Computer Sudoku Solver Freaks Out!
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- Опубликовано: 11 сен 2024
- Today's puzzle is another in the series of sudokus we've been featuring where the world's best setters showcase a brand new classic sudoku technique they've discovered. It's called Boomerang and it's the work of Sam Cappleman-Lynes. As you'll see from the start of the video, the computer solver has no clue how to solve this puzzle logically... can you discover the trick? You can play Sam's Boomerang sudoku at the following link:
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Rules:
Normal sudoku rules apply.
Sam has also made an extremely clever 6x6x6 set of puzzles. We have released a solution video for this puzzle on Patreon and you can try to solve it yourself at these links (one to our software, one to penpa (which allows you to increase the size of the grids):
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git.io/JuB3x
PS We've managed to reach 400,000 subscribers - thanks so much to everyone who has joined us on this journey. We've released a celebration video where Mark and Simon answer community questions here:
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Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships.
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Fantastic solve! You got exactly what I was intending and nothing makes a setter happier!
As for the name... (spoilers follow)
1) Yes there's a boomerang in the grid
2) The action of the setup pushing 1234 out into the corner cells and then one of each being sent back might, if you squint a bit, remind you of the action of a boomerang
3) The real reason is that this puzzle has lots of similarity to Cobra Roll, which directly inspired it, and Boomerang was the first rollercoaster model to incorporate a cobra roll element
So what is it about the technique that makes the computer not able to solve it, Sam? Are they simply not able to do the logic to work out that the 1/2/3/4 are all unique? Or is it the bit with the rows? (computer solvers are notoriously bad at being able to do geometric techniques)
Hi Sam!
@@TheGerkuman I'd also be interested in it. Nerdy details welcome ;-)
I'm not that good in solving sudokus, but as a programmer I always think how to let the computer solve it. At my first job we were basically paid for just being available in case of emergency for two weeks and I had a lot of time to kill. Iirc I re-implemented the first 9 techniques of the Andrew Stuart's solver. The techniques > 9 are mind bending. How did you even come up with a setting that breaks the solver? I had a very hard time wrapping my head around the advanced techniques and didn't fully understand most of them. Very impressive.
Do you have a react video to him solving it?
That was a fantastic puzzle! I didn't solve it but I loved watching the solve!
"It wasn't that difficult"
"I hope you all solved it"
🤨
I think Simon needs to be reintroduced to ordinary humans at some point, he seems to have forgotten we exist!
Give it a few more generations of no one getting offended, everyone buying new stuff if something has the slightest malfunction, user friendliness has already eradicated the last shred of will for "ordinary humans" to learn anything about computers except how to buy new ones... then being able to forget about ordinary humans will be a blessing.
As a viewer of this channel you have already surpassed humanity.
@@asbjrnfossmo1589 Sorry to hear you had a rough day
@@asbjrnfossmo1589 I would almost disagree. It has also pushed a greater need for the ordinary person to understand some about coding, since money is buying less and less
While all the variants filled sudoku videos are fun to watch, there is something very refreshing and extra enjoyable watching Simon try to "beat the computer" in a classic sudoku from time to time.
Honestly these are the best for me.
the guitar at the intro alone is worth a thumbs up
And outro!
yes.. giving a very fresh and new mood
How about dat outro tho, DAMN!
intro was nothing compared to the outro!
I knew Sam was intelligent, but I didn't know he was THIS intelligent. HOLY COW is this puzzle a work of utter genius
I iwas thinking the title might have been "One genius solves a Sudoku set by another Genius"
Simon, a scissor arm for the microphone is a great thing to have. It allows you to sit properly when recording AND it allows you to have your normal scanning position if you sit back :)
Good idea
Zoom in the camera and keep the mic _still_ out of frame.
I was thinking he could get a clip-on mic.
Simon is impressed by the setter inventing new techniques. We are impressed by Simon inventing new techniques. On video. With 400000 watching.
The new technique is hidden in the puzzle for Simon to find. Finding it is still incredibly impressive, though.
@@ragnkja Sure. I am very impressed by both but we do not know if Sam needed two weeks to set it. We know Simon needed less than an hour to solve it. That is impressive to me.
@@StefanPettersson
It is _incredibly_ impressive. I’m really impressed by both of them.
Love how Simon explains his thinking, really helpful for a rookie solver like myself!
