Do You Need Theorems To Solve This Sudoku?
Рет қаралды 34,217
Күн бұрын** TODAY'S PUZZLE **
It's always a treat when a new Aad van de Wetering sudoku makes its appearance and that's what we've got today in the form of Angular Arrows. The intriguing geometry and choice of given digits (45 & 9) is classic Aad and we'll be interested to hear how everyone goes about solving this one!
Have a go at the puzzle here:
sudokupad.app/p2qL4hj8DG
Rules:
Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Digits cannot repeat along a blue main diagonal.
** CIRCLE SUMS by JESPER **
Simon's solve of this unbelievably good (and very challenging) sudoku is now available to watch on Patreon. It is over 2 hours long and is suitable only for those who enjoy movies...
/ crackingthecryptic
There's also a new sudoku hunt from Riffclown for our February competition! Get it here for just $2:
Other bonuses on Patreon currently include:
Simon's 2.5 hour solve of Roller Coaster Nurikabe
Mark's latest solve of The Times Club Monthly Special Crossword
** HEXCELLS STREAM **
Our latest Hexcells stream happened last night and you can watch it at the following link:
kzfaq.info7fsRf0Q28s8
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▶ Contents Of This Video ◀
0:00 Theme music & puzzle introduction
0.55 Patreon extras
1:45 Happy Birthdays
4:35 Rules
5:37 Start of Solve: Let's Get Cracking
▶ Contact Us ◀
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@GeekRedux 4 ай бұрын
24:40 "There Might Be A Much Simpler Way To Do This Puzzle" -- A Memoir by Simon Anthony (Just some light ribbing from a fan who will never be anywhere near as good as Simon at solving these things--might be a good quote for CtC merch, though.)
@AyaAlef 4 ай бұрын
I'd definitely buy that T-shirt! Feels like a metaphor for my life
@strangest_cacti 4 ай бұрын
Aad's ability to take simple constraints and create absolute magic of sudoku geometry is truly one of a kind.
@lhood8263 4 ай бұрын
Every time he said phistomefel I had a drink. I was drunk by the 13 minute mark
@longwaytotipperary 4 ай бұрын
🥴
@ejgoldlust 4 ай бұрын
"Phistomefel" "Phistomefel" "Phistomefel" "Phissomefel" "Phishomefel" "Phishimafoo" "Phoogoomagoo" "Phhhhhhhhhhhhhhhhhhhhh" "Phistomefel"
@tb7448 4 ай бұрын
Today was the FIRST time that I solved a puzzle more efficiently than Simon. I am feeling very pleased with myself ;-)
@alanfuller4278 4 ай бұрын
Yes. Thank you Simon, for my unexpected birthday present.
@Teetuetenmogli 4 ай бұрын
I normally not even really try solving, but when I started watching I was like… how does he not see … and had a try and solved it without any theorem
@DanielCoto93 4 ай бұрын
Same here!! I was just watching him and shouting things he did not see lol
@JacksonNewhouse 4 ай бұрын
You know that the ring sums to 60 and only has 4 numbers above 5. If the inner circles aren't 6789 then you'd need to make more than 30 off of 4 digits
@ingiford175 4 ай бұрын
Nice way to look at it
@benjaminvazquez1243 4 ай бұрын
I think you can go a step further. Because you have to use the same digits as are in the arrows in the outer boxes you know you can't do better than 6/7/8/9, and I THINK you know immediately that the compositions of their arrows need to be the same as their compositions in the outer boxes. Not 100% certain about that last claim, though.
@user-gj5uc4yx3i 4 ай бұрын
The 6 and 7 arrows on the ring were fixed compositions but 8 and 9 almost could have been 2-2-4 and 1-3-5. The 2-2-4 arrow would have done massive damage and broken the puzzle.
@martinbull-gundersen8878 4 ай бұрын
Thanks - I had the exact same thought in a slightly different way - because of Phistomefel he new the sum of the 12 smallest digits were 30, so it was impossible to make 12 of them sum to anything less without breaking one of the arrows in box 5.
@ingiford175 4 ай бұрын
@@martinbull-gundersen8878 The old check the minimum, hey, its the same as the max of the 4 value trick he uses on many things except things involving SET.
@emilywilliams3237 4 ай бұрын
Simon, as you know by now, I don’t care if you do a puzzle the most efficient way ever. I love to watch you solve these puzzles and I love how you explain that theorem. I never am tired of hearing it. Thanks so much for this great video!
@longwaytotipperary 4 ай бұрын
@emilywilliams3237 and if he didn’t know, I feel the same way!! 🙂
@studgerbil9081 4 ай бұрын
Well said.
@martinbull-gundersen8878 4 ай бұрын
100% agrees, but truth is probably that 90% of the followers of this channel would have done exactly the same thing: that grid screamed Phistomefel, and if there was an easier way, I think most of us would've found it just the same way as Simon - after checking out what the ring had to offer 😀 We just don't have to articulate it as we do it.
@davidrattner9 4 ай бұрын
Always perfectly written from you Emily!!
@davidrattner9 4 ай бұрын
@longwaytotipperary you know it my friend!!
@JohnRandomness105 4 ай бұрын
11:30 Use the given 1 to prove that it's impossible for all four corner arrows to have 1s. That means that 9 = 234. So 6 is never on an arrow, and that complication is removed.
