Thank you very much Simon for featuring another puzzle of mine and for very kind comment! I’ve been exploring Wheels Sudoku lately, it feels like a very underrated constraint. Would love to see more puzzles with it. Normal Wheels Sudoku didn’t have the number of rotation rules, but I think it works very well for this puzzle. Shoutout to Chameleon for the software and to Malrog for Pivots mechanic inspiration. Hope you all enjoy the puzzle as well!
1) Simon has the brilliant insight that each coloured centre cell has to come from one of the mod-4 sets {159},{26},{37},{48} (excluding the set that's common to those particular coloured wheels). 2) Simon forgets the above for most of the solve! You have the purple {159} set in box 3, so you can remove 159 as candidates from the box 4 centre! Also, disjoint sets allows you to remove 9 from r1c2 for ages, starting a whole string of deductions.
Yes; if he'd thought in terms of equivalence classes mod 4 he could have made his life much easier, I think. You don't care at first whether such-and-so central digit is a 2 or a 6, just that it is one or the other of those. Very nice puzzle, though, and I greatly enjoyed watching the solve.
Yeah I ended up painting in the [159][26][37][48] triples into the boxes and removing colors they couldn't be and it helped a lot in the beginning, and then near the end I completely forgot about disjoint sets on a 279/79/79 triple for the 2.. So I can't blame Simon for forgetting about earlier logic lol!
I love these videos where Simon gets confronted with a new logic. We get to enjoy his genius at work. I'm quite sure that if I had tried this myself, I would have been lost a long time in figuring out where specific digits could or couldn't go. Simon, in contrast, sets out to *truly* understand the logic. And sure enough, he does. And explains it nicely, too, with the three colours and the four rotationally equivalent sets, and the fact that once you determine one set for a given wheel, the sets on the other two wheels of the same colour can be derived. The funny thing is though, it's also typical Simon to immediately forget to apply this logic. Let's call him a "distracted genius"!
I was just gonna sit tight and watch the video... Then I thought to myself to try it out beforehand. Got stuck looking at a blank puzzle for ten minutes. Decided to watch video. Started to watch it, but before actually seeing anything happen I thought to myself to try harder. Then a lot of insights came, one by one, building up little by little from intuition and eventually I understood the mod 4 beauty behind the puzzle. From there I wouldn't say "smooth sailing" but I managed to break in and then I was off to the races. One hour later, with only my wits... I was done! I'm so proud of not having given up in the end!
In other news, I just noticed: if you type two alternating digits in a wheel center (e.g. 1,2,1,2,1,2...) "just fast enough", i.e just before animation completes, the wheel spins faster and faster... then in settings, set animation speed to slow, and they'll spin for a while once you stop typing. Then you can try to make 4 or 5 wheels spin at once! Yeah ok, I solved the puzzle and I was just messing around, it's about midnight here. But rest assured, I can still be invited to parties. 🤣
Wonderful construct! It was difficult for me to follow Simon's wanderings at first, but once the workings of rotations got through, it made sense. The only thing I can beat Simon on is scanning for simple Sudoku digits!
I frequently joke about "Sudoku Man refuses to do Sudoku in Sudoku puzzle" and I know it's just that much harder when you're on-camera vs. watching or doing the scanning yourself with no pressure to talk it through.
I really enjoyed this video - I am coming to it a couple days after it was initially posted because of busy times here, and I'm so glad I watched it! I disagree with some comments below about your forgetting deductions and logic that you discovered, or failing to use it, or whatever. I felt, from my vantage point of being a watcher and not a solver of this puzzle, that you did keep things in mind very well. I don't really understand the comments that suggest that you didn't. Nevertheless, as always, Simon, your glee at the new constraints and software to support it is almost as much fun as the solve! Thanks for this video and for everything that you (and Mark) do to keep the sudoku puzzles coming two-a-day every day of the year. It is such a source of pleasure to me to know that I will get to see you wrestle with something beautiful every day.
Simon lost the conclusion pretty quickly that you could only have one number from each set in a color. So, once he got 159 in the center in box 3, he could have eliminated 159 in the center of box 4, leaving a 37, which would have allowed him to place the 458 immediately.
Brilliant! Thank you @CrusaderPuzzle for that puzzle, I really liked this totally new, out-this-world constraint. Funny though how Simon is normally quick to mention modularity in some others puzzles but didn't spot (at least not explicitly) that all wheel centers were arranged in a modulo 4 sub-puzzle. I was really expecting Simon to go on with explaining modularity as he always do so well. He was nearly there with his yellow digits set, but ended up resolving centers by combining parity constraints instead. Anyway, in the end, that still made the wheels on the bus go round and round.
What a fantastic puzzle. I had a much faster break in by pencil marking 1, 2, 3, and 4 in all the center squares based on the number of turns they could have (ignoring 5-9 initially). I was able to make a lot of eliminations pretty quickly that way and start pencil marking all the digits on the wheels.
I did the same. It looked intimidating based on the title and thumbnail, but it turned out to be very approachable for me. Plus I appreciated that the puzzle let me know when I got the rotations right.
It came very quickly to me that there was a strong relationship of modularity for wheels in boxes 1-5-9, 2-6-7 and 3-4-8, and once I found what this implies for the modularity of wheel 6 and the consequences in boxes 3 and 9, the rest of the solve went pretty smoothly. Very fun and unique puzzle!
A very lovely solve. Something fascinating that didn't come up in Simon's solve (because he keeps "Auto-Check On Completion" turned off) is that there's actually two stages of completion check-- one for the wheels, then another for the puzzle as a whole. When I filled in the last digit in the center of a wheel, I got a pop-up confirming that the wheels were all correct. Which I found pretty interesting.
it's great that it's there honestly. i have a history of making mistakes in these puzzles and getting all the way to the end before being told "you are dumb" is one of the reasons i don't do these puzzles often. (i did do this one tho, it was too interesting to pass. :P)
This just happened to me too. I made 4 sets of numbers: [159,26,37,48], then the 3 sets of wheels [Red, Green, Blue] - from those 2 sets, I made out 8 different solutions to the wheels, and with knowing R5C2 was forcing 4&8, and R5C8 forced 2&6 into a vertical lock, it was easy to find the solution for the wheels. I was in shock when the popup notified me.
26:00 finish. I took each pair on the wheels and mapped out possibilities, noting that some combinations of positions will break the disjoint sets. This proved that the wheel in box 1 had to be even, and in box 6 had to be odd. This break-in allowed me to finish the wheels quickly, leaving a tricky disjoint sets puzzle remaining. Excellent!
I also played around with the wheels in the beginning, noticed that when you just choose one of the 3 rotation possibilities for each wheel it solves the other 2 wheels. It also makes the parity thing quite obvious. So you end up with the 48 pair and the 26 pair and from there on you get the 9 wheel digits relatively quickly.
25 mins for me - started watching the video and spotted thw breakthrough almost immediately. Used 4 dif colors for the centers of the wheel.. Now came back to watch Simon again.. Must say it feels so good to be able to see stuff he doesn't immediately.. Even if it happens once in a blue moon (oh wait theres a super blue moon tonight! No wonder!!!!)
What a wonderful channel. I don’t watch often, but it never fails to rase my spirits when I do. Keep solving puzzles and problems and make people smile.