This is one of the best puzzles I've seen this year. Hats off for Sam.
And hat off for Simon!!
"sort of almost interesting for a moment". story of my life.
Solving one of Sam's puzzles always, for me, involves the same technique. (1) Stare at it for an hour to identify which bits look suspicious, (2) do a lot of plodding bifurcation with the suspicious bits until I accidentally hit upon the right digits for those cells, and (3) go back to watch Simon solve the puzzle and explain to me how the heck it worked and what the logic was that should have been obvious to me from the start.
Well done, both of you. Brilliant setting and solving.
35min into the video and he had only placed 3 digits, but in 5min he solved the rest, amazing! Beautiful Sudoku Sam!! And incredible solve Simon!!
Simon, you are the most brilliant mind I have had the pleasure of discovering on this website. You see the world in ways I, frankly, cannot, and although I will never be good at sudoku I will continue to follow this channel with rapture. You are not stupid. You are anxious and under a lot of pressure from yourself, but you excel through all of that. Just as you see glimpses into other people's genius through their setting, we see yours every time you upload through your solving.
Also your guitar playing is amazing and we actively encourage more of it
56:06 for me!! I did it!! I solved it without guessing, just pure logic!! Wow, I can’t believe it. This is the first time ever that I manage to solve one of these hard classics without any help or bifurcation, I’m completely ecstatic.
Edit: Hmm… so it turns out that I found another possible break-in. I don’t know how to feel about that, should I be proud? I knew there was something going on with those 4 cells, but after half an hour of not being able to figure out what it was I tried something completely different and it worked.
Rules: 04:40
Let's get cracking: 05:04
And how about this video's Simarkisms?!
Ridiculous: 6x (28:11, 28:36, 28:47, 30:59, 41:00, 41:03)
The Answer is: 4x (29:02, 29:08, 29:54, 30:14)
Sorry: 3x (19:26, 22:15, 22:15)
Naked Single: 3x (13:49, 34:57, 36:34)
Stuck: 3x (07:52, 16:31, 20:24)
Beautiful: 3x (28:52, 41:11, 41:12)
Hang On: 3x (21:50, 26:15, 26:50)
Good Grief: 2x (35:55, 38:30)
By sudoku: 2x (35:10, 37:24)
What on Earth: 1x (19:36)
Bother: 1x (35:55)
Maverick: 1x (02:35)
Nonsense: 1x (22:15)
Bingo: 1x (02:07)
I Have no Clue: 1x (28:23)
Lovely: 1x (41:46)
Brilliant: 1x (01:09)
Fascinating: 1x (02:50)
Incredible: 1x (04:19)
Extraordinary: 1x (40:16)
Oh It Can!: 1x (34:20)
Disconcerting: 1x (02:54)
FAQ:
Q1: What is a Simarkism?
A1: A Simarkism is something that Simon and Mark typically or frequently say.
Q2: How do you do this so fast?
A2: I'm not made of flesh and blood, but of sand ...
Q3: Why don't you include 'XX' and 'YY'?
A3: Probably it's already on the list ('Scooby-Doo' for example), but not mentioned in this video. But if you think it's not, tell me what you'd like me to include and there's a good chance I'll add it!
Q4: You missed 'XX' at 'YY:ZZ'!
A4: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn!
Q5: Could you turn these statistics into videos?
A5: I've been playing around with the idea and I'm open to input as to what people would like to see. Let me know if you are interested in this and/or have suggestions.
On a video of 45 minutes posted 20 minutes ago, how did you manage?!!
@@MariaVlasiou 3x playback speed and skill?
@@MariaVlasiou it's not a human, it's a bot. The auto-generated subtitles are available as soon as the video goes live so it can download them and generate the table fairly quickly.
I love when we get "By sudoku" on puzzles with no rules outside of normal sudoku.
@@MariaVlasiou It's a computer program. That's why it says it's made of sand (silicon).
Simon singing and playing guitar!!! 😍😍
Agreed. Then I got a loud advert after the video, which felt really harsh after Simon’s beautiful, relaxing music.
Not only constructing a sudoku with the pattern, but avoiding solutions that doesn't need it.
This is something I usually wonder in the videos. They have to chose the right amount of clues, so you can get to use the technic, but not enough clues so that you don't have to use it, just like you said.
