Thank you ever so much for the feature, Simon, and glad to be back on the channel!! If memory serves, my latest appearance was a Patreon exclusive roughly 1.5 years ago, so yeah, it's been a while 😄 The title is indeed a reference to Nine Hours, Nine Persons, Nine Doors. It's my absolute favourite piece of media of all time, my profile picture comes from there and in a way, even my username is an oblique reference to it. So when I was setting a variant called Nine Pins sudoku, I absolutely could not resist the temptation 😁(Also, very astute of you, "YOU FOUND IT" is indeed the message you get in the game after you've solved each escape room!) As for the puzzle, the geometric approach was very much the intended one indeed 🤩 When writing up the solution guide, I did realise that you can get the triples for 3s, 4s, 5s, 6s, 7s and 8s solely by considering where each of them could go in a very particular order, which is an approach one would normally take with a Nine Pins sudoku but one that hardly seems inspired to me. So I'm tremendously glad that not only did you think of the geometric approach, but you did so by harkening back to my previous features 😂 Once again, many thanks for the solve, it really made my day 😄 P.S. I see considerable confusion about the rules in the comments. Frankly, this is somewhat justified; I was inspired to give the variant a try after it was featured in a Sudoku Grand Prix round recently and I believe I grabbed the statement of the rules from there. Even though they seemed kind of unclearly worded to me as well, I expected there was some merit to them that I failed to appreciate 🤔
Lovely puzzle (even if I was in the list of people confused by the rules at first). I’m afraid I solved it in the “uninspired” way, though it was nice to see Simon’s method after. It’s a cool ruleset. I like how the digits kind of cordon themselves off from appearing in certain diagonals.
I like even more the (first) sequel, Virtue’s Last Reward. But love the whole series. Just played Head as Code and Birth ME Code, two small games made very much following the style of 999. Good enough to scratch the itch of not having more 999 to play!
Beautiful geometry 👏👏👏. The rules were unambibuous. The confusion about them was due to people not reading with attention, particularly these words: *identical,* *adjacent,* *in a straight line* That's it❗ There's no need to specify the line is oblique (i.e. the digits are "diagonally adjacent," as opposed to "orthogonally adjacent"). It can be deduced. There is no other way. 🤷♂ By the way, you also need to deduce that the three identical digits must be across three boxes 🤷♂
@@Paolo_De_Leva thing is, 'adjacent' almost always refers to orthogonally adjacent in these puzzles. 'Diagonally adjacent' sounds weird - I certainly wouldn't use the word adjacent for that sort of relation.
I did it! This is the first time I’ve solved a puzzle featured on the channel! It took me just under 40 minutes, and I didn’t do it Simon’s clever way, but I actually solved a puzzle featured on the Cracking The Cryptic UA-cam channel! Towards the end of the puzzle, my hands were actually shaking. Awesome puzzle! Very fun!
I would recommend the chinese coin puzzle to you. It's one of my favourite puzzles, because it's in a similar difficulty level as this one (it has 2 spots that are tricky, the rest is straight forward) and the best thing is, it's easy to remember and to be drawn by hand from memory. It's a little harder on paper brcause you need pencil marks, but also possible. If you are interested you can find it in this channel under "chinese coin". Congrats to your solve! This puzzle took me 50 minutes, but I'm ok with it.
You are amazing! It took me 2 hours, but I solved it. This is like the 3rd time now I managed to solve a puzzle from here but significantly slower. I found this channel a week ago, so plenty of room and time to improve I guess. :D
9 hours 9 persons 9 doors (also called 999 for short) is a sci-fi/mystery visual novel featuring many "escape room puzzles" originally on the nintendo DS, but it was later rereleased with voice acting on steam
And the steam version is pretty awful. If you can find it reasonably priced on DS, it's worth playing on it's original hardware. It was made to be played on it, and it uses the hardware for story telling purposes. It's actually some of the smartest story telling+game design around
As mentioned by others, the title is a reference to 999. But also, the message when completed correctly, says "YOU FOUND IT", which is the message shown by that game when you finished each of the puzzle escape-room-esque sections in it. Amazing (both the sudoku, and 999!)
For those who are interested, the title of the sudoku is a reference to a Visual Novel game called 9 Hours, 9 Persons, 9 Doors. It's about 9 people who were kidnapped and placed on a ship that will sink in 9 hours and their only way out is by finding the number 9 door. It's a cult-classic scifi/thriller/mystery story which they re-released on steam with voice-acting and updated visuals,, worth a look if it sounds cool to you, although it is very much scifi and a bit anime, so that might not be for everyone Update: "YOU FOUND IT" is a direct reference to the game yeah, the game consists of Novel/Dialogue parts and 'escape the room' parts, and if you find your way out of an escape-room that quote will pop up,, 'it' refering to the exit slash the solution
I would absolutely recommend this to everyone. It can get a little bit repetitive due to the way its structured, but its one of my favorite visual novels of all time.