@thaumaTurtles 4 ай бұрын
I loved at around 34 minutes in when Simon realised that a cell couldn't be 4 because of the 2 4 pair above it... rather than the 4 in the same box
@mongmanmarkyt2897 4 ай бұрын
solving using sudoku rules isn't his strong suit
@mbakenemdusink9757 4 ай бұрын
we obviously didn't shout loud enough
@shadowofaman69 4 ай бұрын
He's always solving via wild abstract thoughts and misses simple sudoku boxes alllll the time lol
@MatthewDavis-hw4cq 4 ай бұрын
He does the same thing in box 2 realizing the tip of the arrow can't be a 4 due to the pencil marks in box 2 row 2, and completely ignores the 4 already on the corner of the arrow right next to it (and the 1 across the way in box 3) as he considers if a 1-4 pair is possible or not.
@inspiringsand123 4 ай бұрын
Rules: 04:43 Let's Get Cracking: 05:44 Simon's time: 40m52s Puzzle Solved: 46:36 What about this video's Top Tier Simarkisms?! Phistomefel: 24x (07:50, 08:00, 08:19, 08:30, 11:51, 12:53, 12:56, 12:59, 13:01, 13:03, 13:08, 13:23, 14:45, 16:50, 17:04, 17:54, 19:02, 21:25, 22:04, 29:01, 43:05, 43:09, 46:41, 47:13) Three In the Corner: 1x (41:04) Cooking with Gas: 1x (41:14) The Secret: 1x (49:10) And how about this video's Simarkisms?! Ah: 12x (11:39, 12:45, 24:09, 25:29, 25:29, 32:36, 34:03, 35:07, 35:58, 39:07, 41:04, 42:59) By Sudoku: 7x (09:45, 30:48, 35:22, 35:27, 41:16, 41:47, 45:01) Hang On: 7x (14:00, 14:10, 14:10, 14:10, 14:12, 39:36, 40:45) Sorry: 5x (23:45, 24:45, 25:07, 35:19, 40:42) Brilliant: 5x (00:26, 00:26, 03:22, 04:18, 49:05) Pencil Mark/mark: 5x (16:47, 32:31, 34:24, 37:27, 37:31) Goodness: 4x (12:50, 18:56, 24:16, 25:50) Proof: 4x (09:06, 09:09, 09:11, 21:25) In Fact: 3x (06:58, 08:00, 18:35) Clever: 2x (43:27, 43:29) Bingo: 2x (42:59, 42:59) Fascinating: 2x (49:05, 49:08) Shouting: 2x (02:34, 03:43) What Does This Mean?: 2x (07:37, 23:59) Weird: 2x (28:58, 45:40) Naked Single: 1x (45:17) The Answer is: 1x (22:11) In the Spotlight: 1x (41:06) Beautiful: 1x (00:50) QED: 1x (23:45) Wow: 1x (38:39) Cake!: 1x (02:43) Most popular number(>9), digit and colour this video: Sixteen (6 mentions) One, Two (70 mentions) Orange (17 mentions) Antithesis Battles: High (4) - Low (1) Even (5) - Odd (4) Column (15) - Row (11) 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!
@mstmar 4 ай бұрын
the answer to simons question at 43:00 is yes and how i broke into the puzzle. if you start with phistomefel ring, then the orange digits add to 60 (the circles are a 6-9 quad and their arrows are the remaining digits) so the blues add to 60 as well. since you cant put 7, 8 nor 9s on the orange arrows, there are only 1 of each of those in orange, and so also in blue. now we consider the blue arrows: their totals are all in box 5 and so are all different and add to at most 30, so the remaining 30 must go in the 4 blue cells without arrows. since we only have one of each of 7, 8 and 9 in blue, those 4 cells have to be a 6-9 quad.
@jdkemsley7628 4 ай бұрын
Even without "needing" phistomefel logic to solve, you likely helped orient yourself by recognizing and outlining the pattern. Grounding yourself in familiarity is always a useful strategy. So I'm glad you did it!
@JackDeHearts 4 ай бұрын
The ring pattern was trollbait and Simon fell for it lol
@MariaVlasiou 4 ай бұрын
To answer the question in the title: yes, altijd. Theorems are as necessary as chocolate for a happy life. Going to watch now.
@jmrgomes 4 ай бұрын
I love it how Simon’s brain (the size of a computer) can explain in a simple way incredibly complicated logical inferences - and hidden beauty in (sudoku) puzzles that I wouldn’t even guessed were there. And how sometimes he overlooks how sudoku is the simplest way of solving sudoku puzzles😅 32:16 for me and it was smooth sailing just by figuring out exactly the composition of each of the 4 corner arrows, and then where those digits could go on the ring! Lovely puzzle!
@fresnik 4 ай бұрын
Simon is a bit like an American and the given sudoku digits are the metric system. He definitely knows about them, and they are simpler to use, but he'll do anything to not use them. :D
@davidholt4327 4 ай бұрын
I love your videos and the chapters are really helpful for finding the start of the solve. It would be nice if you could chapterise the various proofs that you run through on a regular basis. I do admire your commitment to proving it every time, it was very useful the first few videos I watched!