@@davidthegoldsmith4195 iterating
I absolutely love this "Man vs. Machine" series! Hats off both to Sam for setting the puzzle and Simon for an amazing video!
The "man vs machine" thing is fake, he's using a bad solver. Any IT student can clobber together a recursive solver which solves every possible sudoku in under a second. (A recursive solver has no buit-in strategy, it just tries every valid combination and backtracks if it gets stuck.) Edit: after checking with such a recursive solver it turns out this is just a bad sudoku with as many as 26 different solutions instead of just one (I can post them if you need proof), so the program at the start of the video is correct in its claim that there are multiple solutions for this sudoku.
No, you can't bifurcate correct sudokus because they only have a single unique solution. I'm in IT and I wondered about the weird claim that a human could beat a computer at sudoku because I know from my own experience that solving sudokus is a *very* simple task for computers. I checked this sudoku with a recursive solver to validate the claim and it turns out that it has 26 solutions instead of just one, so the solver program at the start of the video was corect when it indicated that the given sudoku has multiple solutions.
@@JerehmiaBoaz the solver says that there are no known logical steps or the puzzle has multiple solutions, but then Simon checks the number of solutions and there's only one solution according to the program
@@SonicGamesPlayer If a recursive solver prints 26 solutions to this sudoku you can safely assume it has multiple solutions because you can see the proof right in front of you. I can post them here if you don't believe me, but 26 x 10 lines will be a *lot* of text.
@@JerehmiaBoaz I checked it myself and there is in fact only one solution. Also obviously a computer can solve it easily by brute-force, the interesting things about these puzzle is that it's hard for a computer to solve it in a logical way without ever making a guess.
I'm incredibly bad at scanning
*immediately misses 3 pencil makrings*
Oh Simon, never change
Wow wow wow wow wow
This Sudoku perfectly showcases Simon's break-in prowess.
Stunning ouzzle
An ouzzle with poozles of wows.
These videos comfort me so much. Especially today, when it’s the Day of the Defenders in my country and we remember all the men and women who fought and lived and died for our freedom. Thank you.
I did it in 32:02 by using Phistomefel's ring . If the computer solver didn't have an answer I assumed it must be a "set" solution. It might not be what was expected but it worked for me. By the way I would not be capable of solving it the way Simon did.
WHAT A PUZZLE. And a great solve to go along with it as almost always. Geez. Awesome technique. As per Simon’s task in 40:20, he left off one element: that this puzzle must solve beautifully. Sam did that as well. Also Simon, we are always blessed to hear you play music for us. Thank you.
Watching Simon figure this one out is kind of awesome.
This has to be one of the best Solves I have seen. Congrats Simon on unpicking the setting's genius. I love the way your lateral thinking works - exceptionally fast.
Many years ago I wrote a Sudoku solver using a BASIC compiler. I have since lost it but the Qbasic Sudoku solver by an un-named person (I have found his name David Hall- the copyright date is 2005)solved this Sudoku in under a second! I gave up trying to solve it by hand after 8 hours!
Love your solves.
Amazing as always. I like how Simon always puts his hands behind his neck when he has an epiphany and it's so nice to hear him say such nice things about the setters when he appreciates what they have done. As mentioned before, most of us we would never understand what he has appreciated if not for him so I give props to both him and the setters.
After almost two years of watching you, learning incredible techniques and tricks, this is hands down the greatest puzzle and solves I’ve ever watched you do. I’m so incredibly impressed!
I want to say "More guitar!" but then it might diminish the immense joy of the surprise I have when the rare video has it. :)
My backtracking Sudoko solver (i.e. Bifurcating) took 34s to solve this one, which is 8s longer than it took to solve Shye's previous Computer Flummuxors
The brute-force one built into the web app takes about 5ms:
[console.time('solve'), createSolver(PuzzleTools.unzip(Framework.app.createClassicSudoku()).replace(/0/g, '.')).findSolutions(1), console.timeEnd('solve')][1];
A dancing link exact cover solution is 10ms for me but that's 100% cheating
Mine does it in about two seconds, but it's also just backtracking as well. Are you on an old laptop or something?
18:53
“Actually, I did feel like that was sort of almost interesting for a moment.”
The struggle is real 😂
A title I am waiting for:
{insert setter's name} take a bow.