@@SomethingWellesian honestly, l dont really know. There are some moments in the game that you have to solve little puzzles with numbered pins but l dont know if that's the intention behind the title because it feels a bit like a stretch. l think the creator of the puzzle just wanted to give the game a shout-out, maybe the pins just referred to the diagonal triplets in this puzzle and not really to anything in the game update: oh l'm now seeing a comment placed by the puzzle's creator,, he's saying that his puzzle is based on a sudoku variant called "9 pins", and he wanted to combine that with 9hours9persons9doors because that's his favorite piece of media,, so that's that
Simon dazzled me with his quick and elegant geometric analysis of the possible locations of the diagonal triples. His brilliant insights, and tenacity at getting "into" a problem (as well as his obvious joy in problem-solving), make it very clear to me (a PhD mathematician), that Simon was meant to be a "proper" mathematician. I would love to see him do some "real" mathematics. I'd advise him to take up some branch of math like combinatorics (which hasn't been already explored to death) and dive in. Please, SImon - the world of mathematics is awaiting your exciting contributions! (Maybe Full Deck, Missing a Few Cards, and other CTC-mathematicians can add their encouragement!!)
The symmetry I think comes with the territory, but yeah, I was thinking "check the ones by the bold lines, all the diagonals have to cross exactly a vertical and horizontal bold line to hit three different boxes" when he offhandedly mentioned that he was only looking at those middle edge squares, and yeah, of course! The vertical and horizontal jumps have to be offset, or you won't get three separate boxes. Absolutely right and a brilliant observation.
Rules: 01:56 Let's Get Cracking: 05:14 What about this video's Top Tier Simarkisms?! Three In the Corner: 4x (23:48, 23:51, 23:54, 24:00) Bobbins: 2x (21:46, 23:28) Maverick: 1x (04:21) You Rotten Thing: 1x (25:57) And how about this video's Simarkisms?! Beautiful: 4x (02:28, 17:45, 24:30, 26:58) In Fact: 4x (00:41, 00:53, 03:57, 12:53) Obviously: 4x (02:11, 08:22, 09:28, 11:52) Hang On: 3x (19:24, 21:28, 22:32) Ah: 3x (18:58, 19:21, 23:43) Symmetry: 3x (06:06, 07:05, 08:16) Lovely: 2x (27:37, 27:37) Brilliant: 2x (04:07, 04:20) Fascinating: 2x (02:10, 02:11) Approachable: 2x (02:27, 27:35) Whoopsie: 2x (08:51, 21:07) Pencil Mark/mark: 2x (15:52, 17:10) Cake!: 2x (03:55, 04:43) Good Grief: 1x (26:10) Useless: 1x (20:05) Sorry: 1x (12:41) Naked Single: 1x (24:13) Take a Bow: 1x (27:55) Our old Friend Sudoku: 1x (21:14) Come on Simon: 1x (20:01) By Sudoku: 1x (20:53) Shouting: 1x (04:39) Most popular number(>9), digit and colour this video: Ten (3 mentions) Nine (44 mentions) Green (8 mentions) Antithesis Battles: Even (3) - Odd (1) Black (2) - White (0) Row (8) - Column (5) 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!
22:35 for me. Normally I struggle to find the break-in, but it turned out with this one that as soon as I understood the rules and labelled the places where the diagonal sequences could go, things were far more restricted than I expected. A really clever idea and it was pleasant to see it all fall into place so quickly after the diagonals were done.
Very fun puzzle and video. I watched your intro, Simon, as I do no matter whether I will have time to watch the full video or not, because I love hearing the birthday greetings and (used to be) the patreon reward finishers. Then I thought I would try the puzzle, because I could think of a way to get started. I got quite a long way before deciding I needed to watch you solve it. Now that I have done so, I'll finish my own solve - in a few hours. Thanks so much for this video and for all of the fantastic stuff happening on this channel, Simon.
Another way to see candidate lines of 3 digits that are the same is to think of a tilted hash or pound mark around the vertices where 4 boxes join. There are 4 such spots in the grid.
Am i the only one who started shouting to Simon at 21:05 about the 2-9 pair in C7? I had the puzzle in just over 60 minutes. Not a world record time but still proud to finish it.
I was thinking clones (like somewhere else) in the grid. After seeing the beginning of video (I'm seeing it's 'one' "identical digit" in a run of three cells). No wonder you (and I) were confused lol 😂🤔👍🏻👍🏼
Here let me try and explain: At least one of each digit has the same digit diagonally next to the original digit on each side Ie: in this video in Row 4 column 6 there are 3 diagonal sevens adjacent to one another.
19:40, I personally didn’t use colors but out of the 2 sudokus I’ve done today, I beat Simon twice! He also explains every move to the audience, so I doubt I ACTUALLY did either faster than him, but it’s still impressive for me, someone who struggles to even start sudokus that are longer than 40 minutes on this channel.
