The "Approachable" Miracle Sudoku

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** TODAY'S PUZZLE **
We are constantly amazed by so-called Miracle Sudokus - puzzles which, at first glance, seem absolutely ridiculous due to the lack of information in the grid. Sumanta Mukherjee's new one is "approachable" but we don't think it's trivial. Chalk another win up for these magnificent setters and their incredible imaginations!
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Rules:
Normal sudoku rules apply. Along a thermometer, digits must increase from the bulb to the tip. Place 9 straight, vertical thermometers, each of different lengths, in the grid. All the thermometers must start from row 9 of the grid. Ie the thermometers all have their bulbs in row 9. No two 9s in the grid share a diagonal. The clues outside the grid are skyscraper clues ie they indicate how many numbers can be "seen" when looking into the grid along the column. A number is visible only when it is larger than all numbers that appear before it along the line of sight.
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Опубликовано:

5 авг 2024

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Комментарии : 252

@everorizon 10 месяцев назад

I think we can find out the cycling effect of the thermometers more easily by thinking about where 1 goes in the 8-length thermometer's column. It has to go in row 1. Then, in the 7-length thermometer's column there will be 1 and 2 above it. But there's already a 1 in row 1 that gives the order. The logic follows all the way until the 1-length thermometer's column, where 1 goes in row 8, 2 in row 7, etc.

@michaels4340 10 месяцев назад

Oh yeah, that's definitely easier than the row logic, since you don't need to figure out that the thermos are consecutive first...

@TAHeap 10 месяцев назад

@@michaels4340 Well, it's really a dual version of exactly the same reasoning that tells you about the thermos ....

@michaels4340 10 месяцев назад

@@TAHeap True! It's just easier in the sense of being fewer steps.

@HomeoftheWilt17 10 месяцев назад

Funnily enough, Simon said this puzzle didn't contain a Chess sudoku restraint, but it actually does! The standard for Queen Sudoku variants is one chosen diget having chess queen restrictions, and that digit is normally 9!

@AlphaetusPrime 10 месяцев назад

Very clever puzzle. I really like how it basically makes you have the same epiphany twice.

@Muhh1982 10 месяцев назад

Finished it in 6:12, nice puzzle. I realized that the thermometers of length (1,4,7), (2,5,8), (3,6,9) should share the same box very fast at the beginning.

@daveturner5305 10 месяцев назад

My immediate thought was of a traditional 159 indexing puzzle, but based on rows. Therefore had to be 147, 258 & 369 and full roping to cope for the diagonal constraint. First time I've ever beaten Simon to the break-in. Of course Simon's brain had to bring another form of logic to the solve. Nice one.

@ceevio_art 10 месяцев назад

Same here.

@frankophetveld 10 месяцев назад

During the solve I was wondering what would happen on 'top' of the thermometers. I was not disappointed. Absolutely magical, thank you!

@AdamGaffney96 10 месяцев назад

It's really funny watching you complete this after I solved it, because we went about it in almost the same but opposite ways. I always started from the bulb of the thermometers, realising that the 9 digit started with a 1, the 8 with a 2 all the way down. Then I used that to realise that we essentially got the modular digits along row 9, since sharing digits on thermometers between the boxes at the bottom got really restricted. So whilst you used the 9's and worked down, I used the row 9 part and worked up!

@258thHiGuy 10 месяцев назад

Reminds me of the rising circles puzzle he did a week or so back, where most of the comments went from 9 to 1 and Simon went in the opposite direction

@AdamGaffney96 10 месяцев назад

@@258thHiGuy I don't remember if I left a comment on that video, but I was also a 9 to 1 person for that puzzle

@spatulamahn 10 месяцев назад

Same! Was so surprised to see Simon do it completely opposite and still solve it and this reminds me again how different each puzzle can be solved.

@coherentramblings7326 10 месяцев назад

Once you place all the thermo’s, the structure of the puzzle is surprisingly similar to Dorlir’s “rising circles”

@Grammulka 10 месяцев назад

this one was a bit more complicated, but yeah, the second part of this puzzle is basically that

@christopherschlosser946 10 месяцев назад

And just like Dorlir's, this one also has maximum roping and rotationally cymetrical cells (about 180°) also sum to nine.

