
Me: "7+2+3 = 13. Looks about right."
Ten minutes later: "Shit."
In the 13 cage top left? I somehow did the same thing, ended up it taking an hour to solve it :\
29:20 I don't know the backend process for this, but I've seen some other channels create sort of segments in the progress bar for the videos. I personally love seeing thing like this explained every time because it's like that nostalgia of the lessons you teach that got me into puzzling, but since others have complained, I thought I might suggest that you guys try that out, so you could label the bit that is the 'phistomefel ring' and people who are bothered by that can know where exactly to skip to. Another advantage might be that those who really want that explanation and know it's in this video somewhere would be able to find it on the bar there.
Just a thought, in case it's helpful to you guys. Thanks for doing what you do!
Not the "Gray"-test thing in the world. Nice pun-intentional pun Simon!
Simon, your Phistomefel 2/5 "Catch" was absolute Genius! Well done Sir!
it was not required. There were 5s already cols 4 and 6.
I figured out a cool trick for adding consecutive numbers fast in my head while I was watching. The sum will always equal the average of the set of numbers multiplied by the amount of numbers in the set. If you have an odd amount of numbers for example 2, 3, 4, 5, 6 the average will always equal the median so you could say 2+3+4+5+6 = 4*5 = 20. For an even amount of numbers the median trick doesn't work but you can get the average quick by using the max + min divided by 2 since it is a linear pattern, so if you have 2, 3, 4, 5, 6, 7 then the average = (7+2)/2 = 4.5 so and average*amount of #s = 4.5*6 = 27.
39:54 Simon putting a 4 twice in the box with a grin on his face makes me crack up XD
Yeah me too 😆
For me that was the rare, "shouting at Simon moment"
FWIW, the puzzle can be solved without resorting to Phistomefel (starting from the position at around 28:00 right before the foray into Phistomefel):
- the 20 cage in box 9 cannot be 5-6-9, because together with the positions of 5, 6 and 9 in box 8 and the 7 in R7C3 this would put 5, 6 and 9 in box 7 into R7C1 and R7C2, which is broken
- the 4-7 pair on the diagonal in the 20 cage resolves the 6 and the 7 in the central box
- the 6 in box 9 now must be in row 7 because of the 6es in boxes 3 and 8, this puts the 6 in box 7 into R8C1 or R8C3 (it can't go in the 8 cage)
- because of the 2 and 3 in box 8 those numbers must go into rows 8 and 9 in box 7; only one of them can go in the 8 cage, so the other must be in R8C1 or R8C3, together with the 6, so candidates for R8C1 and R8C3 are now 2, 3 or 6
- looking at the falling diagonal R1C1 and R2C2 can either be a 1-5 pair (with a 7 in R2C1) or a 2-3 pair (with 8 in R2C1); 1-2 and 3-5 would both break the 13 cage
- the 7 in R5C4 (resolved four steps above) together with the 7 in R7C3 puts the 7 in box 4 into either the 10 or the 12 cage; if it's in the 10 cage that cage is 3-7, which puts a 1 into R6C6 and a 5 in the center (because of the possible combinations for R1C1 and R2C2); if it's in the 12 cage that cage is 5-7, together with the possible positions for 5 in box 7 that puts the 5 in box 1 into column 3, thus the only remaining position for 5 on the diagonal is again in the center
From there on the remaining solve is just straightforward, similar to the video.
That's very close to how I solved it (eventually), although I only found I was getting a 5 in the centre by bifurcating the two options I had for the 12 cage in box 4, and noticing both paths lead to a 5 in the centre quite quickly.
Miss read title and now I can't unsee it 😂 Brutal butterly brilliant
I didn't even see that til I read your comment and now I can't unsee it either! :-P
7:30 I remember this one. And I should have given less time to it in relation to skill. Simon might miss a 9 or a 3 here or there, but his logic solves puzzles. Most of the numbers everybody scream(s) about only gives the number and not much more. Seeing where to look for answers corroborates brilliance. I am learning.
Edit: It looks like the puzzle with the three 7 options without the diagonal. So how did I miss this one? Answer: Always start with the newest puzzle launched.