@KeiFlox 4 ай бұрын
You did indeed say Nanaimo right!! I'll definitely be having chocolate cake tonight, going out to dinner with a friend :) What a treat to get an Aad puzzle on my birthday :D
@BijickY 4 ай бұрын
Happy Birthday! 🎉
@frankjiang1857 4 ай бұрын
Finished in 32:33. Not sure if the theorem is needed though it makes figuring out the phistomofel numbers trivially easy once you get to a certain point in the puzzle. I found trial and error much easier for figuring out what the numbers in the box 1 arrow had to be as that eliminated many possibilities for the other single box arrows. Once I had the arrows down, I don't think I used the theorem much though to figure out what the numbers in the ring were. Fun puzzle!
@Kirbyfan87827 4 ай бұрын
Finished in 31:59. I didn't use the Phistomefel Ring, but even without it there was a logical flow to the puzzle. I was surprised I was able to complete the puzzle! Edit: On another note, I initially misread the title of the video as "Do You Need THERMOS To Solve This Sudoku?" That's really the only reason I gave this one a try to begin with, as I really like thermo sudokus.
@bobblebardsley 4 ай бұрын
Alas no thermometers, although a Thermos flask might have been useful for hydration 😋
@jonhansen9622 4 ай бұрын
What a cool looking puzzle, I bet it's going to be a fun solve!
@alcarkerlomesy8620 4 ай бұрын
There is a simpler way to solve this: At 8:52, the orange cells sum up to 60 (2*(6+7+8+9)) -> the blue cells sum to up to 60 -> R3C5/R4C6/R5C7/R6C6/R7C5/R6C4/R5C3/R4C4 (lets call those cells purple cells) sum up to 60. Since the purple cells which are also blue can sum up to a maximum of 30 (as 7,8 and 9 appears in the orange cells only once), the purple cells in the central box are 6, 7, 8 and 9. PS: Also at 8:52, R8C1 is 1 😋
@pvdleek 4 ай бұрын
11:33 For me. Very surprised by the lengthy solve my Simon. It was immediately clear to me where most 1's are in the puzzle.
@adrianhead6272 4 ай бұрын
Far be it for Simon to spot the obvious.
@dicebar_ 4 ай бұрын
59 minutes and, as ever, out-eleganced by a wonderful solve by Simon ☺
@arturslunga4226 4 ай бұрын
Simon, S-tier sudoku solver: "I accidentally used an overly complex method of solving this, my apologies." Me, who has never solved a sudoku ever: "Lol it ok"
@JPgreekgaming 4 ай бұрын
For me it's never about the solve itself but the journey getting there, and that was a beautiful path to take!
@longwaytotipperary 4 ай бұрын
Agree!
@Mennoo_ 4 ай бұрын
Regarding the end: there was actually. As soon as you figured out the contents of the phistomefel ring by the arrows in the corner box (i.e., 6-123, 7-124, 8-125 and 9-234). You know that the blue digits in total sum up to 60. Adjusting the blue digits from the arrows to the bulb, it gives you that the 4 corner cells of b5 + the 4 non-arrow cells on the ring sum up to 60. Clearly the corners in b5 sum up to a maximum of 30 by 6789. But the 4 remaining cells on the ring (the cells precisely in the middle of each edge) also sum up to max of 30. Best way to imagine that is to see the contents of the phistomefel ring as a scrabble big, we take all those digits out of it and order them all from low to high. We know that those 4 remaining cells on the ring must be take from those digits, so we take the 4 highest digit from that ordered set, of which we know the 4 highest digits are the digits 6-7-8-9. Therefore the maximum those digits can sum up to is 30 as well, combiend summing up to 60 which it has to be. Therefore it is determined that the bulbs in b5 form a 6789 quadruple, and the non-arrow cells on the inner-ring form a 6789 quadruple
@Mennoo_ 4 ай бұрын
And to add on this, in my solve I made a lot of use of the Phistomefel ring and the PotatoHead Theorem, and to me it made the solve a lot easier. The reduction you can make with that that you need 2 four times , hence in every corner and on every edges is very helpful, especially combined with the 6789 quadruples as described above. So I'm glad you introduced those theorems in this video Simon. It's never a bad thing to (re)introduce theorems to the public :)
@dustpan5356 4 ай бұрын
To answers the question: No, you don’t NEED the theorems to solve the puzzle. Seeing the video title, I decided to try to solve it without theorems (though as soon as you look at the grid it screams Phistomofel so how could you not? 😂). My opinion is that Simon’s solve path was quicker than mine especially if you take out his time to explain the theorems. Either way, gorgeous puzzle and I enjoyed it very much!
@danitajaye7218 4 ай бұрын
Very enjoyable and informative solve! Don't ever doubt your skills. You are an exceptional puzzle solver! Wonderful.
@longwaytotipperary 4 ай бұрын
Agree!
@franzelmagetower 4 ай бұрын
Beautiful puzzle as always by Aad. 18:38 here. Just used Phistomefel ring judiciously along with the main diagonal restrictions. Probably could have saved some time had I remembered the old rule about the central square, the ring, and diagonal restrictions but a fun solve that felt interesting as well expertly guided. That given 9 was key!
@ghosttwo2 4 ай бұрын
The two in the center was knowable as soon as it was known there were four of them in the corners. The need for a two on the diagonals forces it into the central box, and the central circles limit it to the central square. Doesn't seem to do much work, but it's an early deduction.