@MaierFlorian 10 месяцев назад

Me: having a glass of wine too much for sudoku. Simon: approachable miracle sudoku Me: screw it, I'll give it a try 31 minutes later... yay, solved it :D

@jonhansen9622 10 месяцев назад

That's fantastic! I was just slightly slower than you, at 31:45. What a fun puzzle to solve, once I figured out the break-in

@heatherfyffe3618 10 месяцев назад

12:28 for me. Noticed a couple patterns early on which gave me a little progress but then had that "aha" moment of realizing it HAD to be 8-9 or else the puzzle would break, and that led to the remaining ahas needed to just fill the whole thing all at once, essentially.

@j4v4x 10 месяцев назад

I'm glad I'm not the only one who gets jump-scared by the 3s in the corners... 😂😂 Lovely puzzle, and wonderful solve!! Simple, elegant, approachable, but not exactly easy. 👍

@tdbraun6837 10 месяцев назад

I love puzzles like this the most. It took me much longer than Simon took to figure out how the thermos were going to work. But at least I did the second part faster!

@longwaytotipperary 10 месяцев назад

Absolutely ❤ it!!! Thank you Sumanta and Simon!!

@berlinflight_tv 10 месяцев назад

15:06 for me. Took a bit for me to grasp the concept, but once it clicked, the puzzle pretty much filled itself. Fun puzzle, BTW. I love it when the strategies are simple enough for me to deduce without having to peek at the video.

@mikesummers-smith4091 10 месяцев назад

16:53, and pleased with that.

@mc_davit 10 месяцев назад

26:28 i missread vertical as diagonal and couldn't do anything before watching the video and finally realizing my mistake

@stormfury2152 10 месяцев назад

inst it quite similar as in the Rising Circles by Dorlir? just as much fun to do more thinking, less sudoku grinding

@stevieinselby 10 месяцев назад

Very clever, 10 minutes to finish 👍🏻 Simon does like to go the long way round when working out why the numbers about the 9 have to cycle - a more obvious way of thinking about it is to look at the column with the 8-thermo, which doesn't yet have a 1, so that goes in r1. Then look at the column with the 7-thermo, which still needs a 1 and a 2, but the 1 can't go in r1 so must go in r2, and so on. It's exactly the same logic but with fewer steps to get to it!

@ianward71 10 месяцев назад

Very nice elegant puzzle. Loved the symmetry and simplicity. Great puzzle

@frankjiang1857 10 месяцев назад

Finished in 10:12, even after drawing in all the thermometers and coloring all the diagonals where the 9 cannot be. Definitely a very approachable miracle sudoku!

@sdsign4229 10 месяцев назад

Chain Bear seems cool! We need more puzzle animations, because it can be very difficult at times for me to visualize how some puzzles work.

@srwapo 10 месяцев назад

8:59, took a minute to realize the break in (the thermos had to be 9, 89, 789, 6789, etc), just flowed from there. Reminded me of other one from a few weeks ago where the numbers just filled in neatly at the end.

@spatulamahn 10 месяцев назад

Wow! What a great puzzle! Solved in 22:12 for me without any help from Simon. Took me about 10 minutes to try to disambiguate the 7 before I realized I had to look at where the other digits could go and saw it had to be 369, 258, and 147 in the starting row 9! Loved this one! My only cool takeaway is that it took me way less time than Simon to realize the 8 HAD to have the 9 right above it since every column was a thermo and it had to not be length 1 so it had to be an 8-9!

@neonxvices 10 месяцев назад

when i first learned about sudoku as a kid, i imagined a puzzle like this. my version was one where the thermometers were placed in order across the grid, but i never considered out what rules you'd have to give to solve it. very cool

@nytheris2848 10 месяцев назад

This was definitely approachable. I've only recently starting going through the playlist of GAS puzzles and still struggle with some of them, but was very happy to be able to solve this one in 21:45 while somewhat tipsy. Though I must admit, I didn't even notice that it cycled until I watched the video after solving it.

@gustafstedt7872 10 месяцев назад

That was a true pleasure to solve! Very approachable indeed 😊

@alanclarke4646 10 месяцев назад

That was a lot more fun than i was expecting!😊😊

@LeDoctorBones 10 месяцев назад

Really cool sudoku. Very approachable and has some interesting "aha" moments a couple of times through the solve, with the realisation of roping and always increasing digits. I personally got 9:22, but I was a bit too hesitant to simply believe the pattern would hold even when only the last couple of digits were left.