A super fun puzzle to watch, but it's also given me a thought for when I next try a sudoku. Having each digit assigned a colour really helps the readability, might be a solid "accessibility" system
Speaking of 9 Hours, 9 Persons, 9 Doors, the game prominently features the concept of digital roots, which I think could make for an interesting sudoku ruleset (perhaps cages whose digits must have the given digital root), if it hasn't been done already.
8:34 for me, I very quickly realised that there were only 9 available 3 cells sequences, and filled them quite easily. The rest of the solve was probably GAS level, but I'm really proud of my time for once 😊
Yes, 9 hours, 9 persons, 9 doors - there there was an unique gimmick in each of the game in trilogy with regard who can go through the doors. In 999 that was the people had bracelets with different digits. Group could go if digital root of their digits was on the door. Digital root is fancy name for remainder modulo 9 (but remainder of 0 was called 9). There was a lot of spoilery shenanigans with numbers in the game, but in essence there was already a lot of good of puzzles on the channel exploring mod 9 mechanics.
l appreciate the Zero Escape reference with the sudoku-title, but the rules are kinda confusing to parse... l guess it means that for each row/column/box, for some string of 3 straight-lined adjacent digits, there must be another copy of that same string of straight-lined adjacent digits somewhere in the grid (possibly with a different orientation). Kinda hard to visualize though. _Update:_ watching the video l now realize that for each *individual* number there has to be a string of *the same* straight-lined adjacent digits,, like 333 or 888. Really wouldve appreciated just a simple "(eg 333, 777)",, that wouldve made it a lot clearer l feel :]
No, that’s what I thought at first too. It’s that each digit is found in a diagonal string of three somewhere in the puzzle. Edit: you got it while I was writing my comment😅
You missed the word "identical." The ruleset was unambiguous. The key words were: *identical,* *adjacent,* *in a straight line* That's it❗ There's no need to specify the line is oblique (i.e. the digits are "diagonally adjacent," as opposed to "orthogonally adjacent"). It can be deduced. There is no other way. 🤷♂
@@Paolo_De_Leva l think my actual mistake was misreading 'each number 1-9' as 'each numberS 1-9', which made it sound like everything after it applies to each set of 1-9 ie each row/column/box. Of course you cant ever have repeated digits in a row/column/box, so l thought the identical applied to a certain substring of each set of 1-9s in the puzzle. Of course now that l know what it means l can understand the wording, but you can see how it can be a bit confusing for a puzzle that's being presented as 'quite approachable'. I think it's a valid improvement to keep the explanation as is with just a simple appendage of "(eg. 222, 777)". Couldnt hurt, no?
@@Sponsie1000 An example would appear redundant to me. You misread "numbers" instead of "number." That's the problem to be fixed in my opinion. Sorry, I cannot see _"how it can be a bit confusing"_ when you read with sufficient attention.
@@Paolo_De_Leva l feel like you're misunderstanding me,, my point is not that it's too hard to understand/it's too confusing per se, l'm saying that if you're gonna have an approachable puzzle it cannot hurt to put in a small example to boost the approachability even further. This isnt about me or my reading of the rules, l'm saying that as a general principle. Maybe you value minimal redundancy really highly, but if one values approachability one shouldnt be opposed to including a small example just to make sure everyone's at the same page l feel. No harm no foul.
This is an incredibly beautiful puzzle. It wasn't too hard yet everytime I'd find something before Simon did, I'd still go "Aha! I did it!". I don't know if it was because of watching a lot of these videos, but I thoroughly enjoyed this puzzle and for the first time, I actually figured some things out on my own. I don't usually comment on these, but I really must say: props to Botaku for making this amazing puzzle and to Simon for solving this while I semi-figured things out hehe :>
I think all the confusion is coming from the word "adjacent" - In sudoku variant puzzles, that usually is interpreted to mean "orthogonally" I.E. same row or column. Remove the word adjacent, and add "e.g. 111 or 222" and it becomes perfectly clear.
You cannot remove the word adjacent. First you need to describe the rule, then you may give the example, if needed. In variant sudoku, the expression _"orthogonally adjacent cells"_ is used as opposed to _"diagonally adjacent cells."_ If you only use the adjective "adjacent," it means they are just next to each other, either orthogonally or diagonally.
German whisper lines often move diagonally, and have the usual wording "adjacent digits on a green line must differ by more than five". No reason "adjacent" has to mean orthogonally adjacent, unless stated.
@@RichSmith77 Right. For instance, yesterday's CTC video by Mark _("The Perfect Mix of Green and Purple")_ is full of diagonal *German whisper line* segments. (unfortunately, Google does not allow me to provide the link)
I have now tried 3 sudokus featured on ctc and everytime i work on them for about 2-3 hours (yes the approachable ones) and get very proud when i discover or realize a mechanic only to find that it breaks when i near the finish. This has happened to me all 3 times ive done sudokus. All. 3. Times. Im dumb :))))))))))))))
nice puzzle, and a very nice logical approach to the solve. very impressed. but wish you had stuck only to colours, eliminating those that couldnt work (thus easily having enough colours). those "arrow tips" were very confusing and made the grid messy
Very elegant puzzle. I nearly called shenanigans over the app timing, because I raced through this - no faffing around with colours, and the positions were mostly forced, so I didn't waste time trying to mark where they went, yet I still ended up a minute slower than you. Then I realised I'd got a drink and fixed my supper after loading it, and had forgotten to restart when I returned.
