Simon, I’d like to take a moment to say you’ve really opened up my mind to a new way of puzzle solving with these sudoku puzzles. I’m 21 years old and some of the highlights of my late nights are using my brain to solve these puzzles along with you. I want to thank you for your inspiring personality and spirit.
I'm surprised this proof wasn't the means of discovering the pattern in the first place, or at least quickly recognized by someone smart enough to find the pattern.
@@maljamin I think the fact that the theorem is rotationally symmetric, but this proof isn't, is probably the reason this proof wasn't widely known earlier. I do really like the proof, since it is so clear (lacking the double counting being the main reason), but it does feel a bit more arbitrary in how the sets are picked.
@@tomprince8223 well, actually, this proof works also as a rotationally symetric proof, since you can exchange columns to rows and vice versa and still holds perfectly
yeah for sure, avoiding the bit where some cells are "counted twice" is so much easier to understand, and i believe this proof will be the one shown in all future videos. :)
Oh that's a strikingly good alternative proof of the Phistomefel ring. Great to have a version where you don't need any "okay but remember we're treating this cell as being blue twice" stuff.
The Dark Lord's ring was beautifully telegraphed and most CtC binge veterans probably picked the breakin up fairly smoothly. Getting the puzzle done wasn't insanely hard but needed some careful scanning each and every way - and especially along Diagon Ally. I clocked a satisfying 36:13 without video cheating. Simon's promotion of the clean Phistomefel Lemma is almost a true proof without words. Applying SET theory with entire boxes in and out of SETs works really well in my brain. Bedtime.
But we don't want to share Simon with the rock world. Once they see his magnetic personality ... well the pressure to go full rock star will be tremendous.
I solved this yesterday, and my reaction was basically the same as yours. My solve path was similar but more clumsy. I thought about sending this one in, but something told me I wouldn't need to. ;) Great puzzle, with a great solve.
My personal preference is to color low digits blue (cold) and high digits orange (hot), and it drives me nuts when Simon chooses the opposite convention.
@@collapsiblespork Maybe, to ease the pain, try to think of it as blue as high like the sky and orange (a kind of brownish colour) as low like the ground?
Incredible! Did it all by myself in just 28:47 ! The moment I started noticing the 12345 // 6789 split of the entire grid I was astonished -- and then the phistomephel ring blown my mind. It's only thanks to all the previous videos that I know what can be done with arrow sudokus... Gorgeous puzzle.
I solved much of the opening logic and got stuck, but once I heard the P Word from Simon, I was off to the races and finished in 30 minutes. What an amazing puzzle!
Same here - I could have stared at that partially coloured grid for a very long time before it occurred to me that this was a Ring puzzle, but that was the only hint I needed to finish it.
I did find the Phistomofel ring before Simon mentioned he-who-must-often-be-named. And solved the puzzle in only 28 minutes. Unfortunately that was 28 minutes after staring at the partially colored gird for an hour before I recognized the implication of the ring.
Nahileon, the creator of this puzzle if you are reading this congrats on a wonderful puzzle. At the outset it seemed I only would struggle but found with a little effort the break in and the logical path. So happy!! Thanks!!
Another excellent puzzle being promoted here. Since I started watching your content my solving skills have improved immensely. Finished this one in about an hour, whereas when I first began my journey with this channel it would never have been done. Great content as always!
I spent 10 minutes futiley trying to make the diagonals work out the rest of the coloring until the Ring finally stood out in my brain. Closest I've felt to euphoria in weeks! Wonderful puzzle, absolutely brilliant
Agreed.. except I kept going back to the puzzle every couple of hours while I was doing other things.. Ultimately it took me 4 days to notice the ring.. It only happened because I was looking at the 6789s and how a certain number would have to go in those spots on the ring not occupied by the diagonals and it just suddenly clicked and I knew I had it.
This was one of the most fun puzzles I've ever solved. I didn't think there was any way I was going to be able to solve it without some help from Simon, but I did. And I was almost as giddy doing so as a Simon was. What an amazing puzzle.
you showed of a sudoku that looked like a nonogram but now you have shown off a nonogram that looks like a sudoku. that is amazingly done by the setter just absolute
Lovely Puzzle. Took me a mere 40 minutes. I had colours for all the different 6/7/8/9 options which made it easier although I still found myself doing a little rewinding at times. I find it amazing that since starting watching your show (started just pre pandemic but pandemic cemented it) and I didn't know I could ever solve things like this. It's amazing what practice does.
Awesome puzzle. I would never have been able to solve this without the massive amount of lessons I have learned on this channel. Set theory... Phistomephel Ring... REALLY nice.
I didn’t need SET to solve this, just a realisation that columns 3, 4, 6 and 7 could only have one more low cell each, while rows 2 and 8 needed at least two low cells each from each of those columns, because they could only have two more high cells each.
Yeah all the slow lessons we've learned. I even spotted the phistomephel ring for myself which was novel. It's great how something like this, which would once have been impossible for me to solve has become slowly within grasp.
I did find the break-in on this one, (I think), and solved the whole thing in 24 minutes 30 seconds. A beautiful puzzle that kept holding out without ever being brutally hard. Sure, the break-in is something I would not have found without watching this channel a lot over the last two years, but still. And the puzzle is so clean.
