Is This Puzzle Of The Year?

** TODAY'S PUZZLE **
SSG's Archers On The Quad has had some amazing plaudits with some solvers describing it as the Puzzle Of The Year! See what you think - play the puzzle at the link below:
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Rules:
Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Digits given in one of the circles in the grid must appear at least once in the four surrounding cells.
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[@SSGranor]

Thank you so much for featuring this puzzle! I've been pretty blown away by all the kind things people have had to say about it. As Simon suggests, I very much did have a core idea in my head for the structure of the puzzle while setting it very naturally creates the structure for the puzzle's path. So, let me pull the curtain back on that a little. This puzzle is, in fact, built on an idea from Set Equivalence Theory; but, it's not quite the (totally valid) SET that Simon points out in the video. I've been interested for some time in ways that you can use unbalanced SETs to build some rather deep ideas. (For instance, a relative of what I'm going to be talking about here can be used to prove Potatohead21's theorem - and, in fact, a more general version of it.) In this case, the idea was to compare the contents of rows 23578 with columns 1469. Since this is comparing 5 houses against four, the contents of the first set can be though of as the contents of the second plus one full set. And, eliminating common cells, whats left of the first set will be exactly the four complete quads, the bodies of the four arrows, and the center cell. And, since every digit will need to appear at least once in this set, that immediately forces 9 into the center and 7 and 8 each only at least one arrow. From there, it was just a matter of finding what arrangement of digits in the complete quads and what further quad clues led to a resolved grid with a satisfying path. As Simon's solve demonstrates, of course, you don't need to find this pattern to get through the puzzle. In fact, I've seen at least four ways of looking at the opening that all come at it in different ways. I tend to think of Simon's method as being about empty rectangles in the corner boxes. A similar method involves noticing that the complementary space to the larger set I talked about above creates jellyfish (or finned jellyfish) on high digits. And, a final method uses the SET that Simon pointed out in the video. Because a number of people have streamed or filmed solves of this one, I've had the chance to see a number of these methods in action; and, it's been honestly pretty neat to get to see the different ways people approach it in action.

[@craigthorsen]

Thanks for the information on the construct.

[@johnarmstrong607]

🤯

[@davidrattner9]

Beautiful explanation!! Thank you so much for posting this!! Great to see how minds work from setters.

[@longwaytotipperary]

@@davidrattner9 well said, David!

[@chadburke1938]

Now I have to watch the video to see another path. I was able to go through it pretty quickly looking at the jellyfishes on high digits.

[@RichSmith77]

For anyone wondering, when Simon made use of his false 7 pencil marks to incorrectly place a 7 in box 9, at 21:35, he could have placed the 4 in r3c1 in box 1 (only available spot on the 4 quadruple), followed by 8 then 6 in box 1. That would have then made the 7 pencil marks correct in box 1, which would have validated the rest of the 7 pencil marks, by feeding around the perimeter.

[@troy.s]

Found the same, then was able to continue watching.

[@OlafDoschke]

I spotted that, too. And I wasn't able to continue watching with that in mind, it bugs me. The 7 pencil marks were only from demonstrating how 789 go around the grid in the edge cells, but the 4 was inevitable in r3c1, as Simon also spotted later because of the 34 pair on the arrow in box 4. The 7 in box 9 then follows from small deductions you can make from having the 4 in r3c1. The next thing is still the 6 in r1c1, but then also the 789 in box 1 because 7 and 8 are already placed in column 3 you get a 9 in r1c3 and the 7 and 8. r9c2 finally can't be a 7, the 7 has to be in r7c1 or r8c1 and together with the 27 pair on the arrow in box8 r7c9 can't be 7 anymore. So it's known after setting the 4,7,8, and 9 in box 1. The simplest next deduction at that stage is a 1 in r2c5, but you could get the 7 after just 4 other digits. And if you see that, you can continue watching with the advantage of knowing all the edge digits in box 1.

[@MichaelMerino]

I wonder if Simon reads us when we notice the minor glitch. Well, it's such an enjoyable experience, we love it glitches and all.