For me, Sudoku broke down relatively quickly. (1) Similar to Simon, I first determined the three wheel-groups: 37-group in Box 1/5/9, 26-group in Box 2/6/7 and 48-group in Box 3/4/8. The respective groups must have different settings (Modulo with 4) to satisfy the Disjoint Groups rule. (2) Then I looked at each of the three groups individually and found only the following settings for them (taking advantage of Disjoint Groups rule): Box 1 (Modulo 0,2), Box 2 (Modulo 0,1), Box 3 (Modulo 1,2), Box 4 (Modulo 1,3), Box 5 (Modulo 1,2), Box 6 (Modulo 1,3), Box 7 (Modulo 0,3), Box 8 (Modulo 2,3), Box 9 (Modulo 0,1). (3) Because Box 1 always has a horizontal setting and Box 6 a vertical setting, wheel in Box 3 sees a 2367 quadruple. Thus it loses its modulo 2 setting and is clearly modulo 1. (4) The causal chain now reads: - by quadruplel: Box 3 is modulo 1 with 4 in r1c8, 8 in r2c7. - by disjoint groups: Box 4 is modulo 3 with 4 in r6c2, 5 in r5c1, 8 in r4c2 - by disjoint groups: Box 8 is modulo 2 with 4 in r8c6, 8 in r9c5 - by 48-pair in Box 4: Box 1 is modulo 2 with 3 in r2c3, 7 in r2c1 - by disjoint groups: Box 5 is modulo 1 with 3 in r4c5, 7 in r5c6 - by disjoint groups: Box 9 is modulo 0 with 3 in r8c7, 7 in r9c8, 9 in r7c8 - by 48-pair in Box 4: Box 7 is modulo 3 with 2 in r9c2, 6 in r8c3 - by disjoint groups: Box 6 is modulo 1 with 2 in r4c8, 6 in r6c8 - by disjoint groups: Box 2 is modulo 0 with 1 in r3c5, 2 in r2c4, 6 in r1c5. (5) All wheels have been determined and the corresponding numbers written in the adjacent cells. The rest is simple Sudoku.
Very early I was able to figure out that the fact there were 3 circles from 3 modular 4 groups. 2/6 are 2 mod 4, 3/7 are 3 mod 4, and 4/8 are 0 mod 4. This combined with the inital configurations meant that for each of those there had to be a rotation from each of the other 3 groups. Made figuring out the circles fairly straightforward.
Didn’t think I’d get this one, but then it started cracking open. Love the structure of the logic here. Had to focus so hard just to not mess anything up
Amazing puzzle! A piece of logic left to be admired is that since 159 is the only parity group consisting of 3 digits, each colour has to have one of those digits, for there not to be a repeating rotation on one of the colours.
Fun puzzle didn't have time but usually I do the puzzle with Simon. however, this is one of the few puzzles that I was 20 minutes ahead of Simon so I am happy.
This is a seriously cool puzzle with really cool software to go with it. When I first looked at it, I abandoned ship pretty quickly, but I’m so glad I went back and solved it.
I noticed the disjoint issues so much earlier than you but also you noticed so many things before I did - it;s very interesting to see the difference in what we latch onto int he rules!
Well done Crusader175 for the wonderful puzzle! We actually agreed to do a puzzle test exchange last week as he needed this rated on LMD and this was the puzzle I got to test. I'll definitely be sending in the puzzle I gave to him to test, think you might like it, Crusader175 thought it was fun. (Hint: It's a sequel of sorts to my last feature on CTC). Back on when I tested this one, I was stumped for an hour. I knew it had something to do with mod 4, and all the wheels that had say, 3 and 7, had to have one of 159, one of 26 and one of 48 in the centre, but I couldn't get the logic right. I broke the puzzle twice. Eventually I just deduced r5c8 had to be odd and got a 26 pair in box 6 and went from there. It is an extraordinary ruleset and the constraints work really well together. I'm jealous of the people that experienced the lightbulb moment upon finding the break-in. Well done again Crusader175.
I'm very impressed that Simon went from thinking he was going to have to abandon this puzzle for not understanding it, to then suddenly having the strength to try a few digits, to starting to understand, then completely clearing it within a ridiculously short time. Nice work, and a cool idea for a sudoku puzzle!
Very early, we knew that the top right purple cell was a 159. But those are all the same mod 4, so we know the left purple cell can't be any of 159, so you can reduce it to 37 much earlier. It was figured out pretty early but then forgotten that, for the wheel cells, you get to think of 159, 26, 37, and 48 as equivalence classes (so pencil marking an orange cell as only 37 means no other orange cell can be 3 or 7, for instance).
Yeah, when he deleted the four yellow cells marking the mod-four sets at 36:30, he immediately abandoned all logic involving them. The very next thing he did was spend a minute and a half on a deduction that only would've required checking them.
I love the innovation that sudoku software can bring to the creativity of the puzzles and the solves. Using colored cells to keep track of information, the crazy wheels, and especially the fog of war style grid.
What a break-in on this one! It took me about 20 minutes just to work through the multiple layers of interacting logic that you have to work through just to get a digit in the grid. Solved in about 50 minutes.
That was a really fun sudoku! I struggled to find somewhere to start so after a while I just started trying different configurations of 2-6 wheels to see what combinations I could rule out. That went badly until I realised I had forgotten to rule out the nave of the wheel being 2 or 6. At that point it all started to flow a bit more. It still took me an hour at least.
Simon the way to attack this puzzle after the break in (which I never could fully understand) is to focus on the disjoint subset on C2/5/8 and R2/5/8. You missed some disjoint opportunities here. Yes they can be hard to see normally.......but this puzzle is practically begging you to finish these rows and columns.
Wowwwwweee!!! What a BRILLIANT puzzle , and Simon ! Your incredible deductive reasoning and logic in the beginning was VERY impressive! I was gobsmacked at how you came to each and every revelation, and was so happy to be on that train when it loop-the-looped into that amazing and exciting finale! What a phenomenal roller-coaster ride, and I was so happy to be on board for it ! Bravo, yet again!
I am so happy that I found the idea myself. Mod calculations fit a programmers brain i suppose, but still. So fulfilling and satisfying to finish that without a major hiccup
Disjoint sets and indexing really give Simon fits. He has a brilliant mind for shooting such complex logic to break into these puzzles then often misses the most obvious deductions. At about 40:00, he has a bunch of gimmies from disjoint logic just sitting there not being utilized.
Sometimes when watching these I want to be able to scream at Simon for missing some of the most basic stuff possible, but then he just proceeds to blow my mind and solve something that my brain would take 20 years to process. Funny world I guess. Great job!
I finished in 29:22 minutes. This puzzle must have clicked with me well and I think my time reflected that. I have never heard of this ruleset, but the software is excellent in demonstrating it. The thesis of the puzzle was excellent with the digits in the circles limiting a rotation pattern that only allows three rotations, which perfectly melds with the disjoint constraint. Figuring that out was satisfying, but it was even more satisfying to place digits in the centers of wheels and watch them spin to their correct position. I love puzzles like this that bridge technology and logic. As always, it feels good to beat Simon's time. Great Puzzle!
