The Euclidean Windmill

[@botaku12721]

Thanks for the feature, it's always a delight! You've actually solved another puzzle of mine with this ruleset as a Patreon exclusive way back when but it was great fun to see you rediscover the logic, especially making use of the given digits to lighten your workload towards the end of figuring out the secret of the unnineables 😄 Possibly related to the low solve count you remarked on at the end, this one had a funny backstory: for said speedsetting contest, we were given 90 minutes (+10 minutes extension) but I was delayed by an hour so I had to get a working puzzle in 40 minutes. I created this exact grid, along with some clones to disambiguate (since I didn't see all the logic while hastily solving alongside originally setting it) and managed to submit in the nick of time. However, I then testsolved it and found it to be broken which caused the submission to be disqualified. Since I quite liked how far I'd got with the givens, I decided to tweak it by first removing the clones and seeing where that would leave me. To my complete surprise, I found that the puzzle had already been unique with just the givens, so this is what you saw today 😆 So this would likely only have the solves of me, the testers and whoever decided to check out the unofficial submissions. Best of luck, see you whenever I come up with something channel-worthy next 😄

[@glum_hippo]

This explains why the puzzle didn't win! It is a perfect entry. Thank you for not winning ;-) , as that left room for someone else to win.

[@annikaQED]

I love this rule set! It's neat how the various digits must follow a king's move constraint, or a knight's move constraint. Please create more sudokus using this constraint! (And what happens if the throw in the true euclidean distance and not just its square?)

[@57thorns]

I really like this one, it wasn't too hard to remember what constraint was required for each digit. Thank you.

[@botaku12721]

@@annikaQED Well, instead of X*X + Y*Y being at least N, one could just as well say sqrt(X*X + Y*Y) should be at least sqrt(N); in fact, that's how the rules were phrased in the one Simon solved on Patreon. If you were to suggest that sqrt(X*X+Y*Y) should instead be at least N, that would break rather drastically: for example, consider the 9 in column 5. Whichever row it lands in, either the row above or the row below is part of the sudoku grid and must also contain a 9. However, the distance between those two 9s would be at most sqrt(4*4+1*1) = sqrt(17), a far cry from 9=sqrt(81). In fact, following logic similar to Simon's, without relying on given digits near the end, you can work out that in "standard" Euclidean sudoku, there are only two ways to place all the 9s which are reflections of one another. Since both of those occupy R5C5, we must have that for eight of the digits, the distance restriction cannot exceed sqrt(8).

[@Paolo_De_Leva]

@@botaku12721 Interesting. I wrote something similar in a separate comment, but I did not notice that this ruleset implies *r5c5 = 9.* During my solve, I was only able to generalize the restriction that rules out *9* from the corners of *box 5.* Edit: I have seen now Simon's demonstration @15:03. but I was able to solve without that knowledge.

[@danielszanto2955]

Simon explaining he does sudoku in the most complicated ways and immediately proves it at 24:40 by not using the simple x-wing on 9s in row 1-2.

[@AquaticDot]

Or straightforward sudoku removing 9s from the bottom of column 4.

[@danecarter5454]

@@AquaticDot Or the 3 in box 6

[@debrawilden1971]

(I'm late to the party. He sometimes does have a way of complicating things. I'm thinking--why the P Ring?! I realized that the higher #s are the hardest to place so went about using them 1st. Process of 'trial and error' got the puzzle finished. Some could say that was bifurcating, but I've seen both Mark and Simon use the 'what if this were #x, then...')

[@A_CC_K]

What is better than a CtC video, a CtC video with a musical intro!!! Brilliant as always.

[@longwaytotipperary]

Yes!

[@2beinteresting]

The Ghost of Tom Joad by Bruce Springsteen nonetheless!!

[@longwaytotipperary]

@@2beinteresting yes!

[@masonivinskas5405]

It’s always a fantastic surprise when we get a Simon guitar intro!

[@MatthewMorris6148]

A surprise to be sure, but a welcome one!

[@annikaQED]

I vote that Simon grace all of his CTC videos with either an intro or an outro featuring him either playing the guitar (& singing!) or reciting a poem (or both!!) How many are with me on this? Maybe our half-million combined voices can swell this to a chorus of approval of this suggestion!