@imindo7337 10 месяцев назад

finished it in 3:59 this puzzle has the same satisfying feeling as the ones with the rising circles ^w^

@chomikhunter 10 месяцев назад

07:02! I'm honestly surprised that this miracle sudoku actually felt approachable! Really nice puzzle.

@leeprice133 3 месяца назад

Really loved this puzzle - there's a lovely sort of 'proof by induction' logic that gets you to every thermometer having to increase strictly sequentially and ending in 9, and once you get that you notice the mod 3 constraint in each vertical 'chute'

@crazypantaloons 10 месяцев назад

That 3 in the corner snuck up on him. LOL

@RichardDamon 10 месяцев назад

Amazing discovery for the combination of rules. Did it in about 10 minutes, spending the first minute thinking about the effects of the thermo rules and what it really means, then the sky scrapers give you the initial thermos, and then the diagonals rule just gives you the answer.

@NightShroud092 10 месяцев назад

The logic you used to deduce the nature of the thermometers on row 9 (always ending in 9) could be used to show why it should always be followed by a 1 (unless it's a 9 length). Since the row above the length 8 thermometer needs the 1 to be above that thermometer, and similarly on row 2 we can see that it needs to be in the column above the length 7 thermo. And that logic cascades to every other number. Or simply, it cylces.

@BryanSarlo 10 месяцев назад

28:13 for me.. took me a minute to understand the concept of not sharing a diagonal 😜 lovely puzzle!

@Corn_Curls 10 месяцев назад

24:3x I forgot to remember the exact time. Boy, I really didin't appreciate the fact that each grouping of three thermos in the bottom boxes must be three cells apart vertically, and must only be three cells apart vertically for far too long. And didn't take it the same way that Simon did which was a more Sudoku-based logic. Once I realised that, and the pattern that was developing filling in above the 9's, it solved itself but the mental gymnastics that I had to go through to realise that took me far too long. It is a pretty puzzle and a pretty solve, thank you.

@karlwaugh30 10 месяцев назад

Excellent puzzle. Managed it in 9mins.

@ericpraline1302 10 месяцев назад

Hard to avoid solving this without a smile on your face.

@tinakerr8163 10 месяцев назад

I adore Sumanta's patterns in puzzles.

@spatulamahn 10 месяцев назад

Simon spending several minutes on theory about how the puzzle above the 9s was going to work. Me seeing roping in about 5 seconds! :) Amazes me still how each puzzle can be approached in multiple ways and still get to the same answer.

@deathpigeon2 9 месяцев назад

This exact cycling behavior has shown up before in a puzzle where there was skyscraper clues where all that was given about them was that each one was different. This was enough to force this cycling and a few other outside of the grid clues were enough to pin down the precise locations of each skyscraper clue.

@raysouth1952 10 месяцев назад

Wonderful puzzle. A pleasure to solve.

@Kinada 10 месяцев назад

10 min, nice concept and fun puzzle.

@ElDillas 10 месяцев назад

4th in this morning!! Good morning from New Zealand! ;D

@sandraraituma 10 месяцев назад

It so interesting how Simon started to thing about the thermometers form the top perspective. I started with the bottom :D

@arielmoonsoo9219 10 месяцев назад

I managed to pull a 16:48. My first breakthrough was figuring out that the thermometers had to single step (by asking where the 8 in row 9 lived, once I had determined that the tip of each thermometer was a 9). The next was determining that the 1 in row 8 had to be above the 9, and the extrapolation into the looping nature of the columns. From there, I identified that columns 4 and 5 held the 5 and 8 thermometers, and that columns 1 and 2 held the 4 and 7 thermometers. From there, it was a question of identifying which 9 could live where. Interestingly, I ended with the 3 in the corner.

@ShakalDraconis 10 месяцев назад

13:18 for me, had an inkling how this was going to go because of the thermo lengths, and then having the solution just slide out smoothly was wonderful.

@Orenotter 10 месяцев назад

At first i seemed to be quite stuck But there was a change in my luck. Though my solves are the worst On this day, I was first Despite how i usually suck. I actually finished before Simon today! Hooray!

