Is This A Genuine Miracle?

** TODAY'S PUZZLE **
What an extraordinary sudoku we have for you today. It's called Miracle Once Again and it's by Sumanta Mukherjee. Sumanta has actually discovered a puzzle (which starts with a completely blank grid) where just a paragraph of rules can lead to a unique solution. It's a really beautiful experience to solve this one. Enjoy!
Play the puzzle at the link below:
sudokupad.app/NbqQ2HhP4P
Rules:
Normal sudoku rules apply. (ie place the digits 1-9, once each, in every row, column & 3x3 box). A digit in a circle indicates how many circles contain that digit. Place some circles in the grid such that a box “m” contains exactly “m” number of circles. (Boxes are numbered in normal reading order so the top left box of the grid is box 1, the bottom right box is box 9, etc). ie Box 1 should have 1 circle; box 3 should have 3 circles; etc. If a cell, eg R1C1, contains a circle then all the cells beneath it in the grid (8 cells in this case) must contain circles. No two 9s in the grid can be separated by a single Chess King’s or single Chess Knight’s move; but every 9 must share a diagonal with at least one other 9.
** NEW SANDRA & NALA FOG PACK **
A bonus sudoku pack was released on Patreon this week of 5 fog of war sudokus to celebrate the arrival of spring (in the Northern hemisphere) from Sandra & Nala. It's completely free - just click our Patreon link below.
Other treats on Patreon include:
- the new James Bond sudoku hunt competition;
- Simon's latest forays into the world of Islands Of Insight;
- Mark's video looking at the new OneUp puzzle from Rodolfo Kurchan;
- his solve of Region Geometry by Emre Kolotoğlu (3hr 36min long...!);
- and Mark's latest solve of The Times Club Monthly cryptic crossword
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▶ Contents Of This Video ◀
0:00 Theme music, Puzzle reveal & Rules
4:08 New Dungeons & Diagrams sudoku & video!!
5:43 Leonie's Hip
5:58 Aaron's Weight Loss
7:07 Happy Birthdays
9:28 Start of Solve: Let's Get Cracking
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[@ronjohnson6916]

An approachable blank grid. With a sparse and understandable ruleset. Remarkable. A true miracle in the spirit of the very first one.

[@puritan7473]

Well Said

[@nomore6167]

"With a sparse and understandable ruleset" - If you truly believe that, then you don't think you know the meaning of the word "sparse".

[@jonnanino]

Not to mention, an incredibly beautiful solved pattern!

[@sainio]

Wow😂

[@HunterJE]

Proposed terminology for puzzles like this - "crystalline" puzzles (or maybe "supersaturated" puzzles), the kind where the whole work of solving is finding a "seed" of driving logic and once it's there it rapidly completes itself in a very structured way

[@katiekawaii]

Crystalline totally feels right for this.

[@In_TheMoonlight]

as a chemistry student I really like that terminology!

[@damsonrhea]

ctystalline feels right. It has an internal structure that it inherently enforces.

[@skiesofarcadia4885]

Cool terminology and very apt! However, "miracle" sudoku is well-established at this point and rolls off the tongue a little more cleanly imo

[@HunterJE]

@@skiesofarcadia4885 "miracle" is a totally different thing, it refers to a puzzle that solves despite seemingly insufficient clues (this puzzle being both)

[@thebitterfig9903]

It's one of those puzzles where pretty quickly you kinda know what it's going to be, but then you have to prove it to yourself. I "wasted" a lot of time proving that it wasn't what I already knew it wasn't going to be, if you follow. But that's the joy of this puzzle.

[@adammorse710]

Totally agree. You hit this point where you're like, "I bet this is true..." but then have to prove it, and then you hit a second repeat of that (for the non-circled digits). Truly beautiful.

[@IronLucario2012]

This was a ridiculously interesting puzzle; I stared at it for about ten minutes making no progress, puzzled it over over lunch, then came back and - after realising the trick to it - had it done in 20 minutes.

[@RecreationalCynic]

Solved it in 17:52. I love that ALL the digits incidentally follow the anti-king + anti-knight constraint, but only the 9's follow the shared-diagonal rule.

[@RossReedstrom]

Oh, stating the rules as "all cells follow anti kings and anti nights rule" and only mention the 9s as part of the diagonals rule would be even more fiendish! It would sound like the last rule is just to solve a deadly pattern, instead of being the key to the break in.