First time doing something like this, so it took me a while (55 minutes). The thing that gave it away for me was the 2, 3, and 4 in rows 3 and 4, because they removed a few possible spots to place the triple same-digit lines. And wouldn't you know it, there were only 9 remaining spots to place those lines, perfect as the puzzle required doing it (at least) once for 1 to 9. Beautiful!!! EDIT: Just watched Simon's solve. We concluded the same thing!!! (though he started with triple 8s and 7s, and for some ungodly reason I started with the triple 4s)
I assumed I couldn’t do it so I just messed around shoving triples anywhere… then when it broke my brain finally kicked in. Restarted and got it in 33:53 🎉
13:04 for me. I saw this kind of puzzle on the channel a while back. Once you know where the triples can go, there are far too many given digits. Still, not a bad puzzle to revisit this ruleset.
A lovely puzzle. I didn't understood that there had to be straight line of adjacent same-digit cells /for each digit/ so at first I was like ??? But very much enjoyed Simon's solve.
25:15 - "Have we got any easy wins?" Simon wonders just after having put a nine in r4c1 and an eight-nine pair in r3c1 just above it. Although the very idea of doing sudoku in a sudoku puzzle is frankly preposterous. :P
30 minutes (once I saw what the rules were). Each of Simon's possibilities has to be one of each (I don't know why he didn't say that - and get rid of that non-possibility line up top). [[Edit: if he had done that -- he would have seen there were only 9 possibilities counting them - and been able to continue]] 30 mins, though. Nice one.
15:10 was my time (conflict checker off), but I will admit I had to bifurcate once (which ended up being the wrong path, so needed to back up). Still a really cool puzzle!
I’d say this was nice and easy, but I managed to make two false starts before I really got the logical principle solid enough to show the option I was overlooking. 41:31. It’s a really nice principle, though.
After you solve the puzzle, double-click the 3s and change them all to 0. Then double-click the 4s and change them to 3s and you get two parties in the corner at the same time.
I'm surprised you didn't notice that you could have taken out a good part of the top squares at 25:03 You had "possible 8 or 9" in r3c1, with a 9 on r4c1 You would then put 9 on r3c9, 8 on r5c2 r9c3 and r1c9, 2 on r5c1 and r4c9, 4 on r4c7, and so on Otherwise, a very nice puzzle and solution, good job!
How I solved this! To find out where the 2/9 triples are, consider the R5C6,R4C5,R3C6 triple diagonal. If that was 9, then where does 9 go in box 4? that Eliminates 9 from R3C6, so it is a 3. This allows you to solve a bunch of sudokus.
31:50 for me -- watching Simon's solve I can see how I could have shaved off some time early on. Coloring with too many different colors throws off my scanning, so was trying to limit that ... but might've helped me in this case.
Rules at 1:55! Even though rules and puzzle start are the most important marks in these videos, I guess the mark got lost somewhere in the editing. At least the birthday presentations mark, of people I didn't know exist and will never meet is there. Awesome!
36:03 for me this time around. I went about it a different way than I think I did before, since I used much more logical and provable inferences. But I didn't save as much time as I'd expected.
For those confused and dont want to watch the video first...picture the solution to Knights move variant....these line strings are abundant in that variant
69:10 I got hung up on the 29 pairs in the bottom right and missed the "A" deduction that Simon got, instead waffling over a 29 pair in column 7 that eliminated 9 from r4c7 for about 20 minutes.
I've definitely considered trying to get that petition going, but I'm afraid that there is a fair amount of blood and violence which would be a tough sell for a channel as wholesome and family-friendly as Cracking the Cryptic. It's also quite a bit longer than anything else they've played, as far as I know. Moreover, [SPOILERS FOR 999 BELOW!] the final puzzle is a sudoku only in the DS version, the remaster replaced it with a completely different puzzle that is in equal parts inane and obtuse. So you'd have the extra deliberation of whether you want Simon and Mark to have an easier time (and not be accused of piracy) by playing the remaster, or whether you want them to experience the story and the finale in its full glory but have them go through the extra hassle of either getting a DS or an emulator and setting up screen capture for it.
It took me considerably longer than the video, 75:22 to be exact, but I finally broke the code. The concept was fairly easy to work out, but deducing the exact layout was considerably harder for me. Solve #7212. And come to think of it, I stopped halfway and got some sleep before finishing, so it probably did take me somewhere in the area of nine hours to do.
It took me way too long to realize that the 16 3-cell sequences only allowed for 9 total, so I wasn't able to get the 8 and the seven so easily. Simon didn't notice that the three cell sequences can only happen at corner intersections, which was the other way of quickly drawing all 16 lines.