@arielmoonsoo9219 4 ай бұрын
A rare puzzle where my solve time came in under the video time at 45:55 (admittedly with conflict detection on). I recognized that phistomephel would be a useful tool while solving, but couldn't figure out how to apply it. After completing the solve, but before watching the video, I mused on the relationship between the outer circles (c/r 2/8), inner circles (c/r 4/6), and the ring leftovers (those squares on the inner ring not on an arrow - c5r3/7,c3/7r5). Proving the outer circles come from the set 6789 was done in video. Proving the inner ring requires recognizing that there are no possible sets of digits in the ring that are smaller than the sets on the arrow lines in the corners. This then leaves the leftovers as being the same set.
@OlafDoschke 4 ай бұрын
43:45 The simple answer - at this point - you need a 6789 set in the ring for the 4 2x2 corners of the grid. Well, you can see that even from the get go by a bit of juggling digits on the Phistomefel ring. Start in the grid corners and you can remove the arrow cells and double the arrow circles, that means the arrow circles sum to 30 and the Phistomefel ring sums to double 30=60. Now, also remove the arrow cells on the ring and instead colour the arrow circles in box5, which means instead of the ring you now highlight a diamond of 8 cells that need to sum to 60. too. It's not necessarily two sets of 6789, but of course the cells in box5 can only be 6789 at max as they see each other in the box. The low digit ring cells need to be 30 with the exact combination of digts as in the grid corners and they need to be in the ring corners so the box 5 arrow circles are minimum and maximum 30 and now need to be 6789. The diamond corner cells now also need to be 30. They could theoreticlly be two 7/8 pairs, but then, as initially said, they are actually the four digits in the grid corners so they also have to be 6789. qed, you have the 6789 on the ring in the cells r3c5, r5c3, r5c7, r7c5. And also a 6789 in the corners of box5 as the other 12 cells of the ring need to sum to 30, too, with the exact digits as on the grid corner arrows.
@johnh2052 4 ай бұрын
At 41:33, Simon almost calls out the 68-pair in column 3, then thinks it's always been there and moves away. I laughed aloud, because of course the arrows for that pair are completely filled in, and he could have simply placed the 6 and 8. :)
@Freezeezy3 4 ай бұрын
one way to see the four circled digits in the central square must be high is to use Phistomophel again. They are the sum of 12 of the 16 phistomophel digits, and the absolute minimum of 12 of those digits is 30, so the circled 4 digits must be maxed at 6, 7, 8, and 9
@nonyobisniss7928 4 ай бұрын
Interesting. I somehow did it completely without invoking phistomefel at all.
@H0lyMoley 4 ай бұрын
Think this is the first time I've ever beaten Simon's time. I worked out quickly that 1) you can easily pair up the 6, 7, 8 and 9 circles, giving you a whole bunch of numbers that have to match, and 2) the middle digit has to be a 2, making the rest of the solve vastly easier (because it cuts down so much on the possibilities for the outer digits on the diagonals). Still interesting watching Simon solve it in a way more involved way.
@JamesRisse1 4 ай бұрын
This is also the first puzzle I've ever solved faster than Simon. 42.01
@sampathkumar-ej7xl 4 ай бұрын
A great pleasure to solve one of Aad's creations that have no complicated rules but elegant solution paths.
@DanielCoto93 4 ай бұрын
26:38 for me. I love how Simon can deduce the most incredible difficult things and sometimes he just does not see the easy things lol.
@piarittersporn 4 ай бұрын
Very beautiful and relaxing puzzle.
@eorrfu82 4 ай бұрын
I used set and equivalence on the diagonals adding to 90 to figure not only where 6789 must be but the 2 is the center and the digits must be 12345. It was a much smoother feel than what Simon did.
@maggieelliott5896 4 ай бұрын
Maybe I just fell into the right path, but for the first time, I managed an Aad puzzle in less than 20 minutes without help from the video, and without a thought of Phistomefel! Simon, you really overcomplicated this one!
@bobblebardsley 4 ай бұрын
Rhyming Rules (with apologies to Aad for once again poorly attempting to rhyme with his surname)... In every column, every row, insert the digits 1 to 9, and also in each box they go, but into each box just one time. Along the main diagonals (both positive and negative), the nine inserted numerals must never be repetitive. On every arrow's arrowed cells the digits entered must combine to match, in sum, the cell that dwells upon the base of those cells' line. If you can keep these rules aligned, with attitude unfettering, you'll crack the grid so well designed by famed Aad van de Wetering.
@pouletbelette 4 ай бұрын
Happy to see that you are still very much inspired. Good job!
@bobblebardsley 4 ай бұрын
@@pouletbelette I can't promise to do it every day but if people keep wanting it, I'll keep doing it when I'm able 😊
@longwaytotipperary 4 ай бұрын
@@bobblebardsley 👋🏻 count me as someone who always enjoys your poems!!
@bobblebardsley 4 ай бұрын
@@longwaytotipperary Duly noted 😉
@greenoil6628 4 ай бұрын
Solved in 20:31. My fast break-in is just like Simon wondered at the end of video.The 4 circles in box1,3,7,9 must be different due to blue diagonals and therefore must be 6,7,8,9. The phistomofel ring equivalent to sum of the 4 corners 2x2 squares then must be sum to double of 30 = 60 due to 4 arrows at the corners. And we know that the ring sum is also equal to the inner circles in box5 with 4 remaining middle cells in the ring due to the inner arrows. The inner circles sum to max of 6,7,8,9=30; hence 4 remaining middle cells in the ring must be sum to at least 30. But we learn from 4 corners 2x2 squares that there is no way to have 2 7s, 2 8s or 2 9s due to the corner arrows. So they are 6,7,8,9=30, and so do the inner circles.