[@OlafDoschke]

@@MichaelMerino Well, how does Simon always say? He likes comments, especially when they are kind. A comment on a glitch is not necessarily that, but I think Simon and Mark are overall thankful if a glitch is reported and "fixed" by us, as Mark recently also said that their videos are not verified by their testers before going up. So their only verification is having a solution in the end. I remember sometimes Mark and Simon will mention a comment that has shown them how they could have done better at some stage, especially if they ask for better ideas. But often they fix their glitches themselves or don't come back to it at all. To me, it's simply educating, if I read better solutions by others, and so I also share mine. It adds a bit of value, I think. And certainly, it does not push Simon and Mark from the throne of all Sudoku channels.

[@imadslimani1234]

thank you i thought i was going mad

[@ritchards]

Naughty Simon - left those 7 pencils marks there, which happen to be accidentally correct

[@pacman52280]

I was hoping he'd be wrong.

[@giddyaunt9953]

the force is strong in this one

[@troy.s]

I was just about to comment about that at @21:35. Most confusing to follow along with.

[@Epinardscaramel]

Ah I thought I was going mad! 😅

[@zarazabara]

Yeah, I had to wind back to 13 minutes where he put them in to see what logic I had missed. Turns out it was the logic of a lucky guess.

[@greghill7759]

@28.35 It felt as if the World was coming perilously close to tilting off its axis when Simon failed to celebrate "3 In the Corner".

[@alejandrogabrielmonastra8795]

I can't believe that Simon didn't spot the 3 in the corner!

[@majedal-baghl4917]

Yes, I've been hoping to hear the same note 🎹 on both of the syllables of "spotlight." Let's see what happens Monday . . .

[@kirrix5781]

I was losing my mind. He's always so disappointed that he doesn't get a 3 in the corner and finally it happens and he completely misses it!

[@gilesbrennand7529]

It was the last cell that I completed! Made it hard to overlook …

[@bibliopolist]

That Simon doesn't use the numpad and mistypes every single number first, we can live with that. Colouring cells long after the colours have any use: why not, it just makes it so much more difficult for him to scan. Ignoring simple Sudoku all the time: it's part of the fun. But WHY THE BOBBINS does he never use the undo function of Sven's great software???? It would prevent so many mistakes.

[@inspiringsand123]

Rules: 01:48 Let's Get Cracking: 03:11 Simon's time: 26m20s Puzzle Solved: 29:31 What about this video's Top Tier Simarkisms?! Schrödinger Cell: 1x (17:17) And how about this video's Simarkisms?! By Sudoku: 9x (19:39, 19:43, 19:47, 19:57, 21:28, 22:07, 22:26, 26:16, 26:41) Beautiful: 7x (00:44, 13:23, 13:27, 16:17, 18:25, 22:24, 29:30) Ah: 6x (09:49, 09:49, 12:57, 13:00, 15:48, 22:52, 24:17) Pencil Mark/mark: 6x (04:20, 05:46, 06:35, 18:52, 24:30, 25:16) Hang On: 4x (04:04, 11:00, 11:00, 29:07) Clever: 3x (21:25, 23:47, 25:32) Obviously: 3x (04:16, 05:29, 07:35) Good Grief: 2x (13:00, 20:09) Goodness: 2x (29:22, 29:32) The Answer is: 2x (14:34, 21:04) Stuck: 2x (07:45, 08:15) Lovely: 2x (13:00, 23:07) Our old Friend Sudoku: 2x (21:36, 23:10) In Fact: 2x (00:54, 02:57) Sorry: 1x (19:31) Brilliant: 1x (20:15) Ridiculous: 1x (10:41) Deadly Pattern: 1x (29:19) Disconcerting: 1x (00:52) Approachable: 1x (00:38) Surely: 1x (16:11) Proof: 1x (30:34) Whoopsie: 1x (12:40) We Can Do Better Than That: 1x (06:00) Marries Up: 1x (06:37) Intriguing: 1x (00:35) Next Trick: 1x (27:26) What Does This Mean?: 1x (17:32) Nature: 1x (29:44) Symmetry: 1x (06:48) Most popular number(>9), digit and colour this video: Sixteen (2 mentions) Two (62 mentions) Yellow (10 mentions) Antithesis Battles: High (5) - Low (0) Higher (2) - Lower (0) White (2) - Black (0) Row (10) - Column (6) 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!