Sam Cappelman-Lynes take a bow.
30 minutes for the break in and 10 minutes for the actual solve. The mark of a Simon approved Genius level puzzle.
Brilliant solve, Simon. i tried solving before watching and I got stuck hard. I could not see any meaningful pattern or restrictions. You are helping me see Sudoku's in a different light.
Appropriately when the universe sings to Simon, Simon repays the favour with his own in- and outro. Today's offering was full of wonderment and song - on so many levels.
I managed to squeeze in a solve prior to the treat of the recorded solve. The hi/lo arrangement was a beautiful telegraph. If those digits would not have been separated - in well-nigh The Witness fashion - this SCL puzzle would have been truly monstrously hard to crack. My break-in resulted from colouring the hi/lo parity. A little bit of an inkling that 5 would probably occupy the central squell gave a push in the back. I suffered from over-Goodliffing and saw clearer once I rolled back the Goodliffing and concentrated on the telegraphed geometry. It still took a goodly 30 minutes to put the last digit in.
Early days tomorrow so I will turn in now.
Well done, Amos!
Absolutely incredible, Simon!
Well done, Sam.
Stunning.
No way I ever would have solved this. Brilliant solve...way above the capability of most.
how? HOW?!!! how is is that i cant pay attention to anything for more than 2 mins and yet I watch your videos in full just watching this beauty unfold. knowing that i will have full satisfaction at the end. being able to follow your logic and observe you expressing your intelligence so delicately.
Too tough for me ...
I'm sure I *could* actually finish this by just guessing a lot (I started doing such), but even if I make it to the end, it would feel hollow. I'm just gonna watch and see what I missed.
EDIT ... *jeebus* ...
EDIT EDIT ... and on top of everything else, I erred in pencil-marking 8s in Box 7. Truly one of my worst performances in some time.
Simon and trying to figure out why a puzzle is named the way it is, name a more iconic duo.
(Saying CTC and failing to scan is cheating)
Mark and the word "approachable".
Simon starts a video playing guitar, for sure it's gonna be a great video...
But when it starts with the regular intro it's also great, so it's not a good measuring point, I guess...
I came upon this channel by accident about 3 months ago and quickly got hooked.
At that point this would have been completely unsolvable to me but after dozens and dozens of videos from Mark and Simon even grids like this have somehow become approachable. 35:00 on the dot is a testament to their educational skills. Thanks to you both, and to the incredible setters.
Just... wow!
For both the construction and the solve!
I did try... and I got some restricted cells. Almost found the 1234 quad... but had no real idea of how to apply it.
Brilliant job by Sam and Simon.
🤯
Mind blown!
Love the "Its ridiculous" in the 30+ min mark
Outstanding. These type of classic sudoku are my favorite. Thank you for sharing.
Finding that first 8 not only helped with the 5's, but it restricted the 9's to only two places in row one. I overlooked that at first and I believe Simon did as well since he never marked the Snyder notation there. Apparently he didn't really need that anyway. I could see all those 1-2 and 3-4 combo's lurking there in the corners, but had no idea that they formed the quadruple square which was so powerful in eliminating so many candidates. My break-in point was the 15 and 25 pairs in column 2 which, if not a 5, then eliminated both 1's and 2's from the top and bottom, leaving a pair of 34's. It was not as elegant as Simon's discovery and I still had to pick apart the rest of the thing as usual.
What I did not understand is how the computer could say that the puzzle had only 1 solution, yet could not find that solution. Excellent Puzzle!
The computer could not find a logical path to solve the puzzle, but it could use brute force to try to find solutions, and by doing that guarantee there's no possibility of multiple solutions.
A clever sudoku solver can speed that process up a lot by only making a single guess when they don't know what step to take next and continue from there (this is the Bowman's Bingo approach that the solver explicitly chose not to use for determining whether the puzzle could be solved logically) but even if you don't there's only a finite amount of permutations to try.
Like I'm not great at writing sudoku solvers, so the one I wrote is really bad (bowman's bingo is basically the only trick it knows, and it doesn't even use it particularly cleverly) but it could still solve this one just fine.
The intro and outro were particularly wonderful Simon. 🎸 🎤
Very interesting puzzle and solve!
Sam is just a genius. That puzzle was awesome to solve after seeing the break-in from Simon.
The title of this video should just be "Sudoku Solver Freaks Out!"