21:30 - alternative way of getting that 8 in R8C4: You've already used 3 of the four low-digit colors in C4. The 3-Cell 17 cage must have a 1,2,3, or 4, (because 5+6+7 = 18). Therefore R8C4 cannot be any of the four low digits. And you already have the 5,6,7, and 9 elsewhere in Box 8. So that 8 is actually a naked-single. :-)
Pulverizing Pancake is another genius.
One of the things that I noticed is that once you lock in the 12 and 34 in each of the cells, the column that has the 7 and 17 cage in it has two solutions for the remainder, 15 and 17 and it can't be 15 since it shares a digit with a 15 cage.
Simon found a harder earned first digit. Thinking about green in box 7 would give away green as a 9 fairly quickly. 8 or 9 cant go in an 8 cage, which locks it into row 7, and therefore row 9 in box 8 where the only possibility for green is 9
Indeed - he never saw the X-wing on 8s in boxes 8 & 9.
Simon got to where he needed to go with more complicated logic than he needed? He would never do such a thing.
During the big drought around 20:00, working on column 4 would have advanced quickly. The 13-cage in box 8 contains digits 8-2-3 or 8-1-4, so R8C4 is 1, 2, 3, 4, or 8. Column 4 contains a 7-cage, a 17-cage, a 1/2, a 3/4, and a 6/9. If you total up the max of all of these you quickly see that R8C4 must be 8, the next smaller value 4 is too small to make up 45 in the column. Once R8C4 is 8, you have a 7-cage, a 17-cage, an 8, a 1/2, a 3/4, and a 6/9, and you can total these again and observe that the 6/9 must be a 9, as 6 is too small. Once again, add up the 7-cage, 17-cage, 8, and 9, for a total of 41, so the remaining cells must total to 4 and so must be a 1 and a 3.
There were 2 really neat bits of logic i think were missed and wanted to share
1. After you place the 57 in the 22 cage, note that forces it it puts it in the 17 cage in in column 4 box 5. However, the other 57 pair can't go in the 17 cage! A 5 and a 7 in a 17 cage would need another 5 there. So If the other of the 57 pair can't go in column 4 in box 5, then it must go in column 4 in box 2, putting it in the 7 cage, so it is a 5, and the 7 goes in the 22 cage!
2. You get that green is a 9 after placing it in the 20 cage since green can't go in the 8 cage, so and must be in row 7 in box 7. This means green goes in the 15 cage and so it's a 9
Oh wow. I'm still new to the channel (and new solver in general) but this was amazing!
One thing I will say is that I love the reflection on the puzzle at the end and wish the Cracking the Cryptic apps (I went and got the thermo one after the brilliant thermo solve earlier this month) would allow you to view the final solution rather than bringing you to a congratulations page as soon as the final digit is placed.
As always, great work and look forward to seeing more!
worked hard for 44 minutes and then got stopped stone cold. I had no idea that I needed to use the Phistomefel on the 5s. Once i saw that in the video, I finished in 5 minutes. I was so close but so far at the same time.
You could have resolved the colored cells at 12:12, although it would have been slightly complicated
Column 4 had a 7 and 17 cage adding to 24.
Yellow plus orange adds either to 4 (1+3) or 6 (2+4)
If it was 2 and 4, the bottom two cells would add to 15, but those cells overlap with the 15 cage in box 8, meaning r8c4 would be equal to r9c5, which isn’t allowed since they share a box.
Therefore orange and yellow are 1 and 3
Yes, I found that and for the first time felt like I caught something important that Simon overlooked!
You can tell how hard Simon’s puzzle is by counting the different colors at the halfway point.
A bigger palette could prove useful.
I put this one on for listen to while going to sleep, but it was so thrilling I couldn't sworn you were only about 10 minutes in when all of a sudden you were finished.
An alternative way to resolve the colours for the break in was that once you had placed the green in the 20 cage of box 9, between that and the red in box 9, and the 8 in the 13 cage in box 8, the only place to put an 8 in row 9, looked back up at green
Also, I know it's 90% joking, but just for any bad days when you focus on the 10%: When we point out alternatives or things you missed, we're not really "shouting at [you]". At least in my case, even when I spotted the trick with the 8, I'm well aware that I wouldn't have got to the point where that was possible, nor known what to do after the fact. It's more that we hold you and Mark in such high regard that on that rare occasion that we see something before you two do, it's a noteworthy event worthy of celebration.