@zirco77 4 ай бұрын
Yes, a "better use" Phistomefel ring is the answer to Simon's question at 43:14. Here's how (spoilers below...) . . From the start you find that the four 2x2 corners are 6789 in circles and their "constituents" on arrows. Then through Phistomefel ring theorem, you can tell that the minimum sum of all arrows on the ring is the sum of all low digits in corners, that is 30. All circles for those arrows are in box 5, and the maximum sum for those circles is 30. So it's got to be 30 and 6789 as well. Many deductions flow easily from that point.
@andykillsu 4 ай бұрын
The second you proved that 4 of any digit (2 in this case), was in the 4 cell corners, you knew immediately that it had to also be in the center cell. Because that digit cannot go in the diagonal cells in the 4 cell corners, that means in the 4 corner boxes, they do not have a 2 in the diagonal cells. That means the only cell that will satisfy putting the digit (2 in this case) on both diagonals, is the middle cell. It’s basically the opposite of the phistomefel ring extension you mentioned.
@steve470 4 ай бұрын
That works for this puzzle, but it doesn't generalise. It requires the circles in the outer 2x2s to fully prevent 2 from appearing on the diagonals.
@andykillsu 4 ай бұрын
@@steve470 No, it works in any diagonal sudoku. If you can prove 4 of any digit must be in the 4 cell corners, then it is impossible for that digit to be placed on the diagonal in the corner boxes because you then cannot place 4 of said digit. Thus it needs to go into the center cell to satisfy the diagonals.
@steve470 4 ай бұрын
@@andykillsu If it weren't for the circles, why couldn't you place that digit in r2c2 (on the negative diagonal), r1c9 (on the positive diagonal), r8c1 (on neither), and r9c8(on neither)?
@RedBarchetta2019 4 ай бұрын
Amazing - I just solved a very similar puzzle on LMG today - Battle of Evermore by kuraban - and what a treat these two puzzles are! Both are quite interesting and use great deductions. Aad gave us an easy one today. Kuraban's took me twice as long. Thanks Aad! Great puzzle and fun!! Now to watch Simon solve this :)
@21nck93 4 ай бұрын
I honestly had a great time with this puzzle, it took me 28.5 mins and the logic just came one by one. It's an intermediate puzzle that's perfect for a quick break ❤
@craigthorsen 4 ай бұрын
WOW! This was a fun one.
@NicoLeDahut 4 ай бұрын
For the 4 high digits in circle in grey, it is the same as the 4 circle digit in orange. Due to arrows. Then diagonals and given 9 place in middle on neg diag.
@Kinada 4 ай бұрын
29 minutes. Very cool puzzle and thankfully I'm pretty familiar with how this geometry can restrict itself by this point.
@CrankyOtter 4 ай бұрын
Right after Simon proves that if the number can’t be on a diagonal in the 4 corner boxes, it must go in the middle square, he places 2s in the corner boxes, not on diagonals, and doesn’t use that logic to plop 2 in the middle box because there’s an even more obscure way to logic it there.
@chocolateboy300 4 ай бұрын
I got 68 minutes. This puzzle is really good at testing your scanning. I was a bit slow on it, but caught them all. Really nice!
@andrewcook4873 4 ай бұрын
Great puzzle. My solve was much different. I didn’t figure out the 2s in the corner boxes and it took me ages to finally figure out where the 2s went.
@rhysm2526 4 ай бұрын
The proof of the digit not on the ring being in the center can be quicker than you made it. As soon as you establish the digit isn’t in orange or blue, just ask where is it on each diagonal and on both it must be in on the diagonal in the central box. No need for the green shading.
@rentalcustard 4 ай бұрын
Solved this in 30:39 without using Phistomefel or any other SET tricks, except to restrict the ring digits which were not arrows to being high (6789), and I had a lot of fun doing so! I'm fascinated to see how Simon went about it!
@RantingCentre 4 ай бұрын
Simon after explaining phistomophel + potatohead logic: "I'm sure many of you saw it instantly when looking at this puzzle. Me: nervous monkey meme
@HunterJE 4 ай бұрын
28:32 The 2 in the center can also be had a bit earlier, namely as soon as you placed the 2 pencil marks in the phisto regions (all of which must be off the diagonal to fit them all in, which therefore rules them off both diagonals in all but box 5 and so requires them to be at the intersection)
@stevieinselby 4 ай бұрын
Ironic, isn't it - we started with the Potatohead theorem that a digit that doesn't appear at all on The Ring goes in the central cell, and ended up finding that a digit that maximally appears on The Ring is in the central cell!
@thebitterfig9903 4 ай бұрын
A really cute puzzle. It flows in such a lovely way. I'm generally slow at these, but my 51 minute solve never felt frustrating. Just gorgeous construction. In some ways, it didn't feel like Phistomofel did a lot, since figuring out the way the arrows paired off due to diagonals got a lot of the way there. But then again, it solidly fixes the same triples on the inner and outer arrows (preventing any complications), and then it fills in the four non-arrow cells with 6789, which again, mostly just keeps things clean. My favorite digits were the 4s, first the given 4 in Box 4, which rules out 7 on the arrows in Boxes 1 and 7, and then finding the 4 in box 8, which forces a 5 onto row 9, which fixes the 35 and determines the 6 and 8 arrows. But I suppose that if someone else learned these things in another way, they'd have other favorite digits.