[@kevinsurget8571]

Simon giving up immediately on the 8s in box 8 while having used the same logic for 7s and 6s in the grid is just sad, would have made the whole 9s logic easier and more fluid

[@Stratelier]

Inference from this ruleset: Digits 3,4,5 are effectively constrained by a king rule. Digits 6,7,8 are effectively constrained by a king-knight rule. Digit 9 cannot repeat within _any_ 3x3 group of cells. (To explain: According to the distance formula, if two cells are X and Y distance apart, then if they contain the same digit that digit must have a minimum value of: 1,1 (king's diagonal): digit >= 2 1,2 or 2,1 (knight's move): digit >= 5 2,2: digit >= 8

[@IdoN_Tlikethis]

or alternatively: Digits 3,4,5 cannot repeat within _any_ 2x2 group of cells. Digits 6,7,8 cannot repeat within _any_ 2x3 or 3x2 group of cells. Digit 9 is effectively constrained by a double-king rule.

[@ilmgard1762]

This was how I solved it too!

[@nomore6167]

THANK YOU! When I read the ruleset, my head just about exploded, which only increased the frustration I was already feeling (which is why I wanted to solve a puzzle in the first place -- to relax and let the frustration dissipate).

[@aliengeo]

I know a 35° day is less tolerable in England than Texas since nobody expects it and infrastructure isn't built for it, but last year my area had 80 days at or over 38° so I can't help but have a gut reaction of "that low?" 😅 (Seriously though, I know heatwaves are dangerous-for anyone who doesn't get this kind of weather often: hydrate with electrolytes, limit your exposure to direct sun, and avoid overexerting yourself physically. If you feel "a little off" in the heat, that is your warning sign to get to cooler temperatures NOW.)

[@njihnjihnjih]

The "Euclidean" in the name has to reference the euclidean metric, the normal notion of distance on a flat plane. You can rephrase the rule to: "Given two cells with the same digit N, the distance between the midpoints of the cells must be less than the square root of N". Then you could solve the puzzle with a ruler :P

[@Orenotter]

A windmill whose math is Euclidean Like notes on a scale mixolidian The digits play sound As they whirl round and round Else from lack of sleep I'm just too giddy-an.

[@LiquorStoreJon]

It is a true treat to get SO MANY given digits! Now, will Simon use them or ignore them, as he often does? Stay tuned to find out :D

[@alexandrostheodorosnteris3917]

What a beautiful moment of the intro with playing the guitar Simon So proud to hear you!!! Love from a musician from Hellas Greece 😊😊😊

[@Squishy3757]

I think you abandoned 8’s before you were going to pin them to row 9 in box 8 and then went on the 9 goose chase.

[@glum_hippo]

HONK

[@easternbrown]

Yes, an unnecessary weight

[@wolf7215]

I think the 8 in box 8 could actually have been placed. the 8 pencilmarks in box 7 ruled out the 4 cells in the bottom left of box 8 and the 8 pencilmarks in box 5 ruled out the 4 top right cells in box 8. And the top left cell was a 6 already.

[@longwaytotipperary]

Enjoyed the intro - Bruce Springsteen song with a character from .grapes of Wrath. Always ❤ Simon’s guitar intros.

[@chocolateboy300]

I finished in 37 minutes. This was a neat ruleset that was like a drunk kings move restriction. I think my favorite part was utilizing a sudoku trick that I learned from this channel. I noticed that 9 couldn't have a square of 3x3 around it, so as soon as I placed a 9 in r5c5, I was able to use the potatohead theorem to rule 9 out of every single 2x2 box in the corners of the grid. That was fun to do. Great Puzzle!

[@zachariasis]

25:29 I love when Simon is always trying to find the multiple ways to think about the logic. I loved that although pretty much all of us know about the phistomefel ring at this point, he still always feels the need to make sure everyone is included! But I will say, here I would have just used the x wing you created with the yellow dominos in boxes 2 and 3 to rule out the the top two cells of the triomino in box 1. That would prove the 9 would go in r3c1, and therefore proving the logic you mentioned earlier using the phistomefel logic

[@marcod53]

"Well maybe we have to use the given digits" What a thought

[@bobblebardsley]

I almost didn't attempt this one but decided the rules looked like something I should be capable of understanding. Once I started thinking of it as "a-squared plus b-squared" and noticed the 'important' values within that (e.g. 2-squared plus 1-squared is less than 6, 7, 8 or 9) it started to feel like a knight's move sudoku on the high digits. Solved in 44:39 which is quite fast enough for me to be a happy Bobble. I was quite surprised how early I placed the 3's, all things considered.

[@rcabr31]

Why go for 8's "knights" move restriction when you can try a deep thought for 9's restriction?