@Aliessil 10 месяцев назад

Finished in 11:42, what an amazing puzzle! I didn't expect the columns to all cycle - I was up in row 3 by the time I realised 😊 I didn't even notice the roping or modularity until reading the comments, bet you could get some seriously quick times if you noticed those early on ... For Simon - I'm solver #6207 in 1.9 days!

@tomgalli1188 10 месяцев назад

This one was such fun! I don't think I've every played with colored lines like I did in this solution. Wheeeee!!

@kittycatpilot 10 месяцев назад

Wow, this is the first time I've ever beat Simon on time. I just solved all the 9s a la chess Queen sudoku via a lot of grid coloring, then everything else fell into place. Beautiful puzzle.

@chuckmanion1128 10 месяцев назад

6:56 Clever logic, but once you figure out the logic, it just all falls into place too easily. My mind was going faster than my fingers could fill it in.

@lilaroseg 10 месяцев назад

20:29! im not a sudoku-er (and did have to check back to the video a couple times to make sure i wasn’t in crazy town at the start) but i’m so proud!! this is the first variety sudoku i ever did myself

@bertbergers9171 10 месяцев назад

Had to watch a bit of Simon after the break in. Thank you for puzzle and video! 43:14 for me, had some distractions in the mean time but found finally the last bit of understanding.

@piarittersporn 10 месяцев назад

What a funny puzzle. First I thought, it would be difficult.... after a second look it was even very easy.

@nicolascortes6951 10 месяцев назад

Idea for another sudoku app: mini sudoku or little sudoku, an app that would have 4x4, 6x6 and/or 8x8 puzzles. Love the video and the approachable it was, greetings from Colombia 🇨🇴

@olivier2553 10 месяцев назад

After watching you a bit, and you asking the question about the series in the thermos, I had the missing clue and was able to finish the puzzle. with a 3 in the corner to make it even better.

@ShOcKxCoRe 10 месяцев назад

I spotted the nature of the thermos (always ending with 9) pretty easily by looking at row 1: all numbers must be a bulb of a thermo, so the only way that works is that 8 is the 2thermo, 7 is the 3thermo and so on. Also the 8-9 thermo is the only one that can give a 2-skyscraper. From there, it was smooth sailing doing the same deductions Simon did :) beautifully constructed puzzle!

@jeremyblack1929 10 месяцев назад

man, what a fun puzzle. So 'easy' to solve, but the logic is just crazy.

@Claire-ing 10 месяцев назад

My solve path was very different than Simon's. After the intial 3 digits, I differed. My next digits were the 1s in column 3 and 6, because you can deduce those are the only places a 1 can go, due to a 1 in row 8 having to go in a column where the thermo already ended, and so on. Then figured out how this pattern just applies over and over again in the puzzle and will make everything consecutive. I had all of columns 3 and 6 filled in before I started going for other digits. Then it was a matter of sudoku'ing and figuring out where which thermos were, with a lot of help from the 9 diagnol rule. Then once you get one digit in a column, it's over for that column. Enjoy these approachable ones!

@BlameItOnGreg 10 месяцев назад

I got the cycle concept immediately, but I didn’t know how to logically find the layout of the 9s after the two skyscraper 9s. I ended up just placing the 9s following the rules using intuition, and got it right on my first try. It was just filling in all the rest of the numbers at that point. One of my fastest solves ever, even if I relied on intuition for part of it instead of pure logic.

@tzeneth 10 месяцев назад

00:12:41 And the only reason I know I was able to complete it was knowing the trick when you have a bunch of thermometers all next to each other. Then again, still got stuck for a bit because I didn't take care of all the cross positions

@rdwells 10 месяцев назад

Basically this is a 9 queens problem repeated 9 times, and the only way to get the solutions to mesh is to have each one offset one square horizontally or vertically from each other. The thermometers just force the copies to be vertical and eliminate the ambiguity regarding what digit goes in each offset copy. Really, really cool. Now if only I had realized that at the beginning rather than after finishing it, I might have cut my time by about 70%!