Wow that was challenging. Pushed my half drunk IQ to the limit. Thankfully the triplets of: 26, 37 and 48 existing and being on different rows/columns made it somewhat manageable to color/name the wheels. If someone's stuck here are my notes that I'm sure will greatly help you: YELLOW: 2: not+1 = 2/3 3+1=not possible 3: nto+3 = 1/2 3/2 or 2/1 RED: not 5, 2: not +3 = 1/2 2+3=not possible 3: not +2 =1/3 2/1 or 1/3 BLUE: 2: not +1 = 2/3 3: not +2 = 1 159 BLUE start1(2/1cont) 26 YELLOW start1(3/2cont) BLUE start2(3/1cont) 37 RED start1(2/1cont) 48 RED start2(1/3cont) YELLOW start2(2/1cont)
Simons already questionable scanning gets even more frustrating when theres disjoint sudoku everywhere 😂 (as i sit here knowing I could never dream of breaking into this puzzle)
Watching him struggle through a crazy wheel based deduction for R8C8 ~38 mins into the video once he knows it's even and there is a 26 pair and a 4 in C8 already was truly frustrating.
This puzzle is absolutely brilliant!! It was certainly no easy task, but the moment that I finally understood how the parity of the different wheels interact was well worth the effort! Final time was 1 hour, 49 minutes, 9 seconds
This was a very fun puzzle! It took me significantly longer to crack than Simon, but I managed in the end. Always such a nice feeling. I even managed to do some (for me) difficult deductions that made me feel quite proud of myself :P Big thanks to everyone involved in its making!
I loved this one! It was challenging but fun. I found a “shortcut” to narrowing down the possibilities for each circle. Possible spoiler: Once I discovered the tricks about number pairs/groups that couldn’t go together and circle parity, I went through and eliminated the possibilities from each circle. If I saw a circle had to contain only digits from one “naughty” number pair/group I could eliminate those possibilities from the partner circles along with the digits from its group (I.e. the center circle had to have 1,5, or 9 so I took those out of the other 3/7 circles as well as the 3 & 7). This along with the pairs helped eliminated digits until I was able to get all center digits and continue from there. Idk if this makes sense because I’m horrible at explaining how my brain works when I see a solve path but it helped a lot
“There’s some trick that allows us to know things.” That’s what I tell myself whenever I look at any puzzle. I just can’t always (usually?) figure that out without help. So waiting to try the puzzle AFTER I watch Simon or Mark is my strategy. 😉
@ 11:07 - "I can't do sudoku" - Finally an admission - I've been telling you that for months. It's not normal sudoku, but you can certainly use the disjoint set rule. You've currently got three wheels with a 3 at 9 o'clock. Each of these needs to be rotated by a different effective amount (i.e. one must be 2 or 6, one 4 or 8, and one 1, 5, or 9). There's only limited relative arrangements of these which avoids a digit in the same position. Having found a relative arrangement with no clashes, you rotate all three by the same amount to maintain their relative rotations to ensure none of the three had a 3 or 7 in the centre. You've also got three wheels with 48 on them, with essentially the same restriction, and also three containing 26. Each of the groups contains one wheel where the 26/37/48 digits are on opposite sides, which means they exclude that rotation from any cells in the same row/column depending on the orientation. E.g. the wheel in box 6 cannot be rotated 2 or 6 times. If it's rotated an even number of times, it means none of the wheels in R5 can be rotated 2 or 6 times. If it's rotated an odd number of times, none of the wheels in C8 can be rotated 2 or 6 times. Summary: the set of wheels with 37 needs a 159, a 26, and a 48, the 48 set needs a 159, a 26, and a 37, and the 26 set needs a 159, a 37, and a 48. Towards the end of placing the wheel hubs you missed out on the one of each type per colour restriction, so for instance you had 15 in one purple, and 13 in another. The latter had to be 3 because the first was the 159 entry, and so the second couldn't be 1. By having the auto-check on finish turned off, you missed out on the celebration when you filled in all the wheel rotations. Although I really enjoyed it, I'm not sure this innovation has the legs for producing others of the same type. It would be a shame for quite a nice bit of code to only get one outing though.
That was an interesting puzzle, I love disjoint set ones and coming up with a way to decide how the wheels was arranged was pretty interesting. Once I noticed that there were three "sets" of wheels I played with how they interacted and found sets of digits that worked and kept them separated since any mod4 of that digit would be the same rotation. Once I did that to another set it started eliminating possibilities and I knew I was on the right track.
From Scotland to white cliffs of Dover Through cities and great fields of clover The bus comes for Simon Who solves it in time an' Avoids being hit and run over!
Great puzzle because right from the start it gives you a lot of info in the way of "if this is A then this must be either B or C and then this over there is (D or E) or (F or G), depending on the second. - And among this clutter of information you have to find the essential first step to enter the first 3-7; 2-6 and 4-8 pair pencil marks.
So I haven’t watched the video in its entirety yet (11.51 minutes in) but I just thought of something before Simon did in the video (idk if he figures it out I’m about to see) The very center square cannot he 3 or 7 cause no matter orientation, normal sudoku rules will apply. I assume he gets that figured out, but I’m happy cause he normally has me stumped and I thought of this before he did in video. Love yalls work btw!
What was interesting for me is that because of the arrangement of the numbers there’s a sort of disjoint sets within the coloured cells with respect to the different combinations of rotations. 4 sets of rotations, one is ruled out by the numbers on the wheels and if you put something from one rotation set in a coloured cell the other two cells of that colour must be from the other two sets of rotations because the numbers on the wheels are a different number of rotations apart.
I was lucky, when trying to get a feel for the first rule. I noticed that the 3’s, 2’s and 4’s are all in the fifth cell of their boxes and that there are exactly 3 such boxes each. That made it easier to spot, that each of the wheels has to be rotated a different number of times. That each 3, 2 and 4 on the wheels was paired with the number 4 higher, meant that the N on the wheels could only be chosen from 3 sets of digits for each group.
Wonderful puzzle. This may be the first puzzle that I significantly beat Simon's time on. Something just clicked about it for me, probably because I had been thinking of constructing a similar puzzle ever since Chameleon offered his services for puzzle mechanics in the comments for Rush Hour.
From the 33 minute mark to the 42 minute mark (so 9 minutes total); Simon could have had the 4/8 disjoint in Box 6 solved.... And he ended up solving it with the 5 disjoint from Box 9. Amazing how he can do such supreme feats of logic and still miss super simple deductions so easily.
After 13 minutes of watching Simon and untold how many minutes of pondering on the problem, I'm questioning if it's possible to have a unique solution... I'm sure it must, but it seems like the wheels don't interact enough, there's no one wheel with a 3 and a 4 on it. So it seems like all the 3-7 wheels could be placed at "correct" orientations relative to each other, but they don't put any pressure on the 2-6 wheels, couple this with modulo automatic that tells me that each orientation can be fulfilled by at least 2 different digits... And it just seems like there's too many options and not enough pressure... So now I'm going to sit back and finish watching Simon to see if it actually works 😂
Something to select all the 'cells in the same relative position in different 3x3 boxes' would have helped a lot here. Would be similar to what you can do with thermometers now, click and hold a cell in a thermo, and automatically cells on a similar position on another thermo with the same length will be selected.