It allows for 10 total, but one of them is ruled out by givens. The fact it allows for 10 total means you could have the same restriction for each digit, but use the digits 0-9 and include schrodinger cells.
Simon, I don't know if you have some alternate color scheme, but why don't you use the colors corresponding to the numbers? You have 3s marked with 4's color (green) and 4s marked with 9's color (blue). All of the color keyboard shortcuts are their numbers on the keypad, so if you highlight the 8s and press 8, it will color them yellow, but you've colored the 7s as yellow, and 7's color is red.
That's quite a weird interpretation. Most people know that a straight line can have any possible orientation in 2D space. Horizontal, vertical, oblique.
Very strange and simplistic rule set(esp if u enjoy Knight move rule)....wonder if the methodoloy of this variant allows you to cheat at Knights move variant. strangely even if u break open this puzzle you can get stuck on a 2nd stage while trying to race the vsimon. Fun puzzle
So, at 28:30,... why is the sequence of 1s set? What gives away that the two lines in the South-East can not in fact also be sequences of 1s? Was this an oversight and luck, or am I missing something?
I'm obviously feeling a little slow today, but at 12:30 when Simon deduces that the 8's go on "red", could they not have gone on "orange"? I know he deduces later on, that the outside colors needed to be 3,5 & 6, but he hadn't got to that stage yet.
@@djyarnsworth No. The reds have the oppotunity to be the same digit, its not a given. There are 16 chances to fill 9 triplets. I posted a comment, I think he accidentally lucked out on the 7s and 8s because they had a bunch of other spots where they could have gone.
That's exactly where I am confused, and I looked in the comments for validation. The rules state that the sequence can be somewhere in the grid, but the fact that the 7 in r5c7 falls in a possible sequence doesn't mean that has to be its sequence, as 7s are also possible in r6c5/r7c4/r8c3 at this stage of his solving. Others have commented that only 9 of the 16 three-digit sequences are possible, but I must be missing something because I cannot see that yet.
I concluded correctly to use the line tool but entered all the possible lines. Then unfortunately got hung up on the rule stating at "least" one set of each digit. ie there could be more. Watching Simon do the solve had me asking why has he dismissed that possibility and of course asking myself why did I accept it as the only possible one?
Simon did explain why only 3 of his arrows would work, 4 of the outside colors, and so he needed 2 (not 1) on the inside colors to obtain 9 triples. I got hung up on "at least" too, but didn't immediately see the constraints that he explained which gave a max of 9 options.
Thank you ever so much for the feature, Simon, and glad to be back on the channel!! If memory serves, my latest appearance was a Patreon exclusive roughly 1.5 years ago, so yeah, it's been a while 😄
The title is indeed a reference to Nine Hours, Nine Persons, Nine Doors. It's my absolute favourite piece of media of all time, my profile picture comes from there and in a way, even my username is an oblique reference to it. So when I was setting a variant called Nine Pins sudoku, I absolutely could not resist the temptation 😁(Also, very astute of you, "YOU FOUND IT" is indeed the message you get in the game after you've solved each escape room!)
As for the puzzle, the geometric approach was very much the intended one indeed 🤩 When writing up the solution guide, I did realise that you can get the triples for 3s, 4s, 5s, 6s, 7s and 8s solely by considering where each of them could go in a very particular order, which is an approach one would normally take with a Nine Pins sudoku but one that hardly seems inspired to me. So I'm tremendously glad that not only did you think of the geometric approach, but you did so by harkening back to my previous features 😂
Once again, many thanks for the solve, it really made my day 😄
P.S. I see considerable confusion about the rules in the comments. Frankly, this is somewhat justified; I was inspired to give the variant a try after it was featured in a Sudoku Grand Prix round recently and I believe I grabbed the statement of the rules from there. Even though they seemed kind of unclearly worded to me as well, I expected there was some merit to them that I failed to appreciate 🤔
Lovely puzzle (even if I was in the list of people confused by the rules at first). I’m afraid I solved it in the “uninspired” way, though it was nice to see Simon’s method after.
It’s a cool ruleset. I like how the digits kind of cordon themselves off from appearing in certain diagonals.
I like even more the (first) sequel, Virtue’s Last Reward. But love the whole series. Just played Head as Code and Birth ME Code, two small games made very much following the style of 999. Good enough to scratch the itch of not having more 999 to play!
Beautiful geometry 👏👏👏. The rules were unambibuous. The confusion about them was due to people not reading with attention, particularly these words:
*identical,*
*adjacent,*
*in a straight line*
That's it❗ There's no need to specify the line is oblique (i.e. the digits are "diagonally adjacent," as opposed to "orthogonally adjacent"). It can be deduced. There is no other way. 🤷♂
By the way, you also need to deduce that the three identical digits must be across three boxes 🤷♂
Nice puzzle, I enjoyed it a lot. Took me one hour thirty seconds
@@Paolo_De_Leva thing is, 'adjacent' almost always refers to orthogonally adjacent in these puzzles. 'Diagonally adjacent' sounds weird - I certainly wouldn't use the word adjacent for that sort of relation.