Great job, Simon! I was just as blown away as you were, and I couldn't even figure it out without watching you solve it.
"I did feel that that was almost interesting for a moment."
My mood most of the day.
I-was-sick-last-week Simon has a voice as smooth as butter.
Just discovered this channel a few days ago , gotta say I love it and hope one day I might be able to do something reasonably close to solving that. I've used Stuarts solver and learned quite a few things from it myself as well as a few strat guides.
Have you tried the GAS puzzles yet? Mark solves them in batches (so don’t be put off by the length of the videos; it’s because he’s solving multiple puzzles per GAS video), and they’re usually quick and fairly easy but not trivial puzzles, set by three excellent setters, including Sam Cappleman-Lynes featured here.
@@ragnkja Ill take a look thanks.
Welcome and you are in for a treat with everything that had been published here.
Have we seen 5-colored cell before?
Wow, this puzzle captivated Simon so much he even ignored the Maverick.
While I spotted the 1234 square early on (and even the two rows/two columns pattern) I couldn't for the life of me solve it. With most techniques spotting is the problem. Here it was the logic that was beyond me before you explained it. Great work.
Just starting to learn the techniques for solving hard sudoku's. I'm happy with saying once you figured out the pattern I was able to understand it. Thanks for you help/tutoring
Freaking tough, but fascinating. I didn't solve it until you provided the breakthrough.
In my quest to improve at sudoku, some puzzes {videos) I study closely. This is one of them.
Love Simon doing the intro.
The guitar intros and outros are always lovely.
@@ragnkja Indeed.
Lovely intro! Looks more like a crossbow. I gave it a shot and knew I was missing the magic...I wrote in a bunch of candidates and stared awhile before I gave up and watched the video. But wow, I did not expect it was that bonkers. What a great solve!
This has got to be by far the best classic sudoku I've seen on this channel so far.
I was able to solve it by looking at 4s (there are 3 rows in which 4 can only go in 3 positions), and then eventually I got the same for 3s.
I’m proud I solved it, but I could have never come out with Simon’s solution, that was really incredible.
Simon: "I feel so stupid"
Continues to solve sudoku that was deemed impossible by computer...
Amazing stuff. There is one fairly common technique that Andrew Stuart's solver doesn't count, 2 String kite (or pivots and pincers if you like.) That wouldn't be any use here, but just pointing out.
I'll beat my head against the wall until I solve a gnarly Phistomefel, but a 40 minute classic sudoku? I KNOW I'm not finishing that without bifurcation. I was happy to get that first 6 -- then Simon goes and says we shouldn't be too proud of ourselves for that! Way to bring me down, Simon.
Brilliant solve.
When Simon said that stuff about his field of vision it reminded me of basically the same problem I had with a Sudoku program. The solution for me was actually quite simple: make the sudoku smaller. By reducing the size that it displays at I was able to take in the whole of the grid at once which drastically improved my own scanning without having to move way back like Simon does.
Amazing puzzle. You are an awesome sudoku solver.....hats off to you. My brain could never put that 1-2-3-4 xwing solution together. Impressive to watch you work through it
Great solve, but also very beautiful guitar playing! Nice to see Simon passed the Turing test :)
Great setting and solving, that was really enjoyable to watch.
i remember playing that one on your classic sudoku app the other day. which is the best sudoku app ever in my opinion
At this stage Sam Cappleman-Lynes is at the Olymp of Sudoku setting
My spidey senses had me convinced 1 was in the top left corner and 5 in the middle, going with my gut the solution dropped out.
It's interesting that the computer just threw up it's hands without doing a thing considering that there's a free "8" in Row 1 Column 5...
When the solver provides a grade, it attempts to solve it first; it just doesn't show it
@@BryanLu0 Ah, I see...I missed that Simon just attempted to get a grade on the sudoku rather than use the "Take Step" which is what I've usually seen him use...That makes more sense...Thanks.
@@tank2045 I suspect the reason "grade" was suggested (and used by Simon) was to ensure he didn't even get to see the free "8" or any of the other pencil marks the computer would have discovered.
The fact the computer didn't find the 8 confused me as well but re-watching that part I came to the conclusion "grade" meant something slightly different to what we've seen before.
Great puzzle, great solve, great explanation!!! I think a year or two ago I would have thought what the hell is he talking about?