21:20 an easier way of getting that first digit is realizing that in box 2, 7 is _always_ in a vertical line on column 5, it's either up in the 22 cage (where it can only go on the side that's on column 5 thanks to the 57 pair on box 8) or in the 11 cage; that forces a 7 in the 17 cage which forces it to be a 476 cage because it's already staring at a 12 pair and you can't make it 737 for obvious reasons. Even though going through this angle didn't pre-emptively give me the digits on the 11 cage of box 2, it triggered the cascade of digits which gave that info a second later anyways
Also, another point I went differently from Simon in this, is that you can get the 69 order on box 8 much earlier, from the moment you create the 57 pair; the 57 pair bounces up to box 2, forcing it's 9 to be in column 6, but the 9 never could go in the 17 cage on box 5, because with it not being able to have a 1 or a 2, the only option left would have been a 359... But if you had 359 on that killerbox, you'd force the 7 killer box to be 16, in which case the 69 pair would be broken on box 8 because you'd already have a 6 _and_ a 9 on column 4. Doing it this way was very sad though, because I got those two digits super early and it felt amazing... But they were useless until much later. Getting it the way Simon did feels a little less contrived, and it's more tied to the rest of the progression so it also just feels _better_
I sometimes come away from these videos thinking "Simon doesn't do enough killers." I think if he did, he might have seen early on the sum of R3C7, R7C7, R8C4 and R9C4 would be 31. This is because the 17-cage in box 5 leaves a hidden 6-for-28 cage. The sum of the cages covering C5 and C6 is 121, leaving 31 in the cells outside the two columns. The two overhang cells in column 7 can then take values from 13 to 17: 13 doesn't work as the overhang in column 4 would need to be 18; 14 could work; 15 could not as R7C3 and R7C7 sum to 15, so R3C7 would have to be the same as R7C3, which the diagonal blocks out; 16 could not work as R8C4 would have to make 15 with R9C4 which is already in a 15-cage with R9C5 (R8C4 and R9C5 would have to be the same), and 17 doesn't work as when combined with the 19-cage in C6, the remaining 4 cells would have to sum to 9, which is not possible. Thus, R3C7 and R7C7 have to sum to 14, and R8C4 and R9C4 sum to 17 as an 8-9 pair. That reduces the 12-cage in box 8 to 5-7, which forces R9C5 to 6, then R9C4 to 9 and R8C4 to 8.
After one failed solve I came back and finished it, and when I had to use the Phistomefel Theorem to do it, I came back to watch the video thinking Simon had probably found an easier way...but no, he used the Theorem, too!
Crazy good puzzle and solve. Thank you. Unmarked cage was there just to steer you towards using the Phistomefel ring(?)
What was going on at 39:54 lol.. I want what Simon was smoking here.. its some good stuff 👌 🤣😂😅
39:45 Chocolate Teapot Triple alert 🚨
I found it helpful at 8:45 once you found out what options you had for the 7 cage in box 2, you could deduce that the 11 cage had to be an 8,3 pair thus giving you the digits in each cage in box 2. (Used this later to disambiguate boxes 5,8)
38:34 I'm not sure if this means something, but something I've noticed regarding this - if you add all the completed cages on the phistomephel ring (4 10s and a 19), and then subtract the cages on the phistomefel corners, you get 18. this means that whatever the 4 uncaged digits on the corners are, they also have to add up to the same total that the uncaged digits in box 4 and the partially caged digits in boxes 2 and 8 (which they do - ignoring the 4/6 in the first corner, the 6, 3, and 7 you found add up to the same total as the 8, 1, and the 2/5 necessary to complete column 3, 16)
not sure what that info really influences, though, if anything
Excellent solve Simon!
Not sure if it was intended by the setter (and it sure wasn't easy to spot), but there was a somewhat sneaky way of disambiguating all of the colored digits at around 12:15
Looking in col 4 at the two colored digits outside the 7 cage - they cannot sum to 5 because of the weird 1234 colored quad and the fact that the pairs that sum to 5 are contained in their own boxes. So they must be either 1+3 or 2+4.
If the sum was 2+4, you'd have a problem because then (using the secret) you'd need r8c4 + r9c4 = 15, but this conflicts with the 15 cage in box 8.