I did it! This is the first time I’ve solved a puzzle featured on the channel!
It took me just under 40 minutes, and I didn’t do it Simon’s clever way, but I actually solved a puzzle featured on the Cracking The Cryptic UA-cam channel!
Towards the end of the puzzle, my hands were actually shaking. Awesome puzzle! Very fun!
I would recommend the chinese coin puzzle to you. It's one of my favourite puzzles, because it's in a similar difficulty level as this one (it has 2 spots that are tricky, the rest is straight forward) and the best thing is, it's easy to remember and to be drawn by hand from memory. It's a little harder on paper brcause you need pencil marks, but also possible. If you are interested you can find it in this channel under "chinese coin".
Congrats to your solve! This puzzle took me 50 minutes, but I'm ok with it.
Well done! 😁
@@Gsudi Thanks, I’ll check it out!
You are amazing! It took me 2 hours, but I solved it. This is like the 3rd time now I managed to solve a puzzle from here but significantly slower. I found this channel a week ago, so plenty of room and time to improve I guess. :D
I didn't even properly understand the rules
3 years ago: Only 4 digits in Sudoku? That can't be solvable!
Now: 10 digits in Sudoku? How generous!
9 hours 9 persons 9 doors (also called 999 for short) is a sci-fi/mystery visual novel featuring many "escape room puzzles" originally on the nintendo DS, but it was later rereleased with voice acting on steam
I loved the nonary games
Spike chunsoft bless 🙏
And the steam version is pretty awful. If you can find it reasonably priced on DS, it's worth playing on it's original hardware.
It was made to be played on it, and it uses the hardware for story telling purposes. It's actually some of the smartest story telling+game design around
And it's good
I loved that game a few years ago
I should play the other games
For absolutely no reason at all, I now want to see Mark and Simon play an escape room and then be placed in a prisoner's dilemma against each other.
They would keep shut, because it's the moral thing to do.
They have played an escape room in one of their streams! It was fun :)
As mentioned by others, the title is a reference to 999. But also, the message when completed correctly, says "YOU FOUND IT", which is the message shown by that game when you finished each of the puzzle escape-room-esque sections in it. Amazing (both the sudoku, and 999!)
Simon and Mark should play 999, it's an amazing puzzle mystery game where the entire game itself is also a puzzle!
I am so happy, this was the first "Cracking the Cryptic" puzzle I was able to solve without any hints!!! Only took me 90 minutes, but I got it!
For those who are interested, the title of the sudoku is a reference to a Visual Novel game called 9 Hours, 9 Persons, 9 Doors. It's about 9 people who were kidnapped and placed on a ship that will sink in 9 hours and their only way out is by finding the number 9 door. It's a cult-classic scifi/thriller/mystery story which they re-released on steam with voice-acting and updated visuals,, worth a look if it sounds cool to you, although it is very much scifi and a bit anime, so that might not be for everyone
Update: "YOU FOUND IT" is a direct reference to the game yeah, the game consists of Novel/Dialogue parts and 'escape the room' parts, and if you find your way out of an escape-room that quote will pop up,, 'it' refering to the exit slash the solution
I would absolutely recommend this to everyone. It can get a little bit repetitive due to the way its structured, but its one of my favorite visual novels of all time.
What are the pins?
@@SomethingWellesian honestly, l dont really know. There are some moments in the game that you have to solve little puzzles with numbered pins but l dont know if that's the intention behind the title because it feels a bit like a stretch.
l think the creator of the puzzle just wanted to give the game a shout-out, maybe the pins just referred to the diagonal triplets in this puzzle and not really to anything in the game
update: oh l'm now seeing a comment placed by the puzzle's creator,, he's saying that his puzzle is based on a sudoku variant called "9 pins", and he wanted to combine that with 9hours9persons9doors because that's his favorite piece of media,, so that's that
I played this game on the DS and it was amazing.
I'd also recommend Hotel Dusk Room 215 and its sequel, The Secret of Cape West. Very awesome puzzle games.
Simon dazzled me with his quick and elegant geometric analysis of the possible locations of the diagonal triples. His brilliant insights, and tenacity at getting "into" a problem (as well as his obvious joy in problem-solving), make it very clear to me (a PhD mathematician), that Simon was meant to be a "proper" mathematician. I would love to see him do some "real" mathematics. I'd advise him to take up some branch of math like combinatorics (which hasn't been already explored to death) and dive in. Please, SImon - the world of mathematics is awaiting your exciting contributions! (Maybe Full Deck, Missing a Few Cards, and other CTC-mathematicians can add their encouragement!!)
I agree! I have suspected for some time now that Simon has some sort of mathematics background, but maybe I am wrogn
He would be a joy to watch in graph theory!