Extraordinary setting! Incredible solve! WOWWW
I’ve suggested this before and will do it again. It might be a good idea for Simon to make the sudoku grid a bit smaller on his screen to make scanning easier.
it was a bit funny to watch Simon get more and more desperate to the point where he tried to use psychology as a technique at 19:47
i’m not sure whether psychology is a legal technique haha
I cracked it quite quickly using SET, if you trace just outside of box 1 and box 9, the 7 digits must be the same in them. The bottom right 7 have at least one 4, and the 4 in r5c6 doesn’t allow a second 4. So there can only be 1 4 in the top left 7. There is already one present, so we can prove there cannot be a 4 in r2c4 and r3c4, thus forcing a 4 in r3c5, opening the puzzle for the most part.
Fun, fun, fun puzzle .. To do (barely) and to watch the flow of the solve! .. Actually managed to spot the 1234 and figured it was 'the trick' but then couldn't figure out what to do with it .. even though, in search of wings and fish, did notice (in hindsight) where 1,2,3&4 only placed in two spots in the column/row .. The brilliance of this and other SCL classics is how Sam puts all the clues out there, plain as daylight, and then, like a cat with a mouse, leaves one hanging! .. Brilliant!! .. More please!!!
This deserves a thumbs up for the amazing sudoku puzzle as well as for Simon's guitar intro/outro. A double win!!
I think you need a Djinn and T after that bit of magic! :)
What a monumental task! Incredible work, Sam; Simon picked up on the telegraphs exceptionally well too!
When the geometry of the puzzle came into play I had to say what a break in!
I tried out with coloring the high and low digits different, because I noticed also, that there are so many high digits in certain rows. It brought me quite far, but not to the final point, as there are some places, where restrictions don't obey high/low restrictions.
Amazing puzzle and great solve!!! I love this channel because you have taught me so many different ways that Sudoku can be done, and it's a growing puzzle type!
Also, I ran the puzzle through Andrew's solver until it got stuck. Then I gave it the easy 8, two 6s, the 1 in box 1 and finally the 4 in box 3 and it finished the puzzle by placing the numbers. I had to solve the puzzle for it before it could complete the puzzle! It wasn't that hard, but the solver never spotted the quadruple. It found 1234 in boxes 1 and 3, but not in boxes 7 and 9. It resorted to bingo and various forcing chains before it got stuck.
This is an excellent puzzle and a terrific idea, Sam!
Not sure if anyone else saw this, or even if it was intentional. But as soon as you said 1234 in each box, I looked at the relative positions of the 1234 in the centre box and predicted the order they'd go in. 1423 clockwise.
5:08 AM- 5:17 AM GREAT TEACHER !
What a puzzle. Wow.
Yaaay music box challenge! Can't wait!
12 minutes in you got to where the computer gave up ... 28 minutes in "That is Ridiculous" and the rest is relatively simple ...
Hopefully we have a full length guitar outro
note that if you press the take step button in the solver it will eventually guess and check it's way to the answer by eventually getting the same seven as you did (4th digit placed at 35:22)
Thanks Simon for the most enjoyable solve. The Steve Earl was a great bonus!!
"Normal Sudoku Rules Apply"
That's it. These are my FAVORITE PUZZLES!
Because I will know there is a really cleaver trick like an exorset or a jellyfish... or set theory or just coloring!
Such SImple Rules make really elegant puzzles with great logic. (Tatoine sunset with multiple sword fish anyone?)
Thanks again Simone and Mark.
And the creators who do alot of classics such as Shye and Philip Newman. And special shout out to Rangsk... you make fun puzzle that are really approachable. I'd suggest everyone who reads this comment to go to Rangsk youtube channel and watch (especially the Sudo-Cult "podcasts" so excellent ).
Thank you everyone for all the great puzzle content. Cheers
This is a beautiful puzzle with spectacular technique. If course, this solve technique will never be used again ( unless someone specifically creates a puzzle for it).
Love seeing the logic unfold ~~wonderful setting and solve xx
Brilliant solving and even more brilliant setting, great job both!
Wonderful!
I’d call that method the “3 Rung Ladder”.
I’d love to know what brand of guitar your playing, Simon. Nice job on the song and vocals.
Have you tried a clip on microphone ?
Might improve your scanning !