While opposite side for 8s is true in your post analysis, it's more important that 8 in relation to 4 is always at a different angle in all 3 dots. This would not only require you to use a different set for each center, but you can immediately find the order given by these clues. If you use mod 4, and assume the pair you're using is {n}, then the order will always be when the pair are starting on left and bottom you would have to put n+1 mod 4, if the pair is left and bottom you use n+2 mod 4, and if the pair is left and top you put n+3 mod 4.
Coulda made things easier on yourself by taking 159 out of r5c2 when they appeared in r2c8. Since those two have to be different mod 4 due to being the same color.
I treated it as Modulo 4 and I didn't realize putting a digit in the center square would move the wheel. I noticed the 2/3/4 sets would each exclude a wheel modulation respectively. Then I noticed that the wheels in boxes 1 4 and 6 with the "straight" clues could not fall into the modulation with the 2/3/4 opposite the exclusion. So I ended up seeing the polarity principle in passing but I didn't realize its significance.
Phew that was a tough puzzle, but I made it through with 0 hints. I wish I had a timer on that because I don't think I was actually that much off of Simon's time! Really enjoyed this one!
Wow - what a puzzle. I'm extremely surprised I got to the end - though I did make a mistake and have to unpick all the way back to the wheels (thank you for the message that confirmed you got the wheels right, or I'd have to have gone back even further!!). I did it a totally different method to Simon though. I decided it was hard/impossible to put digits in the centre of wheels that 'saw' the 180 degree splits eg box 1 for 3 and 7. So putting 3/7 in R2C5 or R2C8 created deadly situations for all the 3/7 wheels. The same could be done for the 48 wheel in box 4 for the centres at R2C2 and R8C8. That plus eliminating option positions that related to no longer possible rotations was enough to solve the wheels.
I went through each of the wheel trios (green, purple, and orange in the video) and assigned them a value based on possible final position to them (i.e. 159=A, 26=B, 37=C, 48=D) and found that each of the wheel centers could only be two from the four final positions. I ended up with R5C8 being AC and got to pencil mark 26 above and under it (same as Simon did), which removed the B option from R2C8 leaving it with only one possible final position and it all unwound from there.
Unfortunately no timer, but I think I completed it faster than Simon for the first time ever and on my own as well. It was such an amazing new puzzle for me, I loved it and figuring out the whole thing with the sets of numbers being two away from each other was so satisfying.
The L shape dials needs to form opposite brackets so the I shaped dials have a place to be. I.e. obviously numbers can't overlap but you can't also overlap the Ls into the same corner. It's a wild ruleset.
About an hour for me. As is so often the case, I managed the break in perfectly quickly and then completely failed at properly doing regular sudoku (and disjoint set).
Nice play on %4...funny how u can remember the relative box pos constraint while doing the dials and then forget on the box corners and struggle on the second phase
Spent a few days in a dead end on my own, then watched the video until 15:59 and then got inspired to break through, eventually solving the puzzle. Still felt like some brute-forcing had to take place when constraining the central cells based on how the 6-7-8s are getting constrained by relationship between central cells of threes of respective boxes.
Some videos I watch and just feel carried along by Simon's logic and he figures everything out miles ahead of me. Then there are puzzles like this where Simon is saying "Thankfully there has been very little in the way of disjoint set" all the while, if he just looked at the disjoint set, most of his deductions could have been made WAY faster. To be fair, I've always found disjoint set sudoku puzzles to be really easy while Simon started the video off admitting that he finds them terrifying.
Thank you very much Simon for featuring another puzzle of mine and for very kind comment!
I’ve been exploring Wheels Sudoku lately, it feels like a very underrated constraint. Would love to see more puzzles with it. Normal Wheels Sudoku didn’t have the number of rotation rules, but I think it works very well for this puzzle.
Shoutout to Chameleon for the software and to Malrog for Pivots mechanic inspiration. Hope you all enjoy the puzzle as well!
What an amazing puzzle!
underrated? This is the first time I’ve ever seen it.
I'm not the inventor, it have appears on GAS and competition puzzle I think. Definitely needs more puzzle with it. :)
That was insanely clever, the rulesets worked together like peanut butter and jelly.
I can clarify this my new favourite ruleset.
Need wheel-fog?
Great puzzle! :)
As a bus driver, I approve of this puzzle, and I am glad it is not on the test to renew my commercial passenger driver's license.
Lol
1) Simon has the brilliant insight that each coloured centre cell has to come from one of the mod-4 sets {159},{26},{37},{48} (excluding the set that's common to those particular coloured wheels).
2) Simon forgets the above for most of the solve!
You have the purple {159} set in box 3, so you can remove 159 as candidates from the box 4 centre!
Also, disjoint sets allows you to remove 9 from r1c2 for ages, starting a whole string of deductions.
Indeed. I went from 'wow that's some very nice logic, clever how you worked that out' to shouting at the screen quite quickly
Yes; if he'd thought in terms of equivalence classes mod 4 he could have made his life much easier, I think. You don't care at first whether such-and-so central digit is a 2 or a 6, just that it is one or the other of those. Very nice puzzle, though, and I greatly enjoyed watching the solve.
Yeah I ended up painting in the [159][26][37][48] triples into the boxes and removing colors they couldn't be and it helped a lot in the beginning, and then near the end I completely forgot about disjoint sets on a 279/79/79 triple for the 2.. So I can't blame Simon for forgetting about earlier logic lol!
I think this was one of the hardest struggles I've seen Simon go through. Glad he persevered but it was also the most frustrating video to watch.
Thats just classic Simon, make lever deductions and impressive logic, but then forgets to follow that through or to use simpler logic.
Bet he can....
Ditto! 😉
Not taking that: if he didn't, the video wouldn't have been posted.
I love these videos where Simon gets confronted with a new logic. We get to enjoy his genius at work. I'm quite sure that if I had tried this myself, I would have been lost a long time in figuring out where specific digits could or couldn't go. Simon, in contrast, sets out to *truly* understand the logic. And sure enough, he does. And explains it nicely, too, with the three colours and the four rotationally equivalent sets, and the fact that once you determine one set for a given wheel, the sets on the other two wheels of the same colour can be derived.
The funny thing is though, it's also typical Simon to immediately forget to apply this logic. Let's call him a "distracted genius"!
I was just gonna sit tight and watch the video... Then I thought to myself to try it out beforehand. Got stuck looking at a blank puzzle for ten minutes. Decided to watch video. Started to watch it, but before actually seeing anything happen I thought to myself to try harder. Then a lot of insights came, one by one, building up little by little from intuition and eventually I understood the mod 4 beauty behind the puzzle. From there I wouldn't say "smooth sailing" but I managed to break in and then I was off to the races. One hour later, with only my wits... I was done! I'm so proud of not having given up in the end!
In other news, I just noticed: if you type two alternating digits in a wheel center (e.g. 1,2,1,2,1,2...) "just fast enough", i.e just before animation completes, the wheel spins faster and faster... then in settings, set animation speed to slow, and they'll spin for a while once you stop typing. Then you can try to make 4 or 5 wheels spin at once!
Yeah ok, I solved the puzzle and I was just messing around, it's about midnight here. But rest assured, I can still be invited to parties. 🤣
If you spin enough wheels fast enough, will the bus start moving?