24:59 finish. I love how the diagonals in conjunction with the 10 clues pushed most of the information into boxes 2, 5, and 8, and then spread out from there. Some simpler logic for box 9. The 3-7 10 cage in row 7 and the 19 cage in box 6 pinched the 3 into r9c8, and the 7 into the 20 clue. This left 1-2-3-5 along the diagonal, of which only 2-3 could fit into the 13 clue (leaving 1 and 5 on the diagonal in box 5). Along the other diagonal, I was left with 1-2-3-8. I had 1-8 in r1c9, and 3-8 in r4c6, so the 8 cage in box 7 needed a 2, making it 1-2-5. I didn't even consider the Phisto ring after the first minute or so, seeing how everything was unfolding.
If this is from the position just before Simon applied the Phistomefel trick, say as at 28:49 in the video, how do you know 1+5 couldn't be on the diagonal in the 13 cage in box 1? You say only 2+3 could work in the 13 cage, but I couldn't eliminate 1+5 as an option in my solve at this point.
Alternative logical path to prove green is 9, when it was proven green had to be in the 20 cage, that put green on the top row of box 7. This means that whatever digit was still available out of 8 and 9 in the bottom row of box 8 had to be green.
Took some time to realize the effect of the middle square and corner pairs, but got there eventually, great puzzle, nice break in too
My guess is that the unnumbered cage is purely cosmetic. There is a nice appearance of rotational symmetry that isn't part of the solve.
19:20 I've been shouting a while. NOW I ALMOST SMASHED THE LAPTOP!!! The green 9 in Box 9 was just there for the taking for long.
Brilliant puzzle, though. Using Phistomephel logic without long and tedious mental arithmetic was nice for a change.
The ol 5 in the middle square trick.
Once we had green at r8c9, we could figure out that it was a 9. Applying sudoku to rows 7-9 on green, because of the other green in c3, the gren in box 7 must be in row 7, and therefore the green in box 8 must be in r9. But an 8 already could not go into r9 of box 8, only a 9 could. Hence green had to be a 9.
I bet that unfilled cage total in box 3 is there only to draw attention to the Phistomefel ring pattern. It certainly isn't there to indicate there are no duplicates in the cage, since that's already obvious from normal sudoku rules. It also becomes more significant of an element later in the solve because the logical path fills in several of the unknowns in the ring and corners, drawing more attention to the pattern.
I can see how despite beautiful diagonal logic the puzzle didn't receive the highest of praises. After a few minutes of hurting my brain i concluded there must be a nice way of determining which 14/23 option breaks the vertical cages and i'm just blind to it. The tiniest bit of 14/23 bifurcation i couldn't resist skips the first and best 20 minutes of Simon's solve.
The 8-9 pair in box 9 along with the 8 in the 13 cage in box 8 forces an 8 in the bottom row in box 7, which can only go into column 3. I couldn't do this puzzle without a lot of cheating with the video, but I was proud of seeing that one :3 (at around 15 minutes).
at 26:30 in this video, simon marks 9s in one of two spots in box 3, but you can actually just immediately place the 9 in r2c8 at that point! there has to be a 9 on each diagonal, and that is the only cell on that diagonal where a 9 can go! :)
Thanks Simon. Enjoyed it.
At 15:00, Simon places an 89 pair in box 9. At that point, there's the situation that the 8 has to be placed in rows 7 and 8 in both box 8 and box 9. Therefore, in box 7, the 8 has to be on row 9. Since the squares R9C1 and R9C2 are in an 8-cage, the number 8 cannot go in there. So an 8 can be placed in R9C3 at 15:00, much earlier than 24:24, when Simon had figured out the exact placement of the 8's in boxes 8 and 9.
13:00 Since the 1234 cells must be different and the "pair" in each box must add to 5, the pairs in columns Cannot add to 5 (otherwise you'd have to use the same digit). So [1,2] +[3,4] in column 4 must add to 4 or 6.
Add the 7 and 17 cages and you get 24+ (4 or 6) in column 4, leaving 17 or 15 in the lower cells. By the same logic it can't be 15 since then r8c4 would be the same as r9c5. Therefore it's not 15, but 17 (an 89 pair) and the 1234 pair added to 4, a 1 and a 3.