[@Hertog_von_Berkshire]

I thought "hang on" x 2 at 11:00 must be a mistake but no, there they both are.

[@RainbowDashShadesOfApproval]

Nice bot. Unironic/actual sincere complement, btw.

[@LadyEmilyNyx]

And a poor unnoticed 3 in the corner.

[@Hakucho64]

At least it got to keep its religion.

[@RoselynTate]

I've never seen Simon completely forget to remove pencilmarks he only put in as an example! He got very lucky that the 7s happened to be arranged in the way he chose as an example! But then he also neglected to notice that he could've placed the 8 in box 5 only seconds after he'd pencilmarked it when he placed the 8 box 8 😂 It is these types of things that really make me enjoy the channel though -- makes me feel hopeful about my own ability to improve, knowing that even expert solvers like Simon and Mark still sometimes miss things and make mistakes ^_^ (Edit: typo)

[@leickrobinson5186]

Oh, it’s not the first time he’s forgotten to remove “example” pencil marks! :-D (Usually he’s not so lucky, and he gets quite confused later why those marks are there, with utterly no memory of having put them in as an example, lol.)

[@MaierFlorian]

Sad lonely songless 3 in the corner :(

[@joshrobbins4853]

Can't wait for Simon to repost this puzzle and acknowledge the mistake with the 7's. I think the solve without his mistake is even more beautiful and I know he'll appreciate this puzzle even more after he does it the correct way

[@andrewgrant6516]

You can tell Simon was really enjoying the puzzle because he got a 3 in the corner and didn't sing that bloody song.

[@conexant51]

Well, it's a tradition that ought to be fazed out anyway.

[@KajtekBeary]

@@conexant51 naah, he just didn’t notice. It’s not the first time

[@margaretsinclair6697]

Noooooooooo! Can’t leave the 7 pencil marks from an explanation in place. I just about had a heart attack. The thought of having to undo the work done if it turned out wrong….

[@a_tasty_snack5215]

Ooooo Simon I think you got lucky with those sevens. 21:30 that logic doesn't hold but you got lucky with your example 7 pencil marks. I think you aren't too far off from a logical deduction here though.

[@taptele]

Hello, I'm an avid watcher and learner - can you help me understand why the logic does not hold at that timestamp. Replayed a couple of times and I'm not seeing it - thanks so much. Edit : NVM saw the 7 pencil marks , leaving the comment here just for anyone else who's in the same boat as me.

[@iceberg54321]

@@taptele He put in the 7's as an example, and forgot to take them out. He got lucky and they were in those positions.

[@jussikuusela7345]

@@iceberg54321 lucky sevens, so to say

[@Coyotek4]

28:38 ... "... in the corner?"

[@th.nd.r]

Great setting and solving! Two friendly notes of constructive criticism for Simon: 1) The 3 in the corner didn’t get its song 2) If you want to put in a pencil mark to demonstrate something or to see if something works, I recommend putting in a weird highlight somewhere to remind you to not include that pencil mark in your solve path and to hit the undo button until that highlight is gone As always, loved the video!

[@asbjrnfossmo1589]

Gotta love how the camera goes out of focus while changing glasses :D

[@laughingkoala8623]

Very lucky with those Sevens Simon

[@mr_trever]

Noooo, the 7's we're not valid logic! Very lucky to be correct on that one, but still a beautiful puzzle.

[@RaeconNom]

Those false 7s kind of ruined it for me, what a shame for such a beautiful puzzle

[@SSGranor]

FWIW, the logic that demonstrates that that placement of 7s is correct isn't too hard. Basically, the 8 quad at the bottom fixes which side of the empty rectangles the 8s go in, and the 4 quad on the left takes one of the two possible cells for 8 in box 1, leaving a 79 pair in r1c23.

[@bobfish7699]

Oh dear - lucky the solve didn't go wrong with some example 7 pencil marks being used for real...

[@LixLorn]

I thought I was going to be disappointed when you didnt end up using a Phistomefel solution to this puzzle - but I wasn't! The logic was genuinely beautiful the whole time. Maybe In six months when Ive forgotten the solve, I can do this one myself... Thank you for a lovely video and a great puzzle!