@@gagstersps3 hehe, not quite. Some assembly is required first, given that's a modular bus 😉
You are such a geek. We must be related. Ha. Ha
LOL.
Wonderful construct! It was difficult for me to follow Simon's wanderings at first, but once the workings of rotations got through, it made sense. The only thing I can beat Simon on is scanning for simple Sudoku digits!
I know you're not being too serious, but we sometimes forget how fast Simon can scale through classic sudokus :D
Haven't forgotten.@@sugardude
I frequently joke about "Sudoku Man refuses to do Sudoku in Sudoku puzzle" and I know it's just that much harder when you're on-camera vs. watching or doing the scanning yourself with no pressure to talk it through.
I really enjoyed this video - I am coming to it a couple days after it was initially posted because of busy times here, and I'm so glad I watched it! I disagree with some comments below about your forgetting deductions and logic that you discovered, or failing to use it, or whatever. I felt, from my vantage point of being a watcher and not a solver of this puzzle, that you did keep things in mind very well. I don't really understand the comments that suggest that you didn't. Nevertheless, as always, Simon, your glee at the new constraints and software to support it is almost as much fun as the solve! Thanks for this video and for everything that you (and Mark) do to keep the sudoku puzzles coming two-a-day every day of the year. It is such a source of pleasure to me to know that I will get to see you wrestle with something beautiful every day.
44:13 "almost gonna end up with crosses in every box" proceeds to completely avoid finishing the crosses
Even said the 9 at the bottom gives no information when it was ruling out 9 in r1c2. Let alone the 59 in r3c2 not being a 5 from r6c5
Simon lost the conclusion pretty quickly that you could only have one number from each set in a color. So, once he got 159 in the center in box 3, he could have eliminated 159 in the center of box 4, leaving a 37, which would have allowed him to place the 458 immediately.
Yes, purple in particular, could have been filled far sooner.
Brilliant! Thank you @CrusaderPuzzle for that puzzle, I really liked this totally new, out-this-world constraint.
Funny though how Simon is normally quick to mention modularity in some others puzzles but didn't spot (at least not explicitly) that all wheel centers were arranged in a modulo 4 sub-puzzle. I was really expecting Simon to go on with explaining modularity as he always do so well. He was nearly there with his yellow digits set, but ended up resolving centers by combining parity constraints instead. Anyway, in the end, that still made the wheels on the bus go round and round.
Very happy with the successful solve, that was a joy to watch!
What a fantastic puzzle. I had a much faster break in by pencil marking 1, 2, 3, and 4 in all the center squares based on the number of turns they could have (ignoring 5-9 initially). I was able to make a lot of eliminations pretty quickly that way and start pencil marking all the digits on the wheels.
I did the same. It looked intimidating based on the title and thumbnail, but it turned out to be very approachable for me. Plus I appreciated that the puzzle let me know when I got the rotations right.
It came very quickly to me that there was a strong relationship of modularity for wheels in boxes 1-5-9, 2-6-7 and 3-4-8, and once I found what this implies for the modularity of wheel 6 and the consequences in boxes 3 and 9, the rest of the solve went pretty smoothly. Very fun and unique puzzle!
A very lovely solve. Something fascinating that didn't come up in Simon's solve (because he keeps "Auto-Check On Completion" turned off) is that there's actually two stages of completion check-- one for the wheels, then another for the puzzle as a whole. When I filled in the last digit in the center of a wheel, I got a pop-up confirming that the wheels were all correct. Which I found pretty interesting.
it's great that it's there honestly. i have a history of making mistakes in these puzzles and getting all the way to the end before being told "you are dumb" is one of the reasons i don't do these puzzles often. (i did do this one tho, it was too interesting to pass. :P)
This just happened to me too. I made 4 sets of numbers: [159,26,37,48], then the 3 sets of wheels [Red, Green, Blue] - from those 2 sets, I made out 8 different solutions to the wheels, and with knowing R5C2 was forcing 4&8, and R5C8 forced 2&6 into a vertical lock, it was easy to find the solution for the wheels. I was in shock when the popup notified me.
26:00 finish. I took each pair on the wheels and mapped out possibilities, noting that some combinations of positions will break the disjoint sets. This proved that the wheel in box 1 had to be even, and in box 6 had to be odd. This break-in allowed me to finish the wheels quickly, leaving a tricky disjoint sets puzzle remaining. Excellent!
I also played around with the wheels in the beginning, noticed that when you just choose one of the 3 rotation possibilities for each wheel it solves the other 2 wheels. It also makes the parity thing quite obvious. So you end up with the 48 pair and the 26 pair and from there on you get the 9 wheel digits relatively quickly.
25 mins for me - started watching the video and spotted thw breakthrough almost immediately. Used 4 dif colors for the centers of the wheel.. Now came back to watch Simon again.. Must say it feels so good to be able to see stuff he doesn't immediately.. Even if it happens once in a blue moon (oh wait theres a super blue moon tonight! No wonder!!!!)
What a wonderful channel. I don’t watch often, but it never fails to rase my spirits when I do. Keep solving puzzles and problems and make people smile.
For me, Sudoku broke down relatively quickly.
(1) Similar to Simon, I first determined the three wheel-groups: 37-group in Box 1/5/9, 26-group in Box 2/6/7 and 48-group in Box 3/4/8. The respective groups must have different settings (Modulo with 4) to satisfy the Disjoint Groups rule.
(2) Then I looked at each of the three groups individually and found only the following settings for them (taking advantage of Disjoint Groups rule): Box 1 (Modulo 0,2), Box 2 (Modulo 0,1), Box 3 (Modulo 1,2), Box 4 (Modulo 1,3), Box 5 (Modulo 1,2), Box 6 (Modulo 1,3), Box 7 (Modulo 0,3), Box 8 (Modulo 2,3), Box 9 (Modulo 0,1).
(3) Because Box 1 always has a horizontal setting and Box 6 a vertical setting, wheel in Box 3 sees a 2367 quadruple. Thus it loses its modulo 2 setting and is clearly modulo 1.
(4) The causal chain now reads:
- by quadruplel: Box 3 is modulo 1 with 4 in r1c8, 8 in r2c7.
- by disjoint groups: Box 4 is modulo 3 with 4 in r6c2, 5 in r5c1, 8 in r4c2
- by disjoint groups: Box 8 is modulo 2 with 4 in r8c6, 8 in r9c5
- by 48-pair in Box 4: Box 1 is modulo 2 with 3 in r2c3, 7 in r2c1
- by disjoint groups: Box 5 is modulo 1 with 3 in r4c5, 7 in r5c6
- by disjoint groups: Box 9 is modulo 0 with 3 in r8c7, 7 in r9c8, 9 in r7c8
- by 48-pair in Box 4: Box 7 is modulo 3 with 2 in r9c2, 6 in r8c3
- by disjoint groups: Box 6 is modulo 1 with 2 in r4c8, 6 in r6c8
- by disjoint groups: Box 2 is modulo 0 with 1 in r3c5, 2 in r2c4, 6 in r1c5.
(5) All wheels have been determined and the corresponding numbers written in the adjacent cells. The rest is simple Sudoku.
I did it by modular arithmetic as well.