[@emilywilliams3237]

This kind of puzzle, where there is a way through it by careful pencil marking, is definitely within my capabilities. I think I'll give it a try later tonight. Even though I just watched the video, I feel sure that I will be able to solve this puzzle without reference to the several observations that Simon made because I am willing to rediscover them for myself! Thanks for this video, Simon (and for the guitar intro! and singing!)

[@laslo67]

yes! been watching for years and I finally got to be the first "thumbs up"! yeah, sometimes it's the simple things that get me through the day. :)

[@kathyjohnson2043]

It is often the little things and I think we all need to remember that

[@longwaytotipperary]

@@kathyjohnson2043thumbs up to both of these comments!

[@scarletmanuka6170]

I found it easier to think about the 9s in the following way: Any two 9s must be at least 3 units apart in either the X or Y direction. Consider the 9 that mut exist in, say, row 7. The 9 in the block immediately above it can only be in row 4, and the 9 in the block above that can only be in row 1. Then we can see that in the block with the 9 in row 8, the 9s above it must be in rows 5 and 2, else they'd interfere with the previous set; and similarly in the other set of blocks we have 9s in rows 9, 6, and 3. Obviously the same logic applies to columns as well. So wherever you place a 9, the 9s in blocks horizontal to it must be in the same corresponding column (left centre, or right), and the 9s in the vertical blocks from it must be in the same corresponding row of their block (top, centre, or bottom). For this it's easy to propagate one 9 around the grid, and you can rule out alternatives very quickly.

[@stevieinselby]

Great fun ... I was a bit daunted initially by the novel rule set, but once I started to explore how it worked it was surprisingly tractable.

[@ianpearse4480]

Wow, that is awesome. Thank you for sharing it.

[@MeriaDuck]

It's quite Sudoku-y, Simon says about a Sudoku puzzle 😂

[@noahhosking495]

This puzzle is amazing, one of the first CTC puzzles which I've been able to complete myself. Thank you so much for introducing me to the realm of variant sudoku! I am now addicted

[@felixbergbauer6098]

8:01 for me. I love these kind of rules that seem so unfathomably complex at first but once boiled down are pretty reasonable and also very restricting.

[@no_name4796]

The rules can be though of as chess move restraints. Two digits greater or equal to 3 cannot be a king move apart, Two digits greater or equal to 6, also cannot be a knight move apart, And lastly two 9 also cannot be at a distance of 2 vertical and 2 horizontal It's way easier to solve, rephrasing the rules like this ;-)

[@samgillmusic]

Loved this ruleset, the way the 9s revealed themselves after the 6, 7 and 8's had been filled in was amazing. Solved in 33:52

[@pairot01]

This was so challenging for me, took me a good 41 minutes and I almost gave up!

[@titusadduxas]

34:42 - Another very ingenious and enjoyable puzzle with a russet that loots bonkers but actually works pretty well,

[@st3phgr1ce]

Enjoying seeing the new variants that have been featured recently! Glad setters are still innovating

[@user-gj5uc4yx3i]

12:20 Simon mentions 9 for the first time. 21:20 Simon places 9 in box 5. That "9" minute proof is the only reason I was able to solve the puzzle faster than Simon today. My gut told me that 9 could only work in the center and I ran with it while also looking forward to Simon's eventual proof. Wonderful video today Simon!

[@JSG-YT]

Personal time: 18m32s Amazing little Sudoku with a beautiful constraint and a nice solution!

[@PinkSupervisor]

It's really surprising how far this rule can take you. Super fun puzzle.

[@richbuckingham]

Simon always seems to come up with complicated proofs rather than just do some simple extra pencil marking which helps reveal the answer directly. Him trying to prove where the 9 goes in the center box is easily resolved by instead seeing the 9 goes in column 7 in box 3 and then cascading all the 9 possibilities around the grid.

[@davidhughes7174]

I always enjoy your pathways through new sudoku variations Simon, thank you.

[@franzelmagetower]

My solve in 19:34 felt relatively straightforward: pencil marked all the possible 8's and 7's and then determined where 9 had to go in box 5 and solved from there. Really nice puzzle!

[@n0bl3hunt3r]

If you could knock the givens down to two or three digits, this would make a wonderful miracle puzzle

[@kn1tt3r]

Thanks for the Springsteen intro! Really enjoyed that.

[@matthewphillips5911]

That was a fun solve. I love when I can watch the video after a solve and see Simon do the exact same thing as me. This time it was coloring the grid for nines.

[@debblez]

26:17 for me Neat puzzle! Took me a while to see that 9 could be placed in box 5

[@iaincook5835]

Simon has pooh-poohed "bifurcation" in the past, but with the nines, he's introduced "polyfurcation"!