Everyday I watch these videos and the puzzles just keep getting better and better. I find myself saying this one is my favorite like 5 times a week, but this one will be hard to trump. Hats off to a beautiful puzzle and solve
This was a gorgeous puzzle! I feel so capable of solving these now that I've watched a few of your vids and picked up on your tricks - punched this one out in under 20 minutes and had a blast doing so! :)
For the first time in almost 2 years of watchin this channel, I got the break in in geometry/set puzzle, and almost immediately at that. Thank you so much for 2 years of videos I would never imagine I could watch for more than 5 seconds. Also, my bottom arrow now sums to 25 max :( time to watch you solve it.
Simon I love you, I've been watching you guys since near the very beginning. I am amazed that you have been able to keep the teacher in you alive and have handled things like the secret and knowledge bomb very well. The Phistomofel ring always kills me a little and I've seen it so many times now. Please don't take offence but I've started watching you at x 1.25 speed and I love it! I can't wait till you guys get to 1/2 million subs and then kicking on further!
Delightful puzzle. So much going on and I am on the last puzzle of the lockout hunt. It has taken all of my weekend but worth every minute. Let’s hope the last puzzle is not too hard!! Nice to take time out to watch you solve this colourful Rose.
I’ve been following the channel for a few months now and this is the first puzzle I’ve tried before watching the video. I was able to solve it and was glad to see Simon tackled it in a nearly identical way! (Though he was more than twice as fast haha!)
The first time I've seen and applied the Ring (recently learned from this channel of course). One minor technique I used in this was that e.g. R3C7 + R7C3 = R4C4 + R6C6 because of diagonals + orange sets - which is useful a couple of times, e.g. to place 2 in the middle and to resolve R3C7. Thanks for the video!
Wow. I love "minimalistic" puzzles. Just a couple of hints ... solvable with a pure logic flow. And I managed to solve it too! So, it's not on the hard side. Thank you Nahileon for this gem! And, as always, thank you Siimon for your solve!
There is a very easy to understand way to prove the Phistomefel ring by trying to prove the opposite. Pick any of the corner squares and put a digit in it. Now we're going to attempt to place the digit across the grid without placing it on ring. Let's do an example. Place a 9 in the top left cell in box 1. In order to avoid the ring, we have to place a 9 in row 2 in box 2. The 9 goes in either column 8 or 9 at the bottom of box 3. Moving down to box 6, we have to place the 9 in column 8 or 9, depending on box 3. The 9 is now forced into column 7 in box 9, either row 8 or 9. Same logic for box 8, it has to go in the remaining row out of 8 and 9. Box 7 gets a 9 placed in row 7, and now 9 is forced onto the ring in box 4. The same logic applies for every single cell in the corner squares. There is no way to fill the grid without placing every digit in the corner squares onto one of the cells on the Phistomefel ring.
I don't think that is a complete proof, as it doesn't account for repeated digits. You have shown that every digit in the corners appears in the inner ring, but you haven't shown that they need to show up the same number of times. You could probably do a case analysis each way of resolving how a digit is forced into the inner ring, and show that placing another of that digit in the corner would force another of that digit onto the ring. Alternatively, you show for each number (1, 2, 3, 4) of times a digit can appear in the corners, that forces the same number of occurences in the ring (you also need to account for the two distinct ways of placing two copies of a digit in corners, along a side or diagonally opposite). But at that point, I think the proof is as complicated as set theory, and not as generally applicable. Also, to be mathematically rigorous, you'd need to say something about the symmetry that means the example you gave is enough to force a digit into the ring, no mater where the initial digit is. That said, your proof may be enough to help somebody understand, why the theorem is true, even if it isn't a complete proof.
This "try and disprove it" approach is fun and thought provoking, but it has a strong drawback. It is "easy to understand" only if you accept partial proofs of Phistomefel's theorem: 1) If a digit _x_ is contained in a corner square, that digit must be also contained (at least once) in the ring. 2) Vice versa, if a digit _x_ is contained in the ring, that digit must be also contained (at least once) in the corner squares. These partial proofs are not enough to conclude that the two sets are identical, i.e. that each digit is repeated the same number of times in both sets: 3) Each digit _x_ is repeated exactly _n_ times both in the ring and the corner squares, where _n_ can be zero for some values of _x._ Phistomefel's theorem proves that the two sets are identical (i.e., it proves the third statement). This implies that also (1) and (2) must be true, but (1) and (2) are only a partial, incomplete, proof of Phistomefel's theorem. It is very difficult to prove statement (3) "by trying to prove the opposite" (I am not even sure it is possible). It is much easier to prove it by using Set Equivalence Theory, as shown by Simon.
@@Paolo_De_Leva I think you can extend the proof to show that a digit being in two corners and once in the ring is impossible (and similarly for more occurences). There are a bunch of case to check, but it is possible to do so. You end up getting a stronger version of (1), which says that if the digit x is contained n times in the corner squares, it is contained in the center ring at least n times in the center ring. Given that there are a finite number of digits in the corners, that is enough to prove 3. Certainly not as easy to understand, once you've done all that, though. And the mathematician in me doesn't like the lack of symmetry ( you can also prove the stronger version of 2, but either strong form is enough to prove 3).