[@luiscarlosdelagarzabecerra7373]

Those 7 pencil marks were quite stressful to watch.

[@5t757]

Proud of my 14:38 today. Sometimes clever puzzles all click into place for me, sometimes they don't, but this one certainly did!

[@johnharriman85]

28:37 that cell's 3 IN THE CORNER!!!!

[@SekGuy]

@21:38 When the mistake is made to use the faulty pencil marked seven, the way forward is to look for 8 in row 5. And where the 4 goes around the small circle clue around r3/4 c1/2

[@jamesblanton3744]

Simon failed he missed 3 in a corner

[@doriswlongAgoandfarAway]

wait I thought those 7 pencil marks were there as an example and should have been deleted afterward. am always missing stuff going by too fast for my slow mind - sigh.

[@BryanLu0]

Yes, Simon just forgot to remove the pencil marks

[@ibn_klingschor]

look at the other comments. he accidently forgot to delete the 7s. your brain is young!

[@eloiaranda3518]

Amazing content I keeo on watching more and more of your videos before I go to sleep and when they are this short (less than 45 mins) I can't take my eyes off the screen is just amazing how clever you are and the way you solve them it's just too relaxing. Me personally I'm from Spain and although my English level isn't really that good I can still understand all your thoughts and the conclusion you get out of them perfectly. I hope you keep on doing this you are amazing. The milion mark isn't really that far btw...!

[@tombulous]

I waited so long for that 3 in the corner...and then no song. Such sad.

[@johnportwood4211]

And a songless three in the corner.

[@SweetChuckPi]

I have the same problem with my glasses, I'll be working on something and suddenly, "Why do my eyes hurt?" "Oh, I'm wearing the wrong glasses."

[@fufighter100]

think he lucked out with the 7 pencil marks

[@maartenmarien]

I somehow ended up on this puzzle. I realize I’m a year late with my comment, but I have to say: what a beautiful puzzle, and what a smooth solve! Simon takes just minutes, or even mere moments, to spot the core logic. A pity of the mismarked sevens of course, but still: well done!

[@ukdavepianoman]

Found this puzzle relatively easy once I spotted the trick around the edges with 9s 8s and 7s. After that the clues fell into place. Very nice puzzle.

[@davidh.4944]

I struggled with it it for almost 90 minutes on my first run, having trouble figuring out how to break in. I recognized the corner-box interactions, the off-center Phisto-pattern, and found the center 9, but I mis-judged the significance of the corner boxes and brokened it. I needed just a bit of video help to see where I went wrong, but after getting that back on track my second time through went much better, with a 38 minute result.

[@clausewitzianwar]

28:38 Oh Simon, I can't believe you've done this :(

[@srwapo]

28:52, spun my wheels for about 15 minutes and had to look at the video to see the logic about placing the 9 in the center of Box 5.

[@leickrobinson5186]

Same here! I got *absolutely* stuck on that. Once I saw the restrictions on c5 and r5, though, the rest of the solve flowed like magic! :-D

[@facilvenir]

I really loved the 789 corner deduction (not sure if you solved it that way... haven't watched the video yet). Even then I struggled a little, but solved it.

[@leickrobinson5186]

I was quite proud of myself for spotting that! :-D

[@MrGuibig]

I rarely see Simon make so many mistakes in a puzzles 😮. It worked out in the end but it was a sketchy solve! The 3 he finished with was my first digit after like 20 sec!

[@RichSmith77]

It wasn't available at the start, actually, although I made the exact same error. 3 could have gone in r7c8 and satisfied the two quadruple clues. Then the 3 in c9 could have gone in either r4 or r5. I made the same mistake with 2 in r1.

[@zacharybliss4272]

i love your show Simon! thank you!

[@danielepicone1480]

Very fun, and super proud I could spot a SET theory pattern without any help. Probably not the best puzzle of the year for me, but regardless it is an amazingly tight construction. 44:55 time for me.

[@dotantsur496]

12:43 You forgot to remove the pencil markings for the 7's from your example. 21:35 You start placing 7's based on those pencil markings that were luckily correct.