[@grahamania]

00:33:15 for me. That was a great unique rule set! Love that we can still have such unexpected ways to set a puzzle. Kind comment.

[@Jonasz314]

Super fun puzzle, but I found it WAY easier than other puzzles on this channel.

[@ZacharyDial]

Simon, I've been a long-time viewer and I cannot stress how much I need you to make another KZbin channel for you to post you playing guitar and singing. That intro was brilliant!

[@Paolo_De_Leva]

What a smart variable constraint❗Its power is a function of *N.* Totally powerless for *1s* and *2s.* As powerful as a combination of anti-king and anti-knight for *6s, 7s* and *8s.* Even more powerful for *9s.* By the way, X*X + Y*Y is the squared distance between the *centers* of two cells. I.e., *distance* = square root of (X*X + Y*Y). This implies, for instance, that the _"forbidden zone"_ around a *9* is a circle with *radius* *r = sqrt(9) = 3.* Namely, no *9* can be placed less than *3* units away from another *9.* Similarly, no *4* can be placed less than *2* units away from another *4* ... The *unit of length* in this case is equal to 🔹the side of a cell, or *🔹1* horizontal (or vertical) *step,* that is the distance between the centers of two adjacent cells that share a side, such as *r1c1* and *r1c2.*

[@Paolo_De_Leva]

(as some of you already know, I abhor using the word "orthogonal" to mean "horizontal or vertical")

[@mudscuffer]

26:11 solve for me. Unusual but cool ruleset. The math is easier than the rules would have you think.

[@RecreationallyCynical]

32:16 for me. I enjoyed the new ruleset, a sort of conditional anti-king/knight constraint (depending on the value of the digit in question).

[@isidornimages]

That ruleset was too much for me to wrap my head around in the morning after coming home from a night at work, but watching Simon's solve it turned out to be a fun one.

[@user-gj5uc4yx3i]

I waited until I got up the following afternoon. 🌙

[@ericveneto1593]

Yup, the channel has christened that a Tigger Jump.

[@TheSkips8]

beautiful performance simon. bout brought a tear to my eye

[@chipsounder4633]

This is beautiful, anything 5 or above has a king's and Knight's move restriction. Roping is caused.. love it ❤... Edit.. oops, i ment to say above 5😮.. i had a look at the rules again and its a equal to or greater sign rather than an inequality.. Logic wins 😊

[@Fun_maths]

Very creative rule, I must say

[@taseennahi]

Loved the intro

[@MyriamTT]

I like this puzzle. A plain Sudoku for a change.

[@jaega4247]

Very enjoyable puzzle, and much -easier- more approachable than the weird new rule may suggest at first glance.

[@bait6652]

That is beautiful twist on King/knight combo rule

[@kathyjohnson2043]

When you said that you were trying to beat the heat, I checked the length of the video! (It is unseasonably cool here in the U S Midwest: only 26c/79f)

[@longwaytotipperary]

90’s F all week here. 🥵

[@debrabowen4276]

Beautiful intro music!

[@frankjiang1857]

Finished in 30:27. Interesting how the ruleset acted like an expanded chess moves constraint. Fun puzzle!

[@JapanoiseBreakfast]

Where does Botaku publish their puzzles? They don't seem to be on logic masters, which probably explains the low solve count somewhat.

[@piarittersporn]

Interesting puzzle.

[@ngarrett16]

Simon!! that intro was amazing!! i thought it was a recorded song not you singing 😱😱

[@colleenscottcarmello5103]

* * * Wow Simon.. you could make a guitar music video for us too. would Love to watch that.. Your voice is so calming and nice to listen too.

[@raysouth1952]

Very enjoyable variation. Great puzzle.

[@TPH250290]

14:00 You could've made far more progress with 8s in box 8 if you'd thought about it.

[@nemonamenlos7330]

1:05 No, I won't forgive you for the musical introduction. Instead I'll thank you for it! ;)

[@edztyMKWII]

I managed to complete this puzzle without realising how to do the 9's or with phistomofel. Brain wave

[@donaldsnyder1543]

Very interesting puzzle , the rules are quite mad lol.

[@TurquoizeGoldscraper]

23:30 for me - my biggest surprise was solving the 3's, I figured that I'd have to solve the 4's or 5's before getting to that one.

[@alanclarke4646]

I found this one quite tough. Well over an hour for me .

[@Kirbyfan87827]

Finished in 26:22 with help from the video. This was a fun one!