Rules: 03:45 Let's get cracking: 05:13 And how about this video's Simarkisms?! By sudoku: 6 (10:13, 22:49, 22:56, 24:46, 24:49, 24:52) Lovely: 5 (11:05, 11:07, 18:02, 34:59, 35:29) Hang On: 4 (11:53, 21:33, 27:15, 28:59) Clever: 3 (07:33, 07:33, 35:05) Beautiful: 3 (17:30, 34:53, 35:25) Brilliant: 3 (01:45, 02:51, 03:29) Sorry: 2 (12:51, 21:20) Maverick: 2 (03:25, 18:38) Bobbins: 1 (27:58) Knowledge Bomb: 1 (08:03) Naked Single: 1 (34:09) The Answer is: 1 (14:28) Incredible: 1 (02:46) Elegant: 1 (13:26) Ridiculous: 1 (07:16) Deadly Pattern: 1 (34:28) Off and Running: 1 (28:52) Take a Bow: 1 (35:02) FAQ: Q1: What is a Simarkism? A1: A Simarkism is something that Simon and Mark typically or frequently say. Q2: How do you do this so fast? A2: I'm not made of flesh and blood, but of sand ... Q3: Why don't you include 'XX' and 'YY'? A3: Probably it's already on the list ('Scooby-Doo' for example), but not mentioned in this video. But if you think it's not, tell me what you'd like me to include and there's a good chance I'll add it! Q4: You missed 'XX' at 'YY:ZZ'! A4: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn! Q5: Could you turn these statistics into videos? A5: I've been playing around with the idea and I'm open to input as to what people would like to see. Let me know if you are interested in this and/or have suggestions.
Me: Wow, I did this puzzle almost 10 minutes faster than Simon! Simon: Proceeds to explain and display proof of the phistomophel theorem. Me: Well, there's my 10 minutes.
Thats brilliant!! i looked at the thubnail and thought oh thats interesting i wonder how many constrains this puzzle will have so it can have unique solution. Turned out, none! Im amazed !
34m 06s. I really enjoyed this puzzle. It took me a while to find the break in but once I did the rest of the solve felt very linear while still being challenging.
Beautiful! Very clever in comparison to most things termed 'miracle'. I managed it in 40:15, and am surprised to hear scrolling down to add my comment that a Phistomefel ring was employed! I went by high 6789 vs low 12345 coloring, aided by realizing I needed 16 more low digits but could only put 8 in (most of the remaining space less 8 spots), and then leveraging the diagonals and proceeding from there. Brilliant setting!
Reviewing the video, and seeing the ring bit at 12:50, I do have to admit I'm also surprised I didn't see the ring at that point! The alternate technique here: you need 16 more low digits, but R3/4/6/7 and C3/4/6/7 can in sum only accommodate 8 of these, color these in and count the rest... Amusingly, my color choice was blue/orange as well, but flipped low-high in comparison.
This is a lovely puzzle, I'm not sure if the X-wing on 5s in columns 3 and 4 may have helped things along but by the time that became useful it was already mostly just cleaning-up time.
Unfortunately I will have to miss the stream as I'll be out of town, but I'll definitely watch it afterwards. Also the Padlock puzzle pack has been great so far. Fairly hard for me, but I'm chugging along with 4 done so far.
19:28 is my time. I must be way too familiar with these puzzles as I found this one really simple. I usually can't even get standard sudoku puzzles under 20 minutes. We've just seen several puzzles with arrows in the corners. Then the 3x 6789's in each corner just telegraphed phisto ring. And the little killers were clearly for disambiguation. Still a cool idea. I would have liked to have seen this puzzle a year ago (granted it's likely a recent puzzle, just saying a year ago, this would have been groundbreaking).
Fun fact, after coloring, i missread my bottom arrows and had the 9-clue as a 2-cell arrow(5-4) and the 6-clue as a 3-cell arrow(1-3-2). This seems to produce an entire new unique solution.
Two lots of SETs, one of which involved cancelling arrow totals which I'm usually terrible at seeing (and the other being the phistomefel ring which is bizarrely standard at this point). Very happy with my 42 minute time on this puzzle, extraordinary as you realize what's going on. The minimalism really helps you spot where to look here, even if as I looked at it waiting for you to list the rules I was wondering "So, is this anti-knight, anti-king, non-consecutive, or some combination of the three?" and saw the rules and just was kind of... "Is there a rule missing"? Wonderful puzzle, and an extraordinary discovery, and bit of setting, from Nahileon. Thanks for showcasing this. Hi/low colour would have helped my solve, since my 42 minute time involved solving for the arrows at the bottoms being the opposite lengths meaning I had to unwind to resolving the 35 little killer when I realized I'd been solving for the wrong arrow configuration, though even that didn't lose too much time since the logic was intact for the most part, I just had slightly incorrect digits in places.
That was fun 72 minutes of my life... I solved it the same way that Simon Solved it. also after colouring it, I guess it does look like a rose... Very clever puzzle =)
Truly a fenomenal puzzle, got it in over an hour, but the first time with no proper help have i completed such a nice puzzle. Went from set to colouring high and low when i noticed the phistomefel trick. With the huge amount of set puzzles being put together recently how about a set sudoku app next? Keep up the good work.