[@Ennar]

@@RossReedstrom Not if you do it how I did it. First I wanted to place all the circles. Of course, it's not possible to do precisely, so I did it up to permutation of columns (columns 1-3 in one group, 4-6 in second, 6-9 in the last) since I just wanted to see the structure of it all. This lets you fill in the whole grid, again up to permutation of columns. I did what felt like the most natural permutation and then at the end I was like: "oh, ok, this solves the puzzle automatically." So, I still needed to prove uniqueness once the grid was solved.

[@jdyerjdyer]

@@Ennar I started similarly, but once I realized how the circles would be forced into two columns each and that the leftover digits from the column box above were forced into the other column in the box below (for boxes 1-3 and 4-6), I recognized that the 9s, 8s, and 7s were forced into certain rows for certain boxes. Placing these, I then examined the chess rules for the 9s to get 3 sets (that I colored) that eliminated some of the positions, but not all. Then I used the diagonal rule to eliminate two of the sets placing all the 9s in the grid. From there it is just a matter of ribbon stripping down the columns with circles and simple sudoku from there. Easy!

[@Ennar]

@@jdyerjdyer yeah, I proved 9's can't be in other places the same way you describe, but after the fact I found one solution. It was kind of funny to have to delete the whole grid and just redo the 9's.

[@terrahyde217]

When I figured out what was happening, I started laughing maniacally and started just filling in the grid to get done as quickly as possible. It was a very fun solve. Watching you do it is neat because it lets me see your thought process as well.

[@compiling]

13:59. I saw what was happening with the circles pretty quickly, then most of my time was spent on checking which columns the 9s could go in to prove there's only 1 possible way to fill them in. After that, the rest just falls into place. Nice ruleset.

[@DisturbedNeo]

This is very reminiscent of "Rising Circles" by Prof.Dori, which had similar circle logic, although the circles were already placed in that puzzle. This one uses the king + knight + diagonal rules for 9s to place the circles. It's impressive that Sumanta found a way to force the circle placement from an empty grid using such a simple ruleset, very elegant.

[@davidanderson5830]

I thought the pattern of roping looked familiar. I solved it in less than 10 min. following my intuition of the pattern. Thanks for finding the puzzle that was similar and sharing! Props to both constructors.

[@leco4529]

Thankyou for your kind words about my hip recovery. I’m getting stronger and less tired each day. Leonie.

[@ryaneakins7269]

I thought from the thumbnail that this was going to be a Fog of War puzzle. Is that next years April Fools -- a FoW puzzle with no actual hidden information?

[@pardox28]

I solved it in 16:09; surely my fastest ever solve on a Circle varient.

[@KO47893]

This puzzle was like the "hard" mode of Dorlir's "Rising Circles".

[@changjsc]

Aww, I really wish I started this without looking at the video first. Very approachable and beautiful logic here.

[@studgerbil9081]

This is a clever and fun puzzle and I wouldn't read too much into "beating " Simon's time, since he is patiently explaining it to his viewers instead of just filling it in. Also, I am certain this is a repeat of a layout he had months ago with a slightly different ruleset and given circles.

[@kgbgb3663]

I've got a feeling we've seen it twice before, and that the first setter challenged the second to find another rule-set that gave it. So if I'm right, now there are three!

[@viodragon974]

While watching the logic, it tends to feel above my willingness to wrap my head around, I love watching this channel from time to time to witness some of the best fun logic solutions to amazing puzzles. This is a simple but unique solution that is very simple and fun to witness. Simon probably won't see another faster than fast puzzle like this for a while.

[@dorlirahmeti7576]

It is very interesting idea for a puzzle and very well executed, it reminded me my puzzle with circles, which after you find 9s here the following is the same!

[@foxbot735]

I think this puzzle was almost certainly directly inspired by yours.

[@studgerbil9081]

I believe it is the exact same solution but with a different starting layout and ruleset. Yours was featured here months ago.

[@CaptainSpock1701]

This puzzle deserves way more views and likes! WOW!

[@jacksonphilion3324]

I solved this puzzle earlier today - one of my first - and laying here later in bed, I can’t stop thinking about it! What a beautiful puzzle and an awesome ruleset. My favorite so far.

[@BillLamoreaux]

Miracle roping! Great setting, Sumanta!

[@MichelKoopmansch]

place all the 9 and then it's done in 1 minute

[@tofmill3640]

Today's my birthday, and I solved this puzzle in 23:08. I will consider that as my gift. Thank you Simon for brightening up my birthday with a little miraculous logic.