That was a delight to watch you solve, Simon! And now I'm feeling like I could solve the next one of these that pops up! Thanks!
Very early I was able to figure out that the fact there were 3 circles from 3 modular 4 groups. 2/6 are 2 mod 4, 3/7 are 3 mod 4, and 4/8 are 0 mod 4. This combined with the inital configurations meant that for each of those there had to be a rotation from each of the other 3 groups. Made figuring out the circles fairly straightforward.
Didn’t think I’d get this one, but then it started cracking open. Love the structure of the logic here. Had to focus so hard just to not mess anything up
Amazing puzzle!
A piece of logic left to be admired is that since 159 is the only parity group consisting of 3 digits, each colour has to have one of those digits, for there not to be a repeating rotation on one of the colours.
Fun puzzle didn't have time but usually I do the puzzle with Simon. however, this is one of the few puzzles that I was 20 minutes ahead of Simon so I am happy.
Fantastic solving, Simon!!👏🏻
This is a seriously cool puzzle with really cool software to go with it. When I first looked at it, I abandoned ship pretty quickly, but I’m so glad I went back and solved it.
I noticed the disjoint issues so much earlier than you but also you noticed so many things before I did - it;s very interesting to see the difference in what we latch onto int he rules!
Well done Crusader175 for the wonderful puzzle! We actually agreed to do a puzzle test exchange last week as he needed this rated on LMD and this was the puzzle I got to test. I'll definitely be sending in the puzzle I gave to him to test, think you might like it, Crusader175 thought it was fun. (Hint: It's a sequel of sorts to my last feature on CTC).
Back on when I tested this one, I was stumped for an hour. I knew it had something to do with mod 4, and all the wheels that had say, 3 and 7, had to have one of 159, one of 26 and one of 48 in the centre, but I couldn't get the logic right. I broke the puzzle twice. Eventually I just deduced r5c8 had to be odd and got a 26 pair in box 6 and went from there.
It is an extraordinary ruleset and the constraints work really well together. I'm jealous of the people that experienced the lightbulb moment upon finding the break-in. Well done again Crusader175.
I'm very impressed that Simon went from thinking he was going to have to abandon this puzzle for not understanding it, to then suddenly having the strength to try a few digits, to starting to understand, then completely clearing it within a ridiculously short time. Nice work, and a cool idea for a sudoku puzzle!
The 5 stages of disbelief.
Very early, we knew that the top right purple cell was a 159. But those are all the same mod 4, so we know the left purple cell can't be any of 159, so you can reduce it to 37 much earlier. It was figured out pretty early but then forgotten that, for the wheel cells, you get to think of 159, 26, 37, and 48 as equivalence classes (so pencil marking an orange cell as only 37 means no other orange cell can be 3 or 7, for instance).
Yeah, when he deleted the four yellow cells marking the mod-four sets at 36:30, he immediately abandoned all logic involving them. The very next thing he did was spend a minute and a half on a deduction that only would've required checking them.
I was yelling at the screen *so much* because of that
easy to say when thats the only thing you are looking at
This is SO clever! And a fantastic solve from Simon as well. That break-in was brilliant.
I love the innovation that sudoku software can bring to the creativity of the puzzles and the solves. Using colored cells to keep track of information, the crazy wheels, and especially the fog of war style grid.
What a break-in on this one! It took me about 20 minutes just to work through the multiple layers of interacting logic that you have to work through just to get a digit in the grid. Solved in about 50 minutes.
The wheels fell off my bus pretty quickly ☹️
Singing in my head for an hour.. "The wheels on the bus go round and round...."
Great job of deductions and logic Simon during your solve.
That was a really fun sudoku! I struggled to find somewhere to start so after a while I just started trying different configurations of 2-6 wheels to see what combinations I could rule out. That went badly until I realised I had forgotten to rule out the nave of the wheel being 2 or 6. At that point it all started to flow a bit more. It still took me an hour at least.
Thank you for this great puzzle! I enjoyed it so much while solving.
Loved to watch Simon. But I could not do it without the help of him. Can’t figure out how to start.
Simon the way to attack this puzzle after the break in (which I never could fully understand) is to focus on the disjoint subset on C2/5/8 and R2/5/8. You missed some disjoint opportunities here. Yes they can be hard to see normally.......but this puzzle is practically begging you to finish these rows and columns.
This is the first video I've ever watched on this channel and I'm hooked now. This was a joy to watch.
Wowwwwweee!!! What a BRILLIANT puzzle , and Simon ! Your incredible deductive reasoning and logic in the beginning was VERY impressive! I was gobsmacked at how you came to each and every revelation, and was so happy to be on that train when it loop-the-looped into that amazing and exciting finale! What a phenomenal roller-coaster ride, and I was so happy to be on board for it ! Bravo, yet again!
I am so happy that I found the idea myself. Mod calculations fit a programmers brain i suppose, but still. So fulfilling and satisfying to finish that without a major hiccup
What a fun puzzle, and a brilliant solve! Another great hour spent with the CtC folks
I really enjoyed this one!! It was beautiful!
Disjoint sets and indexing really give Simon fits. He has a brilliant mind for shooting such complex logic to break into these puzzles then often misses the most obvious deductions. At about 40:00, he has a bunch of gimmies from disjoint logic just sitting there not being utilized.
Rules: 02:02
Let's Get Cracking: 09:02
What about this video's Top Tier Simarkisms?!
Maverick: 4x (00:17, 04:25, 11:44, 39:09)
Bobbins: 2x (21:58, 48:36)
Three In the Corner: 1x (51:29)
You Rotten Thing: 1x (44:53)
And how about this video's Simarkisms?!
Hang On: 13x (03:15, 04:12, 04:12, 04:38, 04:42, 11:19, 13:16, 33:45, 34:15, 39:59, 39:59, 39:59, 42:29)
By Sudoku: 11x (36:31, 38:08, 38:27, 41:43, 42:27, 44:45, 46:13, 52:18, 52:31, 52:37, 52:56)
Ah: 8x (16:15, 23:12, 25:39, 25:39, 40:02, 43:03, 48:36, 50:20)
Sorry: 7x (07:20, 10:26, 22:22, 24:55, 28:20, 33:45, 37:52)
Obviously: 5x (03:04, 12:12, 12:13, 18:19, 20:28)
Wow: 4x (33:15, 52:49, 52:49, 52:49)
Pencil Mark/mark: 4x (27:14, 29:00, 42:33, 46:57)
I Have no Clue: 3x (10:26, 10:31, 55:26)
I've Got It!: 3x (33:31, 33:31)
Goodness: 2x (38:56, 42:27)
Naughty: 2x (54:16, 54:18)
Lovely: 2x (46:09, 51:27)
Incredible: 2x (12:15, 53:28)
Take a Bow: 2x (53:34, 55:41)
Plonk: 2x (27:53, 51:31)
What Does This Mean?: 2x (09:33, 33:23)
What on Earth: 1x (11:15)
Apologies: 1x (06:37)
Out of Nowhere: 1x (41:56)
Break the Puzzle: 1x (20:49)
Extraordinary: 1x (00:43)
Shouting: 1x (08:11)
Of All Things: 1x (35:35)
Surely: 1x (36:48)
In Fact: 1x (36:20)
Progress: 1x (21:27)
That's Huge: 1x (40:02)
Cake!: 1x (07:54)
Most popular number(>9), digit and colour this video:
Ninety (5 mentions)
Three (80 mentions)
Purple (12 mentions)
Antithesis Battles:
Even (13) - Odd (11)
Row (15) - Column (8)
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!