This puzzle is great! Looking impossible at first glance, it unfolds beautifully and doesn't even need a lot of fancy tricks for solving (well, one or two maybe, without these, I would consider this a GAS). Even I, not solving for speed, was able to do this in little more than one hour. And usually I take at least 3 to 4 times as long as Simon or Mark, if I can make it at all. And the lovely symmetry at the beginning, only broken - and hence giving the puzzle its unique solution - by the two little killer clues. I am thrilled.
With only one error I had to backtrack on, managed it in just shy of 72 minutes. I had to use SET to break in, because I resisted high-low coloring, but still managed it. Fun solve.
A stunningly beautiful puzzle, not straightforward but clean logic. Loved it all the way. Happy with my 71 minutes. Which, on that note, my solve was so long that I cannot remember how I resolved the early parity colouring, but I most certainly did not use the Phistomefel ring, it did not even cross my mind.
What I find amazing is, when I got to the point of resolving the low digits, i had trouble seeing the arrows on the colored background so I thought the 6 arrow was 3 cells. But once I finished the grid, it created another unique solution and didn't affect any other clue or rule. 😂 What a great puzzle!!!
I did exactly the same 😂. Only when watching Simon get to 25:40 did I realise. "Wait a second, wasn't my 6 a 1+2+3? What did I do?...Oh." I feel like I got to solve two puzzles for the price of one from that point, though. So not all bad. 🙂
I didn't have time to attempt to solve this one, but I suspected just by glancing at it that it would be a P-ring solve. The high digit fill-ins were kind-of all at once, but everything else felt like a very nice linear progression.
I didn't even think of the Phistomephel Ring. My solve path involved considering "well these two squares can't both be high, but this square and THAT square can't both be low, so this ends up as a high/low X-Wing..." I found four of those and sort of "back doored" my way into the conclusions the Phitomephel Ring produces.
This was great, and not too difficult. Finally feel like I've improved at these things, I'm rarely able to get the break in, but this one I saw... and then it just went. Until it came time to get back to the low digits, but that wasn't too long of a holdup.
54 minutes for me, feel really pleased that I spotted the Phistomephel ring without help. I did spend about 15 minutes failing to spot a 35 pair in c3 though 😅
Very nice puzzle, Nahileon, thanks and congratulations! EDIT: I didn't use the Phistomophel Ring, unfortunately - that was far more elegant - I just gradually ruled out various numbers from being high/low.
Really brilliant puzzle. I made a pig's ear of it at first, by trying to give the 6789 different colours and numbering everything to death. So I restarted and just did hi-lo colours, and it worked beautifully. Resisted the temptation to stick a 5 in the middle.
Simon, I’d like to take a moment to say you’ve really opened up my mind to a new way of puzzle solving with these sudoku puzzles. I’m 21 years old and some of the highlights of my late nights are using my brain to solve these puzzles along with you. I want to thank you for your inspiring personality and spirit.
Same.
^^ What he said.
Heartily enjoyed how the colouring revealed the titular Magic Rose.
And it would be more beautiful if he colored the low digits red
this new phistomephel proof is mindblowing because it is very easy to understand.
Yeah - Much easier to get your head round SET stuff when it doesn't involve double counting and adjusting for doing so.
I agree, one of the best proofs I heard so far. Very clear.
I'm surprised this proof wasn't the means of discovering the pattern in the first place, or at least quickly recognized by someone smart enough to find the pattern.
@@maljamin I think the fact that the theorem is rotationally symmetric, but this proof isn't, is probably the reason this proof wasn't widely known earlier. I do really like the proof, since it is so clear (lacking the double counting being the main reason), but it does feel a bit more arbitrary in how the sets are picked.
@@tomprince8223 well, actually, this proof works also as a rotationally symetric proof, since you can exchange columns to rows and vice versa and still holds perfectly
The new Phistomefel proof is definitely much easier for newcomers to understand. Also this specific puzzle was the perfect one to showcase it.
yeah for sure, avoiding the bit where some cells are "counted twice" is so much easier to understand, and i believe this proof will be the one shown in all future videos. :)
Oh that's a strikingly good alternative proof of the Phistomefel ring. Great to have a version where you don't need any "okay but remember we're treating this cell as being blue twice" stuff.
The Dark Lord's ring was beautifully telegraphed and most CtC binge veterans probably picked the breakin up fairly smoothly. Getting the puzzle done wasn't insanely hard but needed some careful scanning each and every way - and especially along Diagon Ally. I clocked a satisfying 36:13 without video cheating. Simon's promotion of the clean Phistomefel Lemma is almost a true proof without words. Applying SET theory with entire boxes in and out of SETs works really well in my brain. Bedtime.
When is Simon’s compilation of full-length guitar recordings coming?
Indeed.
But we don't want to share Simon with the rock world. Once they see his magnetic personality ... well the pressure to go full rock star will be tremendous.
@@ronjohnson6916 In ways that it matters most Simon is already full rock star!
I solved this yesterday, and my reaction was basically the same as yours. My solve path was similar but more clumsy. I thought about sending this one in, but something told me I wouldn't need to. ;)
Great puzzle, with a great solve.