@dolf370 4 ай бұрын
Very fun puzzle. You could kind of see much of where it was going, but then find it logically took me some doing, 79:33 to be exact, but I did manage it.
@ib9rt 4 ай бұрын
As you said at the end, you missed part of the break-in that the middle circles had to contain 6,7,8,9. Because the smallest total it was possible to put on the blue arrows was 30 (three sets of 1+2+3+4 equals 30, using the smallest possible digits in every position). And the largest total you can make from four digits is 30 (= 6+7+8+9). Therefore that is what the circles contain. Sometimes, making a puzzle look like it needs Phistomephel may be a trap for the unwary.
@ib9rt 4 ай бұрын
@@billevans7488You will if you watch Simon's solve.
@thenatundi9009 2 ай бұрын
Do you need theorems to solve this sudoku? No, but it is much more satisfying to see solved that way!
@michaellautermilch9185 4 ай бұрын
Actually beat Simon's time!!! But I didn't take the time to explain or prove each step to an audience either, so I'm sure he's still faster. Great puzzle!
@KrisCadwell 4 ай бұрын
Solved this one, solid puzzle.
@shiftyhexahedron7891 4 ай бұрын
Just over 85m for me! Been awhile since I could manage a CTC solve, what a nice puzzle!
@martinandersen1361 4 ай бұрын
A nice 21:11 solve. actually not to bad of a puzzle, very elegant and great puzzle
@stumbling 4 ай бұрын
Aad makes the familiar strange and the strange familiar. :D
@stevieinselby 4 ай бұрын
I proved that The Ring included a 5 without reference to Potatohead, but by the much more simple expedient of looking at column 1, which has a 4 in it that isn't part of The Ring, meaning that the magic cells must include a 5 or higher, but can't include a 6 because of the 9 being 2+3+4.
@chipsounder4633 4 ай бұрын
Got to give Aad credit as you were sent on a wild goose chase.. you could have had the centre digit too as there had to be 4 2s in the ring 17 minutes in..
@raysouth1952 4 ай бұрын
Fun puzzle. I saw the possibility of the theorem but saw some early wins so pressed on. Pretty straight forward though still requiring some thought.
@brianagnes 4 ай бұрын
Part of the reason Simon took so long was trying not to use or explain Phisto/Potato (even though it was obvious to use them) and then lamenting about whether it was needed or not for half the puzzle. As soon as you get 6789 in corners, then you know total is 30 in circles and 30 on arrows. The 12 cells of arrows on ring (min 30 via Phisto) all have circles in center box (also a 30 max) so 6789. Because arrows on ring are 30 then 6789 go into only squares without arrow on ring. the 45 in middle box get pushed up/down with 123 in box5 row 5. Looking at negative diagonal 5 must be in r1c1, r3c3 or r7c7 so it is on ring, that with 1 in the corner (limiting count to 3) gives exact disposition of 1236, 1247, 1258, 2349.
@GrimReaper1312666 4 ай бұрын
28:51 for me, relocating the arrows into the bulbs and then realizing the sum of the ring is forced broke it open for me together with the realization that you need 4 2's in the ring
@EmonEconomist 2 ай бұрын
Finished this one in 21:11 - I was intimidated by the video length but this was rather approachable :)
@alanclarke4646 4 ай бұрын
This was a fun puzzle 😊😊
@deniseiln 4 ай бұрын
Before I saw the 1 in the corner, I figured that there could only be 4 1s and 4 2s on the arrows in the P-ring, and they would need to be in the even numbered boxes (2,4,6,8). The diagonals meant that the four corners of the P-ring could not have repeats, so the least they could be were 3,4,5,6. (1+2)*4 = 12 and 3+4+5+6=18 and 12 + 18=30. The least the arrows could add up to is 30 ...and since those arrows all start in box 5, and would have be different numbers, the most they could be is 6,7,8,9 ...and then Simon started the solve and pointed out the one in the corner, and I thought... oops, never mind!
@markmcb42 4 ай бұрын
Very fun solve, I was able to solve it pretty quickly without using phistomefel, my time was 29:06. As always though, really interesting to see how Simon attacks the puzzle.
@adnagapot 4 ай бұрын
Very fun watching you solve this, without phisomefel I managed to solve it in about 30 min, but your way was much more entertaining
@RyanBrown626 3 ай бұрын
Simon's so busy worry about whether he needed phistomefel that he doesn't notice he should be using it more.
@F1r1at 4 ай бұрын
43:02 for me, without a phistomefel, didn't even think about it (and very happy it wasn't required!). Even so, the puzzle is not hard at all.
@reidakted4416 4 ай бұрын
I'm sure you've worked it out more elegantly, but I noticed that the 4 and 5 in row 5 means that you have to have a 45 pair in box 5, column 5, which means that row 5 in box 5 must be a 123 pair. There are also a number of triplets and quads along the diagonals. 6789 can only appear in the circles, and using a little more sudoku, I managed to show that there is a 35 and 12 pair in the first and last two cells of column 1. And a 345 triplet in the upward diagonal (and 1345 quad in the downward diagonal) meaning the center cell cannot be a 1 or 3, so it must be a 2. That knocked out the center 2 pencil marks and put the 2's in a cross around the blue ring.
@jimi02468 4 ай бұрын
How does it directly mean that? Why could you not have a four or five in a circle in box five just by thinking of the given digits?