[@kodesart1251]

happy birthday!

[@Paolo_De_Leva]

Very enjoyable. Like eating a huge ice cream. High intensity and short-lasting pleasure. And the result is so well structured, with: 🔹full *roping* in columns and rows 🔹an almost perfectly *mirror-symmetric* configuration of non-circled and circled digits (they become perfectly mirror symmetric if you delete the 9s.) 🔹each column perfectly sorted in decreasing order, if you imagine the grid as rolled to form a cylinder surface with top and bottom sides joined together. Truly a _"crystalline"_ configuration, as described by *HunterJE.* Phenomenal solve by Simon as well 👏👏👏👏👏👏👏👏👏👏👏👏

[@davidstorrs]

Lovely solve and lovely explanations, as always. Thank you, Simon.

[@AndreasKungl]

I'm a bit torn about this kind of puzzle. Sure it's neat, crystalline, whatever. But basically it's figuring out the break-in minus the rest. I'm more fond of the ones which are a real journey, where you tend to forget that "normal sudoku rules" apply.

[@logiciananimal]

Astonishing. What really gets me is that the knights-move constraint plays a role (even if it is one of restricted character).

[@MeriaDuck]

Wow, that pattern of nines is such a discovery! Lovely ❤ Most approachable Miracle.

[@barnabysladden4316]

27 minutes for me, unbelievable puzzle.

[@Fun_maths]

That sudoku solution is so remarkably beautiful, the patterns in it are endless

[@Muhahahahaz]

Took me about 1 hour and 40 minutes… Truly a marvelous puzzle! Over 80% of my time was spent figuring out how to satisfy all the circles and 9’s, which miraculously turns out to be unique, then everything else just falls into place! 😅

[@Jppnametaken]

What a puzzle, done in 15 minutes. Fastest solve for me out of any 9x9 (or more) sudoku I've tried from this channel.

[@46lespaul]

This is one of the best sudoku ive ever seen

[@BlakeLeitch]

Bloody brilliant, Aaron! Well done!!!

[@TomMalufe]

This isn't the first puzzle I've seen that has 45 circles that stack. They all seem to end up with the numbers in orderly columns. It's just a matter of figuring out what number goes on top (in this case, 9) and how the columns are distributed (which just depends on the extra rules). At 15 minutes into the video (after 10 minutes of birthdays and such) I could already see how it would end.

[@Landis963]

22:05! An absolutely sublime chain-reaction of a puzzle.

[@katiekawaii]

Brilliant puzzle!

[@ElectricFury]

I don't think I've ever had as much joy watching one of these videos as I had when I realised after the 1 and 2 were placed in Box 7, that the non circled numbers were also going to step up the grid.

[@aveinmovil]

It was really enjoyable indeed! Love from Spain.

[@LadyEmilyNyx]

took me 11 minutes to find the 9s, and then another 30 seconds to type everything in after. I loved this one.

[@jaredbitz]

I think this is my favorite puzzle to solve of the past few months - really beautiful logic all the way through.

[@raysouth1952]

What a beautiful puzzle. Loved it.

[@MyriamTT]

Amazing !!!! Thank you !

[@ianoz1]

Under 12 minutes... first time EVER beating either Simon or Mark! Brilliant & beautiful proposition.

[@thenatundi9009]

This one was so beautiful... great solve and setting as always!

[@psiphiorg]

Clever rule set. It took me about 15 minutes of fiddling around with ideas before I had a "Eureka!" moment. From there, I was able to erase most of my pencil marks and rush toward the end. Well, maybe "rush" is an exaggeration, but I did get a lot of forward momentum. Still had some figuring out to do, but in the end I got there. My time was 35:19, solver number 10303.

[@samc9516]

Here we're all familiar with variant sudoku, but what about variant chess?... all the 9s initially, and also most of the digits in the final pattern, are a camel's move away from each other (along three squares and up one)! Also this leads to some nice observations of the pattern: The pattern is even more beautiful - the 9s all connect in one set of camel moves. All other numbers are split into two connected groups by camel moves. Numbers which sum to 9 have the same number of digits in each group - there are eight connected 8s and 1s, a group of seven and a group of two connected 7s and 2s, a group of six and a group of three connected 6s and 3s, and a group of five and a group of four connected 5s and 4s. And what's even greater I'm now realising is that all the connected numbers of the same digit are split into the two groups by circles and not circles. The seven circled 7s are connected by camel moves, the two non-circled 7s are connected, the two circled 2s are connected, and the seven non-circled 2s are connected.