"The man's too big , The man's too strong" well done simon!!!!!
This has got to be one of the most wholesome channels on YT
The confusion that breaks out in my head when Simon colors the grid opposite to how I colored it... oO
My personal preference is to color low digits blue (cold) and high digits orange (hot), and it drives me nuts when Simon chooses the opposite convention.
@@collapsiblespork he's a rebel lol
@@collapsiblespork I had blue and red, but my reasoning was entirely the same :-P
@@collapsiblespork Maybe, to ease the pain, try to think of it as blue as high like the sky and orange (a kind of brownish colour) as low like the ground?
YelLOW is best for low digits.
Incredible! Did it all by myself in just 28:47 ! The moment I started noticing the 12345 // 6789 split of the entire grid I was astonished -- and then the phistomephel ring blown my mind. It's only thanks to all the previous videos that I know what can be done with arrow sudokus... Gorgeous puzzle.
Simon playing "The Man's Too Strong" in the he beggining was amazing!
Thank you, I knew it was Dire Straits but I couldn’t remember the title!
I solved much of the opening logic and got stuck, but once I heard the P Word from Simon, I was off to the races and finished in 30 minutes. What an amazing puzzle!
Same here - I could have stared at that partially coloured grid for a very long time before it occurred to me that this was a Ring puzzle, but that was the only hint I needed to finish it.
I did find the Phistomofel ring before Simon mentioned he-who-must-often-be-named. And solved the puzzle in only 28 minutes. Unfortunately that was 28 minutes after staring at the partially colored gird for an hour before I recognized the implication of the ring.
Nahileon, the creator of this puzzle if you are reading this congrats on a wonderful puzzle. At the outset it seemed I only would struggle but found with a little effort the break in and the logical path. So happy!! Thanks!!
Another excellent puzzle being promoted here. Since I started watching your content my solving skills have improved immensely. Finished this one in about an hour, whereas when I first began my journey with this channel it would never have been done. Great content as always!
I spent 10 minutes futiley trying to make the diagonals work out the rest of the coloring until the Ring finally stood out in my brain. Closest I've felt to euphoria in weeks! Wonderful puzzle, absolutely brilliant
Agreed.. except I kept going back to the puzzle every couple of hours while I was doing other things.. Ultimately it took me 4 days to notice the ring.. It only happened because I was looking at the 6789s and how a certain number would have to go in those spots on the ring not occupied by the diagonals and it just suddenly clicked and I knew I had it.
Has to be a word play for "Magical Rows", right? This was magical.
That could very well be true. I have some other ideas, though.
If there was a patreon level where we could request a Simon guitar intro song of our choice I would pay any amount of money for it 😂
This was one of the most fun puzzles I've ever solved. I didn't think there was any way I was going to be able to solve it without some help from Simon, but I did. And I was almost as giddy doing so as a Simon was. What an amazing puzzle.
you showed of a sudoku that looked like a nonogram but now you have shown off a nonogram that looks like a sudoku. that is amazingly done by the setter just absolute
33:55 I like how the Phistomophel ring made this easy. As someoner that knows what that is (now) I would say this puzzle is quite sweet.
Happy day! Intro with Simon playing guitar!!! 🤗
Lovely Puzzle. Took me a mere 40 minutes. I had colours for all the different 6/7/8/9 options which made it easier although I still found myself doing a little rewinding at times.
I find it amazing that since starting watching your show (started just pre pandemic but pandemic cemented it) and I didn't know I could ever solve things like this. It's amazing what practice does.
55:32 the use of diagonal sums is spectacular, bravo
Brilliant use of Phisto's ring, and clever use of little killers to disambiguate.
Wow! So enjoyable and Simons excitement is so compelling! The best channel on RUclips!
Awesome puzzle. I would never have been able to solve this without the massive amount of lessons I have learned on this channel. Set theory... Phistomephel Ring... REALLY nice.
I didn’t need SET to solve this, just a realisation that columns 3, 4, 6 and 7 could only have one more low cell each, while rows 2 and 8 needed at least two low cells each from each of those columns, because they could only have two more high cells each.
Yeah all the slow lessons we've learned. I even spotted the phistomephel ring for myself which was novel. It's great how something like this, which would once have been impossible for me to solve has become slowly within grasp.
I did find the break-in on this one, (I think), and solved the whole thing in 24 minutes 30 seconds. A beautiful puzzle that kept holding out without ever being brutally hard. Sure, the break-in is something I would not have found without watching this channel a lot over the last two years, but still.
And the puzzle is so clean.
Very neat, and I particularly enjoyed the way P's Ring was apparently conjured up out of nothing.
Everyday I watch these videos and the puzzles just keep getting better and better. I find myself saying this one is my favorite like 5 times a week, but this one will be hard to trump. Hats off to a beautiful puzzle and solve
This was a gorgeous puzzle! I feel so capable of solving these now that I've watched a few of your vids and picked up on your tricks - punched this one out in under 20 minutes and had a blast doing so! :)
Wow! I was finally able to solve that one on my own. Thank you so much for providing us with all these intriguing solving strategies!
This is an amazing puzzle. If you’ve been watching CTC, it isn’t too hard. Has all the classic techniques, coloring, rings, great.