[@qazwiz]

25:56 TIME TO SING (now guess how long it takes for Simon to sing?) (28:38?)

[@BakuSudoku]

29:04 loved the sound of a Deadly Pattern

[@Coyotek4]

16:40 ... Phisto-logic may not have been needed, but it sure didn't hurt Nice puzzle!

[@WesleySpikes]

13:09 solve time. Noticed right away that the exploded Phistomephel ring applied, excluding 7-9 from many a border cell

[@S_Black]

Yes there are Schrödinger cells. You've done a puzzle with them :p

[@SSGranor]

I assure you that no cats were harmed in the production of this puzzle.

[@billleiker5314]

Set at the end was a great, thanks Simon

[@BarryKort]

A remarkable puzzle and an equally remarkable solve.

[@pbush071987]

I got deep into the trenches on this puzzle. Stepped away from the puzzle for a bit, came back, immediately spotted the center 9. Puzzle fell apart afterward. Moral of the story, I really need to learn to step back and look for logical steps.

[@Yttria]

Great puzzle! Got stuck after recognizing the phistomofel variation for quite awhile until finally recognizing the constraint in the middle box. Once this constraint was recognized it all fell apart. (64:57 total time with 20-40 minutes of wandering)

[@danielcamp789]

Awesome puzzle & a really fun solve.

[@Jonathanbass1990]

Nice how using the alternate phistomefel ring, you can't have high digits in the corners. Simon comes to the same conclusion using another beautiful piece of logic

[@noahvale2627]

Missed the 3 in the corner today Simon

[@ericpraline1302]

This one took a turn I didn't expect when it was the high numbers that kicked things off.

[@puritan7473]

At 12:10 Simon says "lets just guess where the seven goes" (in box 3) then goes on to solve the puzzle using his guessed pencil marks! 🤔🤨🤨

[@DarrenNakamura]

Finished in 51:19, but I needed a boost to get started. I just did not think those arrows were going to be useful that early on in the solve.

[@Poet13xRatedRKO]

Solved in 22:00. Not puzzle of the year in my opinion, but close. Phistomefel and then searching the 9 in the middle row/column was the break-in. The rest isn't hard.

[@CpnRad]

once I saw the bit about set theory, which admittedly I still don't fully understand, the rest of the puzzle flowed really nicely for a 28:19

[@CauchyIntegralFormula]

36m36s. Took me a while to find the Philostomefel with the four outer circles, then a little less time to notice the R5 and C5 cross. From there it wasn't too bad

[@longwaytotipperary]

Delightful!

[@erickehr4475]

23:54 for me. A nice puzzle which flowed well.

[@mickanlou]

3 IN THE CORNER.....!

[@jakeharrison7840]

I would suggest when given 4 numbers in 4 boxes to pencil mark it in because i saw when you were scanning you missed a 4 numbers in 4 box places at about 28:00 give or take a minute!!! that way you could have worked faster.

[@y_prime]

solved in 24:02 - took me a bit to single out the 9s and get the 9 into r5c5. my solve path checked the 9s, 8s, then 7s similar to the video, not really using SET. still solves nicely though

[@alonamaloh]

This was lovely. I didn't make the early deduction that gives you a 9 in the middle, so my solve was less elegant. But I still enjoyed it tremendously!

[@buster2256]

Three in the corner without a song? Unsubscribing...

[@HunterJE]

6 at 24:36 can get more right away - it places the 6 in r6c3, which means the blues in box 4 are 125, which places the 3 in the corner...

[@HunterJE]

A 3 in the corner that didn't get serenaded when eventually placed, at that!

[@Grandy_UiD]

God I loved this puzzle. From glancing at the video (haven't had time to watch it yet) it seems like Simon's approach was way different from mine. I got the corner pencil marks in boxes 2, 4, 6 and 8 and from there realized you could't put 7, 8 and 9 alongside those pencilmarks. That lead to corner pencilmarked 9s in box 5 for row 5 (giving you the 9 in box 6) and from there it just flowed incredibly nicely. Super satisfying.