The symmetry I think comes with the territory, but yeah, I was thinking "check the ones by the bold lines, all the diagonals have to cross exactly a vertical and horizontal bold line to hit three different boxes" when he offhandedly mentioned that he was only looking at those middle edge squares, and yeah, of course! The vertical and horizontal jumps have to be offset, or you won't get three separate boxes. Absolutely right and a brilliant observation.
Once I got my head around the rules, this was a lovely easy solve. 18:59, my first time beating a video time.
Rules: 01:56
Let's Get Cracking: 05:14
What about this video's Top Tier Simarkisms?!
Three In the Corner: 4x (23:48, 23:51, 23:54, 24:00)
Bobbins: 2x (21:46, 23:28)
Maverick: 1x (04:21)
You Rotten Thing: 1x (25:57)
And how about this video's Simarkisms?!
Beautiful: 4x (02:28, 17:45, 24:30, 26:58)
In Fact: 4x (00:41, 00:53, 03:57, 12:53)
Obviously: 4x (02:11, 08:22, 09:28, 11:52)
Hang On: 3x (19:24, 21:28, 22:32)
Ah: 3x (18:58, 19:21, 23:43)
Symmetry: 3x (06:06, 07:05, 08:16)
Lovely: 2x (27:37, 27:37)
Brilliant: 2x (04:07, 04:20)
Fascinating: 2x (02:10, 02:11)
Approachable: 2x (02:27, 27:35)
Whoopsie: 2x (08:51, 21:07)
Pencil Mark/mark: 2x (15:52, 17:10)
Cake!: 2x (03:55, 04:43)
Good Grief: 1x (26:10)
Useless: 1x (20:05)
Sorry: 1x (12:41)
Naked Single: 1x (24:13)
Take a Bow: 1x (27:55)
Our old Friend Sudoku: 1x (21:14)
Come on Simon: 1x (20:01)
By Sudoku: 1x (20:53)
Shouting: 1x (04:39)
Most popular number(>9), digit and colour this video:
Ten (3 mentions)
Nine (44 mentions)
Green (8 mentions)
Antithesis Battles:
Even (3) - Odd (1)
Black (2) - White (0)
Row (8) - Column (5)
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!
How the hell did you comment that, this video was posted 10 minutes ago
@masnyklaus9896 this is commented by program
Stopped the video to solve the puzzle - lovely logic - and once again admiring Simon's efficiency at uncovering and explaining things.
22:35 for me. Normally I struggle to find the break-in, but it turned out with this one that as soon as I understood the rules and labelled the places where the diagonal sequences could go, things were far more restricted than I expected. A really clever idea and it was pleasant to see it all fall into place so quickly after the diagonals were done.
Very fun puzzle and video. I watched your intro, Simon, as I do no matter whether I will have time to watch the full video or not, because I love hearing the birthday greetings and (used to be) the patreon reward finishers. Then I thought I would try the puzzle, because I could think of a way to get started. I got quite a long way before deciding I needed to watch you solve it. Now that I have done so, I'll finish my own solve - in a few hours. Thanks so much for this video and for all of the fantastic stuff happening on this channel, Simon.
Continually love your writing Emily!!
Another way to see candidate lines of 3 digits that are the same is to think of a tilted hash or pound mark around the vertices where 4 boxes join. There are 4 such spots in the grid.
What a great puzzle! Just needed Simon to identify the process to start the solve. This one really made you think. Thanks!
Am i the only one who started shouting to Simon at 21:05 about the 2-9 pair in C7? I had the puzzle in just over 60 minutes. Not a world record time but still proud to finish it.
Somehow his sudoku scanning is getting worse Oo :)
My time: 26:44. I love how this ruleset yields its lemmas, and the puzzle is well-constructed to showcase that
Finally I solved a puzzle on this channel without any help.
It took me 00:38:07.
I have really improved my skills watching his videos.
What a stunning concept - lovely solve too!
Read the rules 5 times...can't make heads or tails of it. I hope Simon can translate it for me.
Same
Ditto.
Yep. And now it's like we have to hunt for his rule set explanation which is now 'puzzle intro' (?).
I was thinking clones (like somewhere else) in the grid.
After seeing the beginning of video (I'm seeing it's 'one' "identical digit" in a run of three cells).
No wonder you (and I) were confused lol 😂🤔👍🏻👍🏼
Here let me try and explain:
At least one of each digit has the same digit diagonally next to the original digit on each side
Ie: in this video in Row 4 column 6 there are 3 diagonal sevens adjacent to one another.
I love the long videos, but good to see a short but clever one.
19:40, I personally didn’t use colors but out of the 2 sudokus I’ve done today, I beat Simon twice! He also explains every move to the audience, so I doubt I ACTUALLY did either faster than him, but it’s still impressive for me, someone who struggles to even start sudokus that are longer than 40 minutes on this channel.
A super fun puzzle to watch, but it's also given me a thought for when I next try a sudoku. Having each digit assigned a colour really helps the readability, might be a solid "accessibility" system
R3c7 was a 4 (pencil marked 249) because of the 29 pair in the column for the longest time. But Simon found the long way!