For the first time in almost 2 years of watchin this channel, I got the break in in geometry/set puzzle, and almost immediately at that. Thank you so much for 2 years of videos I would never imagine I could watch for more than 5 seconds.
Also, my bottom arrow now sums to 25 max :( time to watch you solve it.
Simon I love you, I've been watching you guys since near the very beginning. I am amazed that you have been able to keep the teacher in you alive and have handled things like the secret and knowledge bomb very well. The Phistomofel ring always kills me a little and I've seen it so many times now. Please don't take offence but I've started watching you at x 1.25 speed and I love it! I can't wait till you guys get to 1/2 million subs and then kicking on further!
Delightful puzzle. So much going on and I am on the last puzzle of the lockout hunt. It has taken all of my weekend but worth every minute. Let’s hope the last puzzle is not too hard!! Nice to take time out to watch you solve this colourful Rose.
Well... the good news is that the last puzzle is fantastic. The bad news is that it's extremely difficult
Simon's too smart
Simon's too humble.
Wonderful strumming of the great Mark Knopler's tune.
Love the little snippets of guitar, very nice playing :)
I’ve been following the channel for a few months now and this is the first puzzle I’ve tried before watching the video. I was able to solve it and was glad to see Simon tackled it in a nearly identical way! (Though he was more than twice as fast haha!)
Very elegant break-in, what a puzzle
What an amazing setting! And great solve!
"And I got to color" he sounded so excited by that lol
That was a great, fun solve. So few apparent clues but it was all there. Thanks Nahileon.
Incredible video again, I got into sudoku thanks to you and just finished your miracle sudoku app, keep on cracking you're awesome
The first time I've seen and applied the Ring (recently learned from this channel of course).
One minor technique I used in this was that e.g. R3C7 + R7C3 = R4C4 + R6C6 because of diagonals + orange sets - which is useful a couple of times, e.g. to place 2 in the middle and to resolve R3C7.
Thanks for the video!
The best way phistomefel has been explained! Very easy to follow the proof 👍
Wow. I love "minimalistic" puzzles. Just a couple of hints ... solvable with a pure logic flow. And I managed to solve it too! So, it's not on the hard side. Thank you Nahileon for this gem! And, as always, thank you Siimon for your solve!
Excellent puzzle today, Simon!!! That one was really fun and even somewhat approachable.
The most beautiful puzzle I've seen so far :)
Can we nominate phistomophel for a Nobel prize? Like always, amazing solve by Simon and a really wonderful construction by Nahileon.
There is a very easy to understand way to prove the Phistomefel ring by trying to prove the opposite. Pick any of the corner squares and put a digit in it. Now we're going to attempt to place the digit across the grid without placing it on ring.
Let's do an example. Place a 9 in the top left cell in box 1. In order to avoid the ring, we have to place a 9 in row 2 in box 2. The 9 goes in either column 8 or 9 at the bottom of box 3. Moving down to box 6, we have to place the 9 in column 8 or 9, depending on box 3. The 9 is now forced into column 7 in box 9, either row 8 or 9. Same logic for box 8, it has to go in the remaining row out of 8 and 9. Box 7 gets a 9 placed in row 7, and now 9 is forced onto the ring in box 4.
The same logic applies for every single cell in the corner squares. There is no way to fill the grid without placing every digit in the corner squares onto one of the cells on the Phistomefel ring.
I don't think that is a complete proof, as it doesn't account for repeated digits. You have shown that every digit in the corners appears in the inner ring, but you haven't shown that they need to show up the same number of times.
You could probably do a case analysis each way of resolving how a digit is forced into the inner ring, and show that placing another of that digit in the corner would force another of that digit onto the ring. Alternatively, you show for each number (1, 2, 3, 4) of times a digit can appear in the corners, that forces the same number of occurences in the ring (you also need to account for the two distinct ways of placing two copies of a digit in corners, along a side or diagonally opposite). But at that point, I think the proof is as complicated as set theory, and not as generally applicable.
Also, to be mathematically rigorous, you'd need to say something about the symmetry that means the example you gave is enough to force a digit into the ring, no mater where the initial digit is.
That said, your proof may be enough to help somebody understand, why the theorem is true, even if it isn't a complete proof.
This "try and disprove it" approach is fun and thought provoking, but it has a strong drawback. It is "easy to understand" only if you accept partial proofs of Phistomefel's theorem:
1) If a digit _x_ is contained in a corner square, that digit must be also contained (at least once) in the ring.
2) Vice versa, if a digit _x_ is contained in the ring, that digit must be also contained (at least once) in the corner squares.
These partial proofs are not enough to conclude that the two sets are identical, i.e. that each digit is repeated the same number of times in both sets:
3) Each digit _x_ is repeated exactly _n_ times both in the ring and the corner squares, where _n_ can be zero for some values of _x._
Phistomefel's theorem proves that the two sets are identical (i.e., it proves the third statement). This implies that also (1) and (2) must be true, but (1) and (2) are only a partial, incomplete, proof of Phistomefel's theorem.
It is very difficult to prove statement (3) "by trying to prove the opposite" (I am not even sure it is possible). It is much easier to prove it by using Set Equivalence Theory, as shown by Simon.