[@steve470]

Simon, if you believe these puzzles are so worthy of a logical showcase that you should prove uniqueness rather than using it, then surely they're worthy enough for you to use the software's undo feature to ensure that they get a logical solve instead of you lucking into the right answer via leftover pencil marks from previous hypotheticals. Please, please, use the software's undo feature to make sure that any hypotheticals get completely unwound. We shouldn't need to turn to the comments to figure out the logical solution path.

[@craigthorsen]

Good solve, explained magnificently.

[@SomethingWellesian]

Got as far as finding the central and c7 nines, but got stuck from there. Oh well. Lovely to see it solved anyway. This was a first for me, though: first time I made a deduction using set theory (which is how I narrowed down the four corners).

[@TDMFAN]

Done in 12:41 using pencilmarks instead of colours.

[@riffswatch1559]

Welcome to today's episode of... Joe90 :D

[@Nok56]

Simon got very lucky with those 7 pencil marks.

[@chrishutchinson5749]

Fantastic puzzle and solve! Am I missing something or is there not a potentially ‘simpler’ break in that doesn’t require set… There is immediately a jellyfish on 9s in columns 2/3/7/8 because the 9 can’t go on the arrows in row 5. Then looking at column 5, the 9 again can’t go on the arrows so must go in r5c5. Once the 9 is then placed in r4c7 there is then a jellyfish on 8s in columns 2/3/7/8 as 8 can’t go on either arrow in row 5 as the arrow total can’t be a 9. This gives the 8 in r7c3 and go from there

[@SSGranor]

To be fair, Simon never actually used SET in his solve. Instead, he treated the corner boxes as an arrangement of empty rectangles on high digits. Your method is sort of complementary to that (and is another of the four ways I know of to start the puzzle).

[@Nevir202]

24:28 Well, no need to pencil it, as there is a 3,4 pair in box 4, meaning there is only one option for it.

[@Rach881101]

22:56 for me. Brilliant puzzle!

[@tman9641]

Woopsie, 7's

[@myfyrmadocjones]

28:36 Losing its religion … 🎶🎶🎶

[@iceberg54321]

Ah, missed three in the corner yet again!

[@mudscuffer]

I liked that.28:38 solve time for me.

[@wanderlustwarrior]

I gave up trying to get this one on my own. After 29:45, I had a feeling I couldn't get the intended path. As usual, it seems a SET puzzle defeated me.

[@miladsajadi1847]

Am I the only one who noticed that Simon solved this possible by reverse Phistemafel technic? He did not focus on the Phistemafel cells but on the non-Phistemafel ones.. First targeting on the corners and then middle edges to deduct that high numbers are not present..

[@Angutut]

You forgot to sing the three in the corner!

[@thescrewfly]

Guilty as charged. Have a subscription.

[@lorenb6066]

I wonder if SSG constructed the puzzle with Simon in mind and that he would of course draw a colourful archery target? 😂 See 15:05 for the bullseye.

[@SSGranor]

While I won't say I specifically had Simon in mind while constructing this, I definitely had the feeling once it was done that it could make a good video.

[@cjextreme]

Where I'm at in Utah is horrible weather as well. So I guess I'll spend some time suffering it out with you 😊

[@DrBiscotti]

Simon not using the undo button once again, resulting in an error 😢

[@guitartailor]

Didn't find this particularly approachable, anyone struggle with this one? Nice solve from Simon though.

[@AndreAy1975]

Solved it with help from the video.

[@piarittersporn]

Finally again a 3 in the corner..... and a wonderful, approachable and not very difficult puzzle.

[@ThePoxun]

nice ludo board :D

[@elementsofsewing5105]

No song for the 3 in the corner and not in the music in the end credits :( what's going on?

[@_-_-Sipita-_-_]

15:44 for me. long time since Aad's SET helped

[@BenCragg1]

Clark Kent takes off his glasses to become superman. Simon changes his glasses to become superman XD

[@robertcousins2274]

30:03

[@adrianhead6272]

🤣🤣🤣 Oh dear! Completed in 13m02s. So simple (789s are screaming out!)

[@BookofAeons]

This puzzle was gobsmacking. Astounding.

[@SSGranor]

Thanks!