[@HalcyonAcorn]

I love that this was more of a logic puzzle than a sudoku. That really scratched an itch for me😂

[@subinmdr]

25 minutes. Ridiculously satisfying puzzle! Spent a bit too long trying to figure out the possible configurations of circled and non-circled cells and digits. But once I realized that the key is the final rule about 9s, it took me about 3 minutes.

[@janeflett4971]

Loved it! Clever

[@Tapio_Tachyon]

When I first started watching the channel I never thought I could solve any of the puzzles features, let alone one with a completely empty grid, but I managed to do it in 20mins!

[@FF_Fanatic]

I guess an interesting point about placing 9s that would count as uniqueness is that because the rules are all symmetrical, there must be a 9 in the middle of the grid or else you'd have two equally valid placements for 9s, which of course solely determine the rest of the puzzle, leading to multiple solutions. I think this would count as Gurth. It's similar to what you did, but it would eliminate the need to even check either of the other two possibilities.

[@treymix]

8:34! Saw the trick pretty quickly. Would love to see the next iteration of this!

[@frankjiang1857]

Finished in 26:53. Great use of only a few simple rules to create a true miracle sudoku! Fun puzzle!

[@twen7yseven]

Awesome puzzle!

[@chocolateboy300]

I finished in 26 minutes. This puzzle was incredibly satisfying to solve. Figuring out the clue in box 9, which cascaded through the rest of the boxes was incredibly satisfying to see. This truly is a miracle of a Sudoku that I thought would give me major trouble. I very much enjoyed this. Great Puzzle!

[@piarittersporn]

Wow. I did it in 20 minutes. At the beginning I thought that it would be very difficult. Absolutely not! Great puzzle. Much fun.

[@reecec626]

For once I actually got my head around these rules before Simon! What a lovely, approachable puzzle x

[@Nixola97]

14: 51! It took me a few minutes to realize how to start, but everything flowed so naturally after that. I love these puzzles with an entirely empty grid!

[@Rubrickety]

Amazing. From the thumbnail I was expecting a FoW puzzle, which I love, but any disappointment was quickly dissipated when I started solving. This is a brilliant piece of construction.

[@Sarcorco]

That was ridiculous. Seeing the pattern emerge after getting the first 9 down on the grid and just being able to fill the rest of it based on that one digit. Brilliant.

[@vk5ztv]

Loved it. Took me about 25 minutes. Very intuitive.

[@jacobcombs1106]

00:42:45 - 57% slower. I can't believe I actually did it. Each realization along the way was an incredible feeling, and when i realized what the final pattern was going to be a smiled really big. I loved the solution as much as I loved finding it.

[@knutolavbjrgaas1069]

That was such a satisfying solve when i finally got there, absolutely bonkers!

[@arturocaissut1071]

Very nice. I like these puzzles where once you break in everything falls suddenly into place.

[@ARockRaider]

the finished puzzle makes me warm and fuzzy!

[@tomgalli1188]

Tis one was so much fun! A proper miracle!

[@mcpecommander5327]

Brilliant puzzle

[@justinbrede4929]

Fun puzzle!

[@jdyerjdyer]

Extremely easy one. Once you realize the key that which columns have circles and where are very restricted as they cascade down into the boxes below further limiting where the 9s and then the 8s and then the 7s go. Once you have these possible positions marked, just work up column 3 with the rule set for the 9s to get three possible sets (using the chess rules only). From there two sets are eliminated from the diagonal rule for the 9s. Then it is just a matter of ribbon stripping and sudoku. :)

[@GuilhermeCarvalhoComposer]

What an amazing puzzle. I managed it in 13:33, which is abnormally fast for me. Really enjoyed it :)

[@ingvarsuigin609]

This is an extremely satisfying puzzle, though I feel like you've colored and solved this exact pattern of escalating digits and stair-like rows pretty recently.

[@NaHBrO733]

15:41 for me The straight forward ruleset made this really approachable, it's quite easy when you think about where the 9's go (the rules told you to look out for 9's) Quite a miracle indeed where all 9's fit together in exactly one placement

[@specialkalberta]

Amazing

[@vulkandrache1928]

33 minutes. This was very strange yet very straight forward.

[@jordicochegrus657]

First of, congrats to Aaron! Very inspiring progression. Secondly, this puzzle was amazing, and surprisingly approachable for a miracle puzzle. Did it in 43:50.