@@Paolo_De_Leva I think you can extend the proof to show that a digit being in two corners and once in the ring is impossible (and similarly for more occurences). There are a bunch of case to check, but it is possible to do so. You end up getting a stronger version of (1), which says that if the digit x is contained n times in the corner squares, it is contained in the center ring at least n times in the center ring. Given that there are a finite number of digits in the corners, that is enough to prove 3. Certainly not as easy to understand, once you've done all that, though. And the mathematician in me doesn't like the lack of symmetry ( you can also prove the stronger version of 2, but either strong form is enough to prove 3).
@@tomprince8223 Interesting, thanks a lot for explaining.
Rules: 03:45
Let's get cracking: 05:13
And how about this video's Simarkisms?!
By sudoku: 6 (10:13, 22:49, 22:56, 24:46, 24:49, 24:52)
Lovely: 5 (11:05, 11:07, 18:02, 34:59, 35:29)
Hang On: 4 (11:53, 21:33, 27:15, 28:59)
Clever: 3 (07:33, 07:33, 35:05)
Beautiful: 3 (17:30, 34:53, 35:25)
Brilliant: 3 (01:45, 02:51, 03:29)
Sorry: 2 (12:51, 21:20)
Maverick: 2 (03:25, 18:38)
Bobbins: 1 (27:58)
Knowledge Bomb: 1 (08:03)
Naked Single: 1 (34:09)
The Answer is: 1 (14:28)
Incredible: 1 (02:46)
Elegant: 1 (13:26)
Ridiculous: 1 (07:16)
Deadly Pattern: 1 (34:28)
Off and Running: 1 (28:52)
Take a Bow: 1 (35:02)
FAQ:
Q1: What is a Simarkism?
A1: A Simarkism is something that Simon and Mark typically or frequently say.
Q2: How do you do this so fast?
A2: I'm not made of flesh and blood, but of sand ...
Q3: Why don't you include 'XX' and 'YY'?
A3: Probably it's already on the list ('Scooby-Doo' for example), but not mentioned in this video. But if you think it's not, tell me what you'd like me to include and there's a good chance I'll add it!
Q4: You missed 'XX' at 'YY:ZZ'!
A4: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn!
Q5: Could you turn these statistics into videos?
A5: I've been playing around with the idea and I'm open to input as to what people would like to see. Let me know if you are interested in this and/or have suggestions.
you missed flurry of activity around 25:33 :D
you missied an off and running somewhere around 32:51
102:53
Yessss. Visually , One of the greatest puzzle hands down
Me: Wow, I did this puzzle almost 10 minutes faster than Simon!
Simon: Proceeds to explain and display proof of the phistomophel theorem.
Me: Well, there's my 10 minutes.
Thats brilliant!! i looked at the thubnail and thought oh thats interesting i wonder how many constrains this puzzle will have so it can have unique solution. Turned out, none! Im amazed !
34m 06s. I really enjoyed this puzzle. It took me a while to find the break in but once I did the rest of the solve felt very linear while still being challenging.
Very nice job of coloring to get out of the initial dire straits!
Aside: "The Man's Too Strong", also nicely done!
initial dire straits ... nice
Beautiful! Very clever in comparison to most things termed 'miracle'. I managed it in 40:15, and am surprised to hear scrolling down to add my comment that a Phistomefel ring was employed! I went by high 6789 vs low 12345 coloring, aided by realizing I needed 16 more low digits but could only put 8 in (most of the remaining space less 8 spots), and then leveraging the diagonals and proceeding from there. Brilliant setting!
Reviewing the video, and seeing the ring bit at 12:50, I do have to admit I'm also surprised I didn't see the ring at that point! The alternate technique here: you need 16 more low digits, but R3/4/6/7 and C3/4/6/7 can in sum only accommodate 8 of these, color these in and count the rest... Amusingly, my color choice was blue/orange as well, but flipped low-high in comparison.
You are an excellent teacher.
Absolutely marvelous puzzle.
Beautiful! This is the first puzzle that I've been able to solve myself that uses the Phistomephel ring and I gasped out loud when I realized it.
This is a lovely puzzle, I'm not sure if the X-wing on 5s in columns 3 and 4 may have helped things along but by the time that became useful it was already mostly just cleaning-up time.
Unfortunately I will have to miss the stream as I'll be out of town, but I'll definitely watch it afterwards. Also the Padlock puzzle pack has been great so far. Fairly hard for me, but I'm chugging along with 4 done so far.
19:28 is my time. I must be way too familiar with these puzzles as I found this one really simple. I usually can't even get standard sudoku puzzles under 20 minutes. We've just seen several puzzles with arrows in the corners. Then the 3x 6789's in each corner just telegraphed phisto ring. And the little killers were clearly for disambiguation. Still a cool idea. I would have liked to have seen this puzzle a year ago (granted it's likely a recent puzzle, just saying a year ago, this would have been groundbreaking).
I must confess, it does make me a bit tingly when someone properly uses the phrase "QED".
Great puzzle. I love this channel.
Fun fact, after coloring, i missread my bottom arrows and had the 9-clue as a 2-cell arrow(5-4) and the 6-clue as a 3-cell arrow(1-3-2).
This seems to produce an entire new unique solution.
Absolutely Stellar puzzle!