My first digit looked at col 4. 7 + 17 + (yellow + orange) + ? (in 13 cage) + 6/9 (15 cage)
yellow + orange is either 4 5 or 6
If 6, then 7 + 17 + 6 = 30. So ? + 6/9 = 15 meaning ? is also 6/9 breaking the 15 cage)
if 5, then 7 + 17 + 6 = 29. So ? + 6/9 = 16, making the 6/9 a 9 and the ? a 7, which breaks the 12 cage.
That leaves 4, so orange is 1, yellow is 3, ? is 8 and 6/9 is 9, and everything flows from there.
At 21:23, you can get the cell more simply by noting there must be 7 in the 17 cage by sudoku. A virtual 12 pair in box 2 and the 7 in the box rule out every way of making up the last 10 except for 46.
I don't think that it matters in any way that the Phistomefel Ring's corner squares have been counted twice with the columns/rows forming the "ring", since you don't interact with them. The dominoes adjacent to those corner squares, next to to the middle box of a tower/story, are removed from both sets of the "Phistomefel equation".
Btw I think you don't have to be sorry for repeating something like that. It's not "unskippable ads" or live TV. It's TH-cam, and it has a seekbar - for those who really heard it enough times and want to skip forward - or didn't quite get it and want to rewatch.
I've been following CtC for a while now, and I am amazed by the levels of intricacy and enigmity[1] some of the featured puzzles have!
[1]: Is "enigmity" a word? My dictionary says "Nope!" but I'll use it anyway, since it sounds less clunky than e.g. "enigmatism" 😄)
8 in R9C3 was sitting there since forever, (8 in 13 cage + 89 pair in 9th box + no 8s in 8 cage in 7th box)
Yep, got the 5 without the Phistomefel Ring.
I like the way you explain the ring theory differently every time. Some explanations are easier to follow than others. When I did not know, I much preferred the step by step approach without shortcuts.
I was one of the first solvers of this puzzle on LMD. I loved it, and gave it a top rating, but unfortunately it seems like not everyone shared my taste!
How could digits repeat in the top right cage? Am I missing something?
I was just thinking about that...I can only assume that the cage was created more for symmetry than anything else (Each corner has a "V" shape cage in it).
Also telegraphing the phistomafel ring.
And as soon as green went in it you'd know it was green-red-1, and get some of the digits that way.
This could be the most beautiful use of Phistomefel since its inception.
I don't think i could've solved it if not for the Phistomefel ring. ~70 minutes in i felt totally stumped, so i started colouring it for the heck of it, and only when i filled the possibilities of column 3 in box 4 that it hit me with the 5.
81:17
I could not see a way to use P's ring, that was a step too far for me, but found another way. I love Brutalist architecture and the puzzle does not tarnish the name at all!
I thought phistomefel trick was not usefull.
Boy, was I wrong. Absolutely brilliant puzzle!
I think I would have solved this faster six months ago. It's been so long since the "standard" Phistomefel ring was all the rage that my brain just refused to notice it until I'd been stuck for ages and ages.
well played Simon. a lovely solve of a very interesting puzzle. Thank you.
Just over an hour. No problem getting started but found the last half very tricky.
16:00 ask the facetious question about rows 7 & 8 and green is revealed.
use the diagonals Luke
9:58 "We're using gray, and I can hardly see gray, it's not the gray-test thing in the world" xD
I'd like to know by the setter if the phistomephel ring was intended to get the 5 in the center, because I didn't spot it and was stuck for 100 minutes and had to bifurcate
Phistomefel ring or not, the puzzle breaks if you try to place two 5s on the diagonals at that point. You can reason your way to that conclusion without bifurcation because of the location of 5s in boxes 2, 6, and 8. For instance, placing a 5 on the diagonal in box 3 or 9 will force it off the diagonal in all other boxes. So only box 1 and 7 remains, which quickly breaks (for instance) column 7. Easy to prove when you know it's supposed to go in the middle, but tricky to spot when you're solving it and don't already know :) That doesn't answer your question, though, but to me the cages were definitely chosen to limit the options for 5s on the ring, to at least hint at that logic.
I managed it in 36 minutes without using Phistomefel. At the point where Simon used it he could have spotted the 4-7 pair in the bottom right that would have led to a solved puzzle.
@@bokmcdok The 4-7 pair isn't available until you've placed the 5 in the centre. But @Jay 40 is right, the inability to place a 5 in the 19 cage makes it impossible to place two 5s on the diagonals.