@flora5090 10 месяцев назад

Can't believe I got that in under 8 minutes. Really fun puzzle

@brenthooton3412 10 месяцев назад

The "sky" above the skyscrapers is easy to fill in almost instantly by looking at the empty spaces in the rows at 21:57. There must be a 1 in row 2, and there's only one place (above the 9). There must be a 1 and a 2 in row 3, there's only 2 places, the 1 can only go in one place (above the 9) and then the 2 must go above the 1... and the pattern continues. After 3 rows it's self-evident how the rest of the "sky" needs to be filled in.

@fuji2086 10 месяцев назад

6:44 for me. This was a really neat idea. Great puzzle.

@Wecoc1 10 месяцев назад

Solved it in 3:05 ! Very cool one! :)

@Gonzalo_Garcia_ 10 месяцев назад

1:55 for me. Pretty intuitive puzzle if you've seen something similar before. Still quite interesting.

@cavalerul10 10 месяцев назад

7:17 for me. It was really approachable! And after figuring out that all thermos end with a 9 and are formed by consecutive digits, it was really easy to pencil mark the bottom 3 boxes and deduce which is which by the diagonal constrain.

@ExodaCrown 10 месяцев назад

I think I over thought this puzzle and my thought process could be right. Watched the video some and it confirmed I was on the right track, made a minor mistake, but once I noticed it the puzzle came together. Overall a nice solve.

@LandOfForeverSummer 10 месяцев назад

Congrats on line sudoku. Now it’s time to start fog of war sudoku app

@timcotton1782 9 месяцев назад

The only way for the diagonal rule to work is for each set of columns to be a modulo set of digits. Once it is determined that the 2 skyscraper clue must begin 89, everything else must be in a fixed pattern with a strict rotation of 1-9 from the bottom up.

@trudain 10 месяцев назад

9 mins for me. Thanks!

@TAHeap 10 месяцев назад

My flabber is more than gasted to see Simon spend 15-20 mins doing actual *sudoku* when there's a very simple logical solution to prove that the _feeling_ he had before starting was indeed correct! 😲🤨

@chipsounder4633 10 месяцев назад

Incredible. Was thinking at teatime about a diagonal constraint but digits in an arrow cell point to how many fillomino regions it sees. Wondering if that would work as a 10x10 build your own boxes with the digits 1-6

@Guerin78 10 месяцев назад

10:13 -- My fastest time on any CTC puzzle so far. (Having solved "Rising Circles" a couple of weeks ago -- which used a very similar trick -- certainly helped!)

@KevFrost 10 месяцев назад

Was totally stumped at the equivalent of the video 17 minute mark, then on watching mark mentioned the magic line about where the 4 cell thermo went. Then chuckles aplenty at just how cyclic it became and a solve in 18:48

@user-kt9vr1wj6y 10 месяцев назад

18:53 for me I didn't find the path at the start. Once I get the picture, it's easy to finish it in 5 minutes. A interesting puzzle! I like it.

@Sidnv 10 месяцев назад

It's not too hard to prove that the columns had to cycle using mathematical induction on the length of the thermometers. You start with the length 9 thermo which is determined. Then the length 8 thermo is determined and the remaining digit is 1, so the column is forced to cycle. Then the length 7 thermo is determined, and the two digits above have to go 1 then 2 due to the position of 1 from the column with the 8 length thermo. This just continues to induct downward. To formalize this, you'd want to use two layers of induction, one on the length of the thermo (downward) and then one on the remaining digits above the thermo (starting from 1 upward to restrict positions of the higher digits).

@annaweigand3884 10 месяцев назад

Of course there is some chess here: a queen's constraint. In analogy to the "eight queens problem" on the 8x8 chessboard, here we have the 9 queens problem on the Sudoku board for the "9"s.

@J3ff_K1ng 10 месяцев назад

I watched a lot the channel but I don't usually try sudokus I did a few that has a gimmick of moving boxes another one that was massively solved and this one I can't remember any other sudoku I've solved Yet 17 min solve A really really approachable sudoku

@jasono8783 10 месяцев назад

12:12 for me today! Very fun, interesting logic!

@badgerfool1980 10 месяцев назад

I'm pretty sure if you flipped the grid horizontally and had upside down thermos with high bulbs and low tips the solve would be identical which is another way of looking at why the actual thermos cycle back over and start again if I'm not mistaken (which isn't out of the question). Edit: forgot to mention that some of Simon's eccentricity may be rubbing off on me, now not only do I sing "that's three in the corner" but have added "there once was a chocolate teapot" to the tune of "there once was an ugly duckling" to my repertoire along with "all the two's are done" (or some variation) to California Dreaming by the Mamas and the Papas with the odd addition of "and the threes are too" for the next line.