[@jeremyburkinshaw8403]

New to sudoku variants and still havent even mastered most generic app extreme challenge modes, but got this in 36:56 😊

[@MattYDdraig]

28:25 Elegant and clever.

[@stevekettel188]

I love how you avoid doing sudoku whilst doing sudoku! 😅😅

[@joekerr3638]

Simon says, "I'm a bit perplexed by this." It's sudoku Simon.😂

[@alumyst2638]

If you ever give up on puzzle solving Simon... you got a promising career in music. I like your voice.

[@stephenmccarthy1795]

8s were placed in box 8 early on by knights move.

[@GeekRedux]

22:42 9 there was just ruled out because of the Phistomefel Ring.

[@popinjayackroyd4526]

I like Simon's version of that song better than the original. I would love to hear an album. You should think about releasing some MP3s.

[@DavidCook-pm4yf]

Your logic is undenineable.

[@visionoftruth6860]

Please apply for a job at MI5 - you're deduction skills are incredible!

[@kathyjohnson2043]

We don't know he isn't already working with them, do we?

[@visionoftruth6860]

@@kathyjohnson2043 thats very true!

[@longwaytotipperary]

@@kathyjohnson2043😁

[@n8style]

@@kathyjohnson2043 he cannot confirm or deny that

[@RichSmith77]

Somewhere deep in MI5 a list has just had a few names added to it. 😎

[@kathyjohnson2043]

If I can keep the rule in my head, I would love to try another one like it.

[@glum_hippo]

This will be the only puzzle to feature this rule set. It's just too niche to permit any further interesting puzzles. (Though it is indeed quite interesting as such)

[@Gonzalo_Garcia_]

12:27 for me. Interesting ruleset!

[@Bearcrapsinwoods]

I loved the intro❤️

[@zobososhizion6478]

01:16:59 ended up having to check nine in every unfilled square in the middle box before I could confirm it went in the center.

[@StephenMarkTurner]

Yes, I had that recording back in the day. Very moody Bruce Springsteen.

[@stiki108]

Now the solve counter stays at 4099. :) Anyway, it's a nice piece

[@ericveneto1593]

“Unnineable”. The things you hear on this channel. :)

[@Lykrast]

The 3/1 chess jump (notated like a knight's move is 2/1) is a camel move. A 3/2 would be a zebra, and a 4/1 a giraffe.

[@tBagley43]

26:59 pretty easy once you figure out how to use the new rule

[@darthrainbows]

Nice, solved in 25:32

[@RealCadde]

SPOILER: It probably helps to translate the rules to less math and more chess. The digits 3 to 5 cannot be a kings move away from each other. The digits 6 to 8 cannot be a kings move or a knights move away from each other. The digit 9 cannot be a double kings move away from another 9. Or for the geometrically inclined. For digits 3, 4 or 5, the same digit cannot appear in a 3x3 box centered on the digit. For digits 6, 7 or 8, in a 5x5 box centered on a digit, that digits cannot appear anywhere BUT the four diagonal corners. For the digit 9, no other 9's can exist in a 5x5 box centered on a 9. Sure, it's a fun way to say X*X + Y*Y >= N as a ruleset. But it's easier to just spell the implications out before solving.

[@sinajakelic]

25:20 x wing of 9s in box 2 & 3 give you a 9 in box 1, same thing happens at the bottom..

[@n8style]

34:22 very enjoyable and satisfying!

[@awilliams1701]

I think we were ~35C yeasterday. It's been 90-100 for a while that's definitely in the 35 range for sure. Today at lunch I went to my car and I'm like.......this doesn't feel that bad. It was 85! It's not comfy, but it's better than 100. So yeah I was hot, but I didn't want to die like I normally do when I go outside. I could not live without AC. I don't know how you guys do it.

[@glum_hippo]

Windmill, windshield, windlass, windswept, windbag, windbreaker, windfall, windpipe

[@emilywilliams3237]

A lovely day for dictionary-browsing!

[@user-kt9vr1wj6y]

30:19 for me nice puzzle

[@FlyingDominion]

Solved in 46:57

[@six_5000]

thought I had catastrophically erred, so I deleted all my pencil marks... only to find I was right all along 🤦‍♂ 45:50

[@jorghimvenerablebosstein7568]

Ur totally good fam! I solved it in 69:56, and I needed one hint(the 9 in the central box). I even used odd/even color logic and the Phistomefel’s ring and it still took me a while. So not worries cause you did better than me! 😂😎💯 69:56 (I wanted my time to light up blue)

[@jorghimvenerablebosstein7568]

Still didn’t 😂