@RichSmith77 4 ай бұрын
Not certain, but it looks a lot like you forgot you could have repeated digits on the inner arrows (at the start)?
@reidakted4416 4 ай бұрын
I don't believe so. Because the circles are all 3 cells, they have to be 6789, and because they lie on the diagonals, they cannot repeat. So the inner set of circles is a 6789 quad, and the outer set is a 6789 pair. So the diagonals already contain 6789 and only need the 12345 placed. Because of the given 45, and that the inner corners of box 5 are a quad (6789), we know that the center 3 cells in row 5 are a 123 triple, and the other 2 cells are a 45 pair. The circles in boxes 7&9 cannot be a 9 because of the given 9. So the circle in box 7 must include 1, which can only be on row 8 (because of the given 1). That gives you a 235 triplet in column 1 (neither corner can be a 6 because of the diagonals). You cannot have more than one each of 6789 in the blue ring (because the circles contain a set of one each and there are only 4 cells that do not see the central circles or the diagonal - rows 5 and column 5 of the ring). So (by Phistamefel) the only 6789 in the ring are the 6789 of the circles in the orange boxes, and therefore a 6 cannot appear on any arrow (not can a 789 appear on a 3 cell arrow). As for the center cell, it cannot be a 3 because there needs to be at least one three in the corner (first, house rules, but second because of the 35 pair I mentioned above) and because of the diagonal, a 3 cannot be in the center and either corner.@@RichSmith77
@RichSmith77 4 ай бұрын
@@reidakted4416 The inner circles are on three cell arrows, but the digits on those arrows don't see one another, so theoretically could have repeats. You could have 1+2+1=4 on one of those inner arrows. There are several people in the comments who have explained why the inner circles have to be 6789, but I don't think it's a trivial deduction. (It certainly eluded Simon). You just started with the claim that they couldn't be 4 or 5 without attempting any explanation.
@stevesebzda570 4 ай бұрын
@@RichSmith77, I think there was foreknowledge that the digits couldn't repeat on those arrows. The orange equaling blue (and 6789 going cross-ways in col5 and row5 -- which he explained-- the arrow cells if they had repeat digits -- it somehow doesn't work out). I don't know (he mentioned "row5 and col5," though). 🤔😆
@Xiuhtec 4 ай бұрын
If after doing Phisto he had just collapsed the arrows on the central square to their circle equivalent sums he'd immediately see the four then-blue squares in box 5 had to sum to 30. This is how I broke in straight away, and finished solve in about 40 minutes with my very slow scanning. (Can also prove with Phisto that the remaining 4 blue squares are also one each of 6789 though that comes in less handy.)
@ol1ver49 4 ай бұрын
Only just seen this one - done in 28.11 and didn't even THINK about Phistomefel until I saw him mentioned in the comments
@thebitterfig9903 4 ай бұрын
Now I’m starting to think that I might have solved this with faulty logic. Technically. I got the right answer and it felt really clean and pretty, possibly doing what was intended, but maybe I couldn’t prove it. You can tell from Phistomofel that all the digits on the outer arrow are on the ring, and that the non-arrow cells on the ring have to correspond to the four bulbs. Where I might have made a mistake is in assuming that there wasn’t any shuffling. My assumption was that the inner and outer arrows matched, and between the blue diagonals and regular Sudoku, starting with the 9s, you can see a pattern. 9 and its arrow is either linked to the box 1 outer arrow, and the bottom-left inner arrow, or to box 3, and the top-left inner arrow. So I colored those blue and green, and then noticed the linkage between the other two pairs of arrows, coloring the corresponding inner-outer pairs yellow and purple. It was a pretty matchup, and it felt great and solved correctly, but maybe that was just unproven intuition.
@robertogonzalezdacosta1836 4 ай бұрын
Simon always says he’s partially colorblind but I suspect he’s grayscaleblind thus his inability to see black giving digits 😃
@theoryjoe1451 4 ай бұрын
When you really get going towards the end, you remind me of a sports announcer.
@elaadt 4 ай бұрын
33:53 was my time. This is the first time I solve in a shorter time than Simon. Even though he explains Phistomefel so eloquently, he's still always quicker than me. I used a different solve path and used Phistomefel only for the 6789 in the ring after I figured out the corners.
@iceberg54321 4 ай бұрын
39:15 was hilarious, it is one, not one or three, because you have a 35 pair in the row. :)
@jimi02468 4 ай бұрын
I discovered a beautiful way to determine from the beginning that the circled digits in box five must all be 6789. In fact, you can know from the very beginning that all of the cells r3c5, r4c4, r4c6, r5c3, r5c7, r6c4, r6c6 and r7c5 must be only the digits 6789. First make the Phistomefel pattern by coloring the ring orange and the corner boxes blue. Then from the "ring" part, remove the colors from the arrows and substitute a color to the circles in box five. By doing so the sum between orange and blue still stays the same. Now by using the diagonal and arrow logic, it is very easy to see that the circled digits outside of box five must all be 6789 (they must all be different and simultaneously six or higher). What this means is that the blue cells altogether sum to 60 - in other words, the digits in the circles sum to 30 and the arrows make it double, so you get 60. Now you have 16 cells that sum to 60 in blue and only half as many cells in orange - but they also need to sum to 60. That suggests that it is very hard to use any low digits in those eight cells. In fact the lowest possible digit that you could use in orange is a four by using a double nine and an eight in the "ring" of the Phistomefel pattern. However, that poses a problem. While you could use a double nine in the ring, you could not use a double nine in the blue cells of the Phistomefel pattern. You are allowed to only one nine in one of the circles in blue (because the circles in blue are all different) and obviously you can't have a nine on an arrow. In fact you cannot repeat any of the digits 789 on the ring. The digit six is the highest that could be repeated. So to maximize the orange area without using a repeated digit from the digits 789 on the "ring" of the Phistomefel pattern, the orange area can not sum to more than 60. But that was the blue sum! So the absolute maximum of orange is equal to the absolute minimum of blue. So orange has to therefore consist of only the digits 6789.