You are a God
How long did this breakdown take to sort out?
@@ScrapFatherScrapSon it's a bot, so... something between seconds and a few minutes?
@@MadMetalMacho that’s insane!
This puzzle was awesome! I am so glad I stuck with it!
"That's going to cause whiz-age" may be entering my book of important phrases. 40:09
Just under 40 minutes! I felt obligated to finish the puzzle with my birthday callout haha
Jason here- thank you, and thank you Damien! Haha
Sometimes when watching these I want to be able to scream at Simon for missing some of the most basic stuff possible, but then he just proceeds to blow my mind and solve something that my brain would take 20 years to process. Funny world I guess. Great job!
What an interesting (I WAS going to say strange) puzzle. WAY over my head, but I really enjoyed watching the solve.
Can't say how long I took, but very fun puzzle. Thanks for featuring this level of quality puzzles again and again!
I finished in 29:22 minutes. This puzzle must have clicked with me well and I think my time reflected that. I have never heard of this ruleset, but the software is excellent in demonstrating it. The thesis of the puzzle was excellent with the digits in the circles limiting a rotation pattern that only allows three rotations, which perfectly melds with the disjoint constraint. Figuring that out was satisfying, but it was even more satisfying to place digits in the centers of wheels and watch them spin to their correct position. I love puzzles like this that bridge technology and logic. As always, it feels good to beat Simon's time. Great Puzzle!
Wow that was challenging. Pushed my half drunk IQ to the limit. Thankfully the triplets of: 26, 37 and 48 existing and being on different rows/columns made it somewhat manageable to color/name the wheels. If someone's stuck here are my notes that I'm sure will greatly help you:
YELLOW:
2: not+1 = 2/3 3+1=not possible
3: nto+3 = 1/2
3/2 or 2/1
RED: not 5,
2: not +3 = 1/2 2+3=not possible
3: not +2 =1/3
2/1 or 1/3
BLUE:
2: not +1 = 2/3
3: not +2 = 1
159 BLUE start1(2/1cont)
26 YELLOW start1(3/2cont) BLUE start2(3/1cont)
37 RED start1(2/1cont)
48 RED start2(1/3cont) YELLOW start2(2/1cont)
Simons already questionable scanning gets even more frustrating when theres disjoint sudoku everywhere 😂 (as i sit here knowing I could never dream of breaking into this puzzle)
Watching him struggle through a crazy wheel based deduction for R8C8 ~38 mins into the video once he knows it's even and there is a 26 pair and a 4 in C8 already was truly frustrating.
I decided to watch the second half of the video on 1,5x speed because of this 😆
The 2 5s in Box 4 meaning you can remove 5 from the rest of Row 5 is the one I was yelling at my screen for the longest. 😀
This puzzle is absolutely brilliant!! It was certainly no easy task, but the moment that I finally understood how the parity of the different wheels interact was well worth the effort! Final time was 1 hour, 49 minutes, 9 seconds
amazing! If Erno Rubik had constructed Sudokus, I think it would have looked something like this
Love the spinning cogs. Great idea
This was a very fun puzzle! It took me significantly longer to crack than Simon, but I managed in the end. Always such a nice feeling. I even managed to do some (for me) difficult deductions that made me feel quite proud of myself :P Big thanks to everyone involved in its making!
That plane must be so annoying to hear daily
I loved this one! It was challenging but fun. I found a “shortcut” to narrowing down the possibilities for each circle.
Possible spoiler:
Once I discovered the tricks about number pairs/groups that couldn’t go together and circle parity, I went through and eliminated the possibilities from each circle. If I saw a circle had to contain only digits from one “naughty” number pair/group I could eliminate those possibilities from the partner circles along with the digits from its group (I.e. the center circle had to have 1,5, or 9 so I took those out of the other 3/7 circles as well as the 3 & 7). This along with the pairs helped eliminated digits until I was able to get all center digits and continue from there. Idk if this makes sense because I’m horrible at explaining how my brain works when I see a solve path but it helped a lot
“There’s some trick that allows us to know things.” That’s what I tell myself whenever I look at any puzzle. I just can’t always (usually?) figure that out without help. So waiting to try the puzzle AFTER I watch Simon or Mark is my strategy. 😉
That is a wonderful trick! 💜🩵😃
@@davidrattner9 ❤️❤️
I agree wholeheartedly with this strategy!!!!!!
omg getting just the wheels might be the most fun i've had with a sudoku in more than a month. the rest though. thanks for sharing.
@ 11:07 - "I can't do sudoku" - Finally an admission - I've been telling you that for months.
It's not normal sudoku, but you can certainly use the disjoint set rule. You've currently got three wheels with a 3 at 9 o'clock. Each of these needs to be rotated by a different effective amount (i.e. one must be 2 or 6, one 4 or 8, and one 1, 5, or 9). There's only limited relative arrangements of these which avoids a digit in the same position. Having found a relative arrangement with no clashes, you rotate all three by the same amount to maintain their relative rotations to ensure none of the three had a 3 or 7 in the centre. You've also got three wheels with 48 on them, with essentially the same restriction, and also three containing 26. Each of the groups contains one wheel where the 26/37/48 digits are on opposite sides, which means they exclude that rotation from any cells in the same row/column depending on the orientation. E.g. the wheel in box 6 cannot be rotated 2 or 6 times. If it's rotated an even number of times, it means none of the wheels in R5 can be rotated 2 or 6 times. If it's rotated an odd number of times, none of the wheels in C8 can be rotated 2 or 6 times.
Summary: the set of wheels with 37 needs a 159, a 26, and a 48, the 48 set needs a 159, a 26, and a 37, and the 26 set needs a 159, a 37, and a 48. Towards the end of placing the wheel hubs you missed out on the one of each type per colour restriction, so for instance you had 15 in one purple, and 13 in another. The latter had to be 3 because the first was the 159 entry, and so the second couldn't be 1.
By having the auto-check on finish turned off, you missed out on the celebration when you filled in all the wheel rotations.
Although I really enjoyed it, I'm not sure this innovation has the legs for producing others of the same type. It would be a shame for quite a nice bit of code to only get one outing though.
Titles a video “I can’t do this sudoku!”
Still tells us “do have a go.”
😅
That was an interesting puzzle, I love disjoint set ones and coming up with a way to decide how the wheels was arranged was pretty interesting. Once I noticed that there were three "sets" of wheels I played with how they interacted and found sets of digits that worked and kept them separated since any mod4 of that digit would be the same rotation. Once I did that to another set it started eliminating possibilities and I knew I was on the right track.
It brought me so much fun watching you solving this puzzle tonight 😊
From Scotland to white cliffs of Dover
Through cities and great fields of clover
The bus comes for Simon
Who solves it in time an'
Avoids being hit and run over!
Interesting, we get to count mod-2 (aka parity) or mod-3 in a lot of puzzles but here's the rare mod-4 puzzle!