@jenniferbrien3408 10 месяцев назад

Looks like well over half of those who viewed this also solved it. Now that's what I call approachable!

@BramCohen 10 месяцев назад

12:21 here. A rare case of me beating Simon's time. The hardest part was realizing that when it said 9s can't share a diagonal it didn't just mean immediately touching

@Jesthers 10 месяцев назад

Beat this one all on my own, though I misunderstood what "no 9s can share a diagonal meant" at first (I think it was like a king's move restriction, when it was meant to be queen's move). Puzzle solved quite quickly after realising that mistake. Good puzzle today, nice and focused :D

@alaguerre6362 10 месяцев назад

Great puzzle. Just under 23 minutes.

@tylerowens 10 месяцев назад

27:39 I guessed what the solution would look like pretty immediately upon seeing the ruleset, but it was fun to rigorously work through the logic and prove it must be the one and only solution

@ddimin 10 месяцев назад

8:47 for me. Never have I solved a puzzle featured by Simon this quick (usually I need more time than Simon to solve a puzzle). I was able to fairly quickly prove that columns are cyclic shifts of 1,2,3...9 sequence, and then I just needed to find where all the 9s go (reminded me of that chess puzzle where you need to place 8 queens that don't attack each other).

@wigermiddelkamp8064 10 месяцев назад

Nice, did this in 17:41, struggled to find the logic here. Could be a lot faster if you get it instantly. Now let’s see how Simon did

@Tepalus 10 месяцев назад

06:28 for me! HOW ON EARTH WAS THIS SET??? Like how does one construct such a puzzle? 11/10 ❤😢

@loafes1352 10 месяцев назад

There should be a few iterations of this grid and I appreciate that he created a grid to put 3 in the corner

@myfyrmadocjones 10 месяцев назад

Cycling and roping in one puzzle - roping vertically and horizontally.

@RMDragon3 10 месяцев назад

The way I thought about filling the missing numbers after doing the thermometers was row by row, starting with row 8. Only digit 1 is missing there, so you can just add it. Then in row 7 you get one more empty space and one more missing digit (so you are now missing 1 and 2), but you can't put the 1 in the column that was already empty in row 8. That means you have to put 1 in the newest empty column, and 2 in the second newest. If you keep going row by row, you keep getting more missing numbers in order, so they need to be increasing by one. Also, at the very start, you can know that 9 must be in r8c6 because the thermometer rule means no skyscraper can be hidden, so you can place that before figuring out that thermometers need to increase by one each time.

@raistlin_dourden 10 месяцев назад

It is chess related. Queens rule says 9 can't be on its diagonals

@TS-cs2pe 10 месяцев назад

What a unique puzzle

@MohdShamlakh 10 месяцев назад

I solved it

@urbanhillebrand1861 10 месяцев назад

I just bought the line sudoku pack and am looking forward to it. Unfortunately I do have a very specific technical problem with this app (doesn't work correctly when run on a chromebook). Where can I report this?

@user-dw2rm2tm7n 10 месяцев назад

3:10 for me! i got on to the trick to solving this puzzle very quickly and flew through it!

@tremkl 10 месяцев назад

The easiest way to prove that the full columns cycle is to just continue your initial thought. Since the length 8 thermo can’t use the 1, it goes 2-9, but then 1 has to go at the top of the column. The length 7 thermo had to be 3-9, so it needed 1 and 2 at the top, but 1 in row 1 is already claimed, so the 2 goes above the one. Etc.

@KC-pe9vt 10 месяцев назад

There is also roping, which is fun!

@Sam_on_YouTube 10 месяцев назад

16:10. Realized pretty quick the easy way to eliminate a lot of possible 9s. Took me a few minutes to realize that more 9s could be eliminated by checking to make sure arrows don't contain the same low digits in the same boxes. Once I got that, I solved all the 9s very quickly. Then I just filled in the lower half. Started doing sudoku on the top half. Went quickly. They I realized the trick and just wrote down the last bit in seconds.