An easier way to proceed at this stage of the puzzle would have been to note the 3's and 7's in row 7 and column 7 outside of box 9, forcing r9c8 to be a 3 and the 20-cage in box 9 to be 4-7-9.
@@matthewmazurek The 4-7 pair is available there at that moment? It can"t be 5-6 because that leaves no place to place both 5 and 6 in row 7.
can someone explain why the unmarked cage was given? in a 3 by 3 the digits cant repeat anyway?
Symmetry
The unmarked cage was there to telegraph that the Phistomefel ring was important.
Aesthetics, I suspect. It makes another leg for the bug-like shape (brutalisk?) on the sudoku
And it was an 18 cage that read 1-8
Symmetry, and drawing attention to the Phistomofel Ring
So yeah I was going great... and then I hit a wall.... and what a wall... no way would I have ever thought to use that logic to solve it.... Great puzzle..
I know nothing about set theory but at this point when I run out of techniques I'm familiar with I throw the Phistomefel ring at the grid and hope
I love that you used a Brutalisk in the thumbnail.
2:10 Ah, so the point of that cage is simply to tell us we can't have a repeat in that cage. And here I thought "Normal sudoku rules apply". Oh, Simon...
I didn't know Cracking The Cryptic huy likes StarCraft :)
Simon mentioned he had even met Jaedong in a match, I think.
@@jpryan90 I think I recall that he played in the Master league at one point. I'm not sure I remember correctly but I believe so. Which means he was indeed pretty effin good.
Simon even did some Starcraft themed sudokus :D great fun
Simon even played some StarCraft on Patreon.
Phistomephel's Theorem. Best friends with Andrew's Law since 1996.
I was happy to have solved it, although it took me 3 tries to finally get it. One remark though: if you're proving Phistomefell, why not color the rows and columns in different colours? Then it is a bit more visual that the corners are double counted...
Personally I like the use of black, it's easier for me to see than light grey. Just wanted to share even if it's just making it more complicated.
Brutal indeed - with a couple brief nudges, I got to the point of the r5c5 proof, and I had groked some of the logic around it, but I couldn't make the leap. Cool puzzle, just way too difficult for me
Dang nice is this the second or third StarCraft reference on this channel
18 minutes in asking about what to do: look at 8 on the bottom row! gives a green 9, which might be handy for the solve
the shapes of the cages also made me immediately think of Phistomefel
As soon as you placed quite early a green cell in box 9 you can immediately ask "where does green go in box 7" and the answer will lead to "so green is 9"
I missed the phistomofel ring but it's possible to solve by looking at what happens when you put 7s and 9s in box 4 in different positions. The end result was always 5 in the diagonal middle
Combined with the math limitations in the killer cage in box 1
Is it only me shouting at Simon around 15:40 that greem is 9 trough boxes 7 and 8?
that is a tidy bit of logic
44:15, a pretty good time for me! I wound up solving it differently from Simon.
The central digit in a puzzle where you need to consider the diagonals is only ever usually one of only 3 options... Or is that just something I've noticed by having done a lot of them?
didn't need to use phistomefel's ring as if you try the logic of putting 2 in center due to row 3 it will be pushed to cage 19 which can only be 3,7 or 9
If you continued with your green after box 9 you would have seen green = 9, in box 7 green have to be in row 7 so in box 8 in row 9.
34:39 for me. I must have missed something for sure because I didn’t find any brilliant logic. All I needed were a couple of chains that gave me a couple of useful numbers and some patience. Time to watch the video and see what is going on with this puzzle that I couldn’t spot.
hey, I was thinking why not to try and make a sudoku prototype for an app where the background colour for the squares is black and the lines of the sudoku is white, including the dashes line for cages where they will be white. I think it will be very nice and easy on the eye
Id like to say my solve time was less than the video length! I'm friggin shocked. Mind you its by like 20 seconds or so, but Thats the best Ive ever done.
It usually takes me twice the time of the video, this time it took half.
I think it's the slightly forced (yet beautiful) use of the Phistomophel ring that wasted a lot of time here
What a strike of genius, how on earth did you find this way to use Phistomefel's theorem?
Wondering if there is a way to get the 5 in the center without the ring. It can be a bit frustrating to need to know a popular set theory construct to break into a puzzle.