[@LukeSumIpsePatremTe]

Puzzle of the year!

[@jasono8783]

0:64:24, took me a LONG time to get that logic flow in my head haha

[@HSSVSR]

solved in 15:44, it's very rare I solve a sudoku before Simon:)

[@grahamania]

00:37:09 for me. Miracle indeed! Loved the puzzle! Kind comment.

[@strawberrymilk3695]

Finished in 11 minutes! Pretty proud of it

[@andybenedict9633]

by far the fastest solve for me on a CTC video ever... 6:10

[@titusadduxas]

24:00 - Yay - I spotted the pattern and assumed it followed through. It did 😋

[@Ryan_Pelletier]

21 minutes!!!!! This one just spoke to me, it usually takes me 3x the time it takes Simon! Amazing puzzle

[@H0lyMoley]

I feel ya - and in fact got the same time. I guess we both have that type of brain that sees these "patterns" very quickly.

[@anaayoung9142]

I did this one today, sunday, and it had a great logic. Of course I need a hint or two, but it was pretty fun! 😊

[@brianarsuaga5008]

I spent about half an hour struggling with 9s because I mis-scanned a diagonal. And because I was able to place the 9s in 4 5 and 6, and thought that must surely be some geometric hint. I'd have liked my time a lot better without that!

[@sinom]

The only puzzle that took me less time to solve than the length of the video. The 9s rule only allows for 2 (pretty obvious) placements, one of them gets rules out by the circle rules. Then the solution is already obvious, but even if you don't want to go through with the obvious solution, and want to make sure there aren't any alternatives by properly going through it it still only takes a few minutes

[@benjaminrealy5661]

10:12. Fastest blank solve for me by probably an hour. Once I realized stacks must be in descending order it was off to the races.

[@GreenMeansGOF]

I was not upset when I realized there was not going to be a 3 in the corner. Absolutely beautiful😍

[@muntedfinger]

14 mins 33 seconds for me (it is EXTREMELY rare that I solve faster than Simon!!), something about this ruleset just clicked with me. Beautiful puzzle. Thank you also for the Sumgeons & Diagrams shoutout!

[@michaelhoffman2011]

Pretty clever puzzle. I started off by drawing lines and seeing the pattern. Once I realised they were all Thermos I just had to try 3 different starting locations for the 9. Fun puzzle but took me 10 mins =)

[@addison_reilly5904]

Solved my first ever miracle sudoku! Not the hardest puzzle for sure, but wow is it satisfying

[@monosophy691]

I liked this one. I had a lot of difficulty proving to myself that the circle columns needed to contain the higher numbers, even after i saw the pattern, but i dont do that many puzzles. Suitable for pseudo beginners i guess.

[@jillyapple1]

4:09. But it helps that I remember solving a near-identical sudoku that had all the circles drawn on already. I just had to figure out how to place the 9s to meet the restrictions.

[@Rach881101]

28:42 for me. Nice puzzle!

[@longwaytotipperary]

Absolutely ❤this!

[@davidrattner9]

Seeing Simon open up "live" and then seeing it be a "Miracle"...extra special ❤💜💜 😀

[@longwaytotipperary]

@@davidrattner9 yep ❤️🧡💛🩵💜

[@sjm6280]

In cases like this one I wonder: when, from a setter's perspective, they start from a set of conditions that happen to lead to a grid arrangement like this one; and when they may start from the grid arrangement and come up with a set of rules that lead to it Regarding this puzzle's arrangement, it may be an interesting exercise to think of other possible sets of rules that led to it; even maintaining the first part of the rules (about circles) and substituting the second part (the nines restrictions) by some other constraint that also reduced the possibilities to this unique grid arrangement

[@federicoscaglione668]

Beautiful puzzle, this is the logic I used without checking the possible 9s: because 9 is an odd number the only way to have all 9s with common diagonals is to have at least a diagonal with three 9s and by the ruleset these leaves only the 9s solution as possible

[@johnbell9074]

20 mins for me. Thanks!

[@Kirbyfan87827]

Finished in 21:46 with help getting started from the video.

[@NeilCrabbe]

11:26. That must be the fastest I've ever solved a sudoku from this channel.

[@tinakerr8163]

Very good, very Sumanta! Confess to filling in all the columns with the required order of vertical digits and circles then imposing the chess constraints to place the columns in the correct order, think I would have been much faster if I played chess.