Omg the game this is named after is EXCELLENT! I love that I knew the reference for once
(21:41) Fabulous break-in, dealing with 2s and 9s was really pleasant in the mid- to late-puzzle. Lovely feature!
Speaking of 9 Hours, 9 Persons, 9 Doors, the game prominently features the concept of digital roots, which I think could make for an interesting sudoku ruleset (perhaps cages whose digits must have the given digital root), if it hasn't been done already.
8:34 for me, I very quickly realised that there were only 9 available 3 cells sequences, and filled them quite easily. The rest of the solve was probably GAS level, but I'm really proud of my time for once 😊
I'm relieved to see that I've interpreted the rules the same way as Simon. Hopefully that means I've interpreted them correctly.
Yes, 9 hours, 9 persons, 9 doors - there there was an unique gimmick in each of the game in trilogy with regard who can go through the doors.
In 999 that was the people had bracelets with different digits. Group could go if digital root of their digits was on the door. Digital root is fancy name for remainder modulo 9 (but remainder of 0 was called 9).
There was a lot of spoilery shenanigans with numbers in the game, but in essence there was already a lot of good of puzzles on the channel exploring mod 9 mechanics.
"I don't think I need to do the rules again" - errm yeah I was confused by what the rules meant... An example would be nice...
I enjoyed watching you figure that puzzle out!
l appreciate the Zero Escape reference with the sudoku-title, but the rules are kinda confusing to parse... l guess it means that for each row/column/box, for some string of 3 straight-lined adjacent digits, there must be another copy of that same string of straight-lined adjacent digits somewhere in the grid (possibly with a different orientation). Kinda hard to visualize though.
_Update:_ watching the video l now realize that for each *individual* number there has to be a string of *the same* straight-lined adjacent digits,, like 333 or 888. Really wouldve appreciated just a simple "(eg 333, 777)",, that wouldve made it a lot clearer l feel :]
No, that’s what I thought at first too. It’s that each digit is found in a diagonal string of three somewhere in the puzzle.
Edit: you got it while I was writing my comment😅
You missed the word "identical." The ruleset was unambiguous. The key words were:
*identical,*
*adjacent,*
*in a straight line*
That's it❗ There's no need to specify the line is oblique (i.e. the digits are "diagonally adjacent," as opposed to "orthogonally adjacent"). It can be deduced. There is no other way. 🤷♂
@@Paolo_De_Leva l think my actual mistake was misreading 'each number 1-9' as 'each numberS 1-9', which made it sound like everything after it applies to each set of 1-9 ie each row/column/box. Of course you cant ever have repeated digits in a row/column/box, so l thought the identical applied to a certain substring of each set of 1-9s in the puzzle.
Of course now that l know what it means l can understand the wording, but you can see how it can be a bit confusing for a puzzle that's being presented as 'quite approachable'. I think it's a valid improvement to keep the explanation as is with just a simple appendage of "(eg. 222, 777)". Couldnt hurt, no?
@@Sponsie1000 An example would appear redundant to me. You misread "numbers" instead of "number." That's the problem to be fixed in my opinion.
Sorry, I cannot see _"how it can be a bit confusing"_ when you read with sufficient attention.
@@Paolo_De_Leva l feel like you're misunderstanding me,, my point is not that it's too hard to understand/it's too confusing per se, l'm saying that if you're gonna have an approachable puzzle it cannot hurt to put in a small example to boost the approachability even further. This isnt about me or my reading of the rules, l'm saying that as a general principle.
Maybe you value minimal redundancy really highly, but if one values approachability one shouldnt be opposed to including a small example just to make sure everyone's at the same page l feel. No harm no foul.
This is an incredibly beautiful puzzle. It wasn't too hard yet everytime I'd find something before Simon did, I'd still go "Aha! I did it!". I don't know if it was because of watching a lot of these videos, but I thoroughly enjoyed this puzzle and for the first time, I actually figured some things out on my own. I don't usually comment on these, but I really must say: props to Botaku for making this amazing puzzle and to Simon for solving this while I semi-figured things out hehe :>
I think all the confusion is coming from the word "adjacent" - In sudoku variant puzzles, that usually is interpreted to mean "orthogonally" I.E. same row or column. Remove the word adjacent, and add "e.g. 111 or 222" and it becomes perfectly clear.
You cannot remove the word adjacent. First you need to describe the rule, then you may give the example, if needed.
In variant sudoku, the expression _"orthogonally adjacent cells"_ is used as opposed to _"diagonally adjacent cells."_
If you only use the adjective "adjacent," it means they are just next to each other, either orthogonally or diagonally.
German whisper lines often move diagonally, and have the usual wording "adjacent digits on a green line must differ by more than five". No reason "adjacent" has to mean orthogonally adjacent, unless stated.
@@RichSmith77 Right. For instance, yesterday's CTC video by Mark _("The Perfect Mix of Green and Purple")_ is full of diagonal *German whisper line