It's kind of a set of simultaneous equations mod 2, 3, and 4
21:21 for me. What an incredible puzzle, loved it!!!
Great puzzle because right from the start it gives you a lot of info in the way of "if this is A then this must be either B or C and then this over there is (D or E) or (F or G), depending on the second. - And among this clutter of information you have to find the essential first step to enter the first 3-7; 2-6 and 4-8 pair pencil marks.
So I haven’t watched the video in its entirety yet (11.51 minutes in) but I just thought of something before Simon did in the video (idk if he figures it out I’m about to see)
The very center square cannot he 3 or 7 cause no matter orientation, normal sudoku rules will apply. I assume he gets that figured out, but I’m happy cause he normally has me stumped and I thought of this before he did in video. Love yalls work btw!
What was interesting for me is that because of the arrangement of the numbers there’s a sort of disjoint sets within the coloured cells with respect to the different combinations of rotations. 4 sets of rotations, one is ruled out by the numbers on the wheels and if you put something from one rotation set in a coloured cell the other two cells of that colour must be from the other two sets of rotations because the numbers on the wheels are a different number of rotations apart.
I was lucky, when trying to get a feel for the first rule. I noticed that the 3’s, 2’s and 4’s are all in the fifth cell of their boxes and that there are exactly 3 such boxes each. That made it easier to spot, that each of the wheels has to be rotated a different number of times. That each 3, 2 and 4 on the wheels was paired with the number 4 higher, meant that the N on the wheels could only be chosen from 3 sets of digits for each group.
Wonderful puzzle. This may be the first puzzle that I significantly beat Simon's time on. Something just clicked about it for me, probably because I had been thinking of constructing a similar puzzle ever since Chameleon offered his services for puzzle mechanics in the comments for Rush Hour.
From the 33 minute mark to the 42 minute mark (so 9 minutes total); Simon could have had the 4/8 disjoint in Box 6 solved....
And he ended up solving it with the 5 disjoint from Box 9.
Amazing how he can do such supreme feats of logic and still miss super simple deductions so easily.
What's funny is that it's a deduction that he had already made, that each of those boxes needed to have one of each "set" of the digits.
After 13 minutes of watching Simon and untold how many minutes of pondering on the problem, I'm questioning if it's possible to have a unique solution... I'm sure it must, but it seems like the wheels don't interact enough, there's no one wheel with a 3 and a 4 on it. So it seems like all the 3-7 wheels could be placed at "correct" orientations relative to each other, but they don't put any pressure on the 2-6 wheels, couple this with modulo automatic that tells me that each orientation can be fulfilled by at least 2 different digits... And it just seems like there's too many options and not enough pressure...
So now I'm going to sit back and finish watching Simon to see if it actually works 😂
I am stunned, and I'm glad that my fears were allayed
Simon is 100% on my wish list of people to have a beer with.
Something to select all the 'cells in the same relative position in different 3x3 boxes' would have helped a lot here. Would be similar to what you can do with thermometers now, click and hold a cell in a thermo, and automatically cells on a similar position on another thermo with the same length will be selected.
While opposite side for 8s is true in your post analysis, it's more important that 8 in relation to 4 is always at a different angle in all 3 dots. This would not only require you to use a different set for each center, but you can immediately find the order given by these clues.
If you use mod 4, and assume the pair you're using is {n}, then the order will always be when the pair are starting on left and bottom you would have to put n+1 mod 4, if the pair is left and bottom you use n+2 mod 4, and if the pair is left and top you put n+3 mod 4.
Nice one. Once you see the break in you can solve this one quite linearly.
Coulda made things easier on yourself by taking 159 out of r5c2 when they appeared in r2c8. Since those two have to be different mod 4 due to being the same color.
I treated it as Modulo 4 and I didn't realize putting a digit in the center square would move the wheel. I noticed the 2/3/4 sets would each exclude a wheel modulation respectively. Then I noticed that the wheels in boxes 1 4 and 6 with the "straight" clues could not fall into the modulation with the 2/3/4 opposite the exclusion. So I ended up seeing the polarity principle in passing but I didn't realize its significance.
That is a cool puzzle. Nicely solved :)
48:39 "Bobbins McBobbins Face" had me dying :D
Phew that was a tough puzzle, but I made it through with 0 hints. I wish I had a timer on that because I don't think I was actually that much off of Simon's time! Really enjoyed this one!
Ok I feel especially good about my solve now because I understood core logic much faster than Simon. That's highly unusual!
Wow - what a puzzle. I'm extremely surprised I got to the end - though I did make a mistake and have to unpick all the way back to the wheels (thank you for the message that confirmed you got the wheels right, or I'd have to have gone back even further!!).
I did it a totally different method to Simon though. I decided it was hard/impossible to put digits in the centre of wheels that 'saw' the 180 degree splits eg box 1 for 3 and 7. So putting 3/7 in R2C5 or R2C8 created deadly situations for all the 3/7 wheels. The same could be done for the 48 wheel in box 4 for the centres at R2C2 and R8C8. That plus eliminating option positions that related to no longer possible rotations was enough to solve the wheels.
I went through each of the wheel trios (green, purple, and orange in the video) and assigned them a value based on possible final position to them (i.e. 159=A, 26=B, 37=C, 48=D) and found that each of the wheel centers could only be two from the four final positions. I ended up with R5C8 being AC and got to pencil mark 26 above and under it (same as Simon did), which removed the B option from R2C8 leaving it with only one possible final position and it all unwound from there.
Unfortunately no timer, but I think I completed it faster than Simon for the first time ever and on my own as well. It was such an amazing new puzzle for me, I loved it and figuring out the whole thing with the sets of numbers being two away from each other was so satisfying.
As per usual Simon finds weird and complex ways to complete puzzles using methods I can't even dream of.
loved this one
12:35 I see three groupings of three. 26 37 48. They are on the circles and you have that rule where you have to look across boxes for same positions.
The L shape dials needs to form opposite brackets so the I shaped dials have a place to be. I.e. obviously numbers can't overlap but you can't also overlap the Ls into the same corner. It's a wild ruleset.
When I completed the centers of the wheels, a pop up came up telling me that I had placed them correctly.
It seems to me it depends on if you have some settings on/off. Not sure which one though, will have to ask chameleon about it. :)
About an hour for me. As is so often the case, I managed the break in perfectly quickly and then completely failed at properly doing regular sudoku (and disjoint set).
Nice play on %4...funny how u can remember the relative box pos constraint while doing the dials and then forget on the box corners and struggle on the second phase
Spent a few days in a dead end on my own, then watched the video until 15:59 and then got inspired to break through, eventually solving the puzzle. Still felt like some brute-forcing had to take place when constraining the central cells based on how the 6-7-8s are getting constrained by relationship between central cells of threes of respective boxes.
41:35 simon try to chequerboard the grid with two colours whenever you have a disjoint set puzzle it helps a lot
Some videos I watch and just feel carried along by Simon's logic and he figures everything out miles ahead of me. Then there are puzzles like this where Simon is saying "Thankfully there has been very little in the way of disjoint set" all the while, if he just looked at the disjoint set, most of his deductions could have been made WAY faster. To be fair, I've always found disjoint set sudoku puzzles to be really easy while Simon started the video off admitting that he finds them terrifying.