@RecreationalCynic 4 ай бұрын
I solved it in 56:29 without the need for any theorem. I colored the Phistomefel ring to see if it would help but I'm not sharp enough to know what to do with it. I struggled a bit with the 6 and 8 arrows, as I didn't realize all of them needed to have 2, so I kept the possibility of 1+3+4=8 for all of them. Normally I'm afraid to try Aad's puzzles because he tends to use weird set tricks that I usually can't figure out, but they're always fantastic puzzles.
@rainerzufall42 4 ай бұрын
6789 in the corners of box 5: Look at where 6789 can be on the diagonals: Can't be on the arrows, can it be in the center? Actually no. So it has to be in the 4 circles each of both diagonals. Does that convince you?
@BryanLu0 4 ай бұрын
I think KZfaq hid my comment because it's only numbers? Naturally you have 126 giving 9, but the arrows on the ring allow for repeat digits so double 1 and 6 or 7 gives 8 or 9.
@rainerzufall42 4 ай бұрын
@@BryanLu0 I can't see, how you can have a 6 on either arrow in this puzzle! Could be for one of these arrows, but not for all 4 of them!
@AngelWedge 4 ай бұрын
My thought once you know the digits on the corner arrows is that you now know all the digits on the ring. The digits on the ring sum to 60. The maximum sum for the non-arrow cells is the 4 highest digits available, so 6789. This means the arrow cells (and therefore the circles in box 5) must add to at least 30. So… the circles in box 5 and the non-arrow cells on the ring are both 6789 sets.
@BryanLu0 4 ай бұрын
@@rainerzufall42 One is all it takes
@anaayoung9142 4 ай бұрын
Not at hard I was thought! Thanks! 😀
@PeterZaitcev 4 ай бұрын
Got in 25:16. Liked the logic behind the puzzle
@philipmetcalfe4736 4 ай бұрын
nice solution..
@nakorbluerider 4 ай бұрын
I'm not sure how great of an impact it had on the overall solve, but I did end up using the Phistomefel ring to deduce that the four cells in the blue ring which were not on arrows were a set of 6789, since otherwise the circles in box 5 would have to add up to too much. (The outer 2x2s sum to 60, and the arrows in the ring mustn't sum to more than 30, but 30 is also the minimum sum that 12 of the digits in the ring can make.) This gets 6 off the arrows in blue, and forces all the small digits onto them. I didn't remember the centre digit trick, but fortunately you can pick up that there's a required 5 from examining column 1. I actually did try colouring 3's and 5's as well, after doing which I promptly realized that I had already placed a 5 in a column with a 35 pair, and that perhaps I need to work on my scanning a little.
@longwaytotipperary 4 ай бұрын
I ❤ magic theorems!!! 🙂
@Gonzalo_Garcia_ 4 ай бұрын
9:00 for me. Great puzzle!!
@johnbell9074 4 ай бұрын
34 mins for me. When I realized the totals for the 4 corner 2x2 arrow sets was forced, then for the phistomophel ring, the same total applies. That forces the sum of box 5 arrow totals as well. It flowed from there for me.
@DerFischStinktVomKopfe 4 ай бұрын
That was Simons question near the end, wether it is indeed forced or just happened to be.
@PathOfShrines 4 ай бұрын
Very nice. Straightforward, no theorems required. 28:59
@jarvisa12345 4 ай бұрын
30:05 “I've realised that I can't put 2 in the corner of the Phistomefel ring… we need 4 2s.” … and the fact that there is a 2 in central cell and thus on both diagonals.
@bobh6728 4 ай бұрын
“Maybe some jiggery pocket going on” or maybe the arrow can’t add up to ten.
@claygaetje805 4 ай бұрын
Right around the 25-minute mark, Simon says there must be an easier way to solve this. Focusing on where to place the corner arrow sums on the Phistomefel ring worked for me, in 17:36. Which is good because the path Simon found is beyond my capabilities!
@wojciechpietrzak1981 4 ай бұрын
It was very funny to see a complex logic again just because of missing 35 pair in r7 and, more important, 2 in r7c4, resolving 23 pair in r3c4 and r4c3. Funny in a positive way 🙂
@Balakin2 4 ай бұрын
I believe you could have proven the central 4 arrows to be 6789 if you kept orange and blue equal to the same sum by removing the arrow digits from blue and adding the same sum back with the arrow's circle then you know the orange sum is 2*(6+7+8+9), and you know that the central box contains, at max, 6+7+8+9, meaning you'd have to get the rest of that sum using only 4 digits also found in orange, which must also be 6+7+8+9
@Balakin2 4 ай бұрын
this would confirm the contents of the box 5's arrow circles and the 4 blue cells not on arrows all at once
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