Two lots of SETs, one of which involved cancelling arrow totals which I'm usually terrible at seeing (and the other being the phistomefel ring which is bizarrely standard at this point). Very happy with my 42 minute time on this puzzle, extraordinary as you realize what's going on. The minimalism really helps you spot where to look here, even if as I looked at it waiting for you to list the rules I was wondering "So, is this anti-knight, anti-king, non-consecutive, or some combination of the three?" and saw the rules and just was kind of... "Is there a rule missing"?
Wonderful puzzle, and an extraordinary discovery, and bit of setting, from Nahileon. Thanks for showcasing this.
Hi/low colour would have helped my solve, since my 42 minute time involved solving for the arrows at the bottoms being the opposite lengths meaning I had to unwind to resolving the 35 little killer when I realized I'd been solving for the wrong arrow configuration, though even that didn't lose too much time since the logic was intact for the most part, I just had slightly incorrect digits in places.
Starts off with Simon playing guitar, instant thumbs up
This was beautiful, beautiful, and actually doable as well! Thanks :-)
Yet another brilliant puzzle that looks so impossible to start with, but with a little logic and colour it comes to an utterly amazing solution!
Really beautiful puzzle. And I didn’t know for this trick, thanks.
I like the aspect ratio of this video, gives it more of a movie vibe
Definitely an improvement!
That was fun 72 minutes of my life... I solved it the same way that Simon Solved it. also after colouring it, I guess it does look like a rose... Very clever puzzle =)
Truly a fenomenal puzzle, got it in over an hour, but the first time with no proper help have i completed such a nice puzzle. Went from set to colouring high and low when i noticed the phistomefel trick. With the huge amount of set puzzles being put together recently how about a set sudoku app next? Keep up the good work.
This puzzle is great! Looking impossible at first glance, it unfolds beautifully and doesn't even need a lot of fancy tricks for solving (well, one or two maybe, without these, I would consider this a GAS). Even I, not solving for speed, was able to do this in little more than one hour. And usually I take at least 3 to 4 times as long as Simon or Mark, if I can make it at all. And the lovely symmetry at the beginning, only broken - and hence giving the puzzle its unique solution - by the two little killer clues. I am thrilled.
Magnificent puzzle!
19:24
Beautifully sparse, especially given how middly the little killer clues are. Fabulous puzzle.
This building man in the top left corner is so funny 😆 12:59
With only one error I had to backtrack on, managed it in just shy of 72 minutes. I had to use SET to break in, because I resisted high-low coloring, but still managed it. Fun solve.
I love how the coloured cells reveal a magical rose.
And through the power of colouring he created a rose, magical :D
A stunningly beautiful puzzle, not straightforward but clean logic. Loved it all the way. Happy with my 71 minutes. Which, on that note, my solve was so long that I cannot remember how I resolved the early parity colouring, but I most certainly did not use the Phistomefel ring, it did not even cross my mind.
Me seeing a Sudoku without any numbers, but some arrows
-" Am I a joke for you ?"
I loved the Phistomephel Ring!
What I find amazing is, when I got to the point of resolving the low digits, i had trouble seeing the arrows on the colored background so I thought the 6 arrow was 3 cells. But once I finished the grid, it created another unique solution and didn't affect any other clue or rule. 😂
What a great puzzle!!!
I did exactly the same 😂.
Only when watching Simon get to 25:40 did I realise. "Wait a second, wasn't my 6 a 1+2+3? What did I do?...Oh."
I feel like I got to solve two puzzles for the price of one from that point, though. So not all bad. 🙂
35 mins for me. Proud of myself. It is good material to practice Set theory and P-ring ,😀
That connection with the Phisto Ring made me whisper "wow..." out loud to my phone.
I didn't have time to attempt to solve this one, but I suspected just by glancing at it that it would be a P-ring solve. The high digit fill-ins were kind-of all at once, but everything else felt like a very nice linear progression.
I didn't even think of the Phistomephel Ring. My solve path involved considering "well these two squares can't both be high, but this square and THAT square can't both be low, so this ends up as a high/low X-Wing..." I found four of those and sort of "back doored" my way into the conclusions the Phitomephel Ring produces.
Now I know what I'm going to listen to next. My second concert I attended was the Dire Straits On Every Street tour.
This was great, and not too difficult. Finally feel like I've improved at these things, I'm rarely able to get the break in, but this one I saw... and then it just went. Until it came time to get back to the low digits, but that wasn't too long of a holdup.
54 minutes for me, feel really pleased that I spotted the Phistomephel ring without help. I did spend about 15 minutes failing to spot a 35 pair in c3 though 😅
I actually purchased baba is you last night. I had a lot of fun with it.
That was fun and really miracle! 44:31 for me.
Very nice puzzle, Nahileon, thanks and congratulations! EDIT: I didn't use the Phistomophel Ring, unfortunately - that was far more elegant - I just gradually ruled out various numbers from being high/low.
Really brilliant puzzle. I made a pig's ear of it at first, by trying to give the 6789 different colours and numbering everything to death. So I restarted and just did hi-lo colours, and it worked beautifully. Resisted the temptation to stick a 5 in the middle.
Happy birthday, Zoe! I hope you had a brilliant day and the best cake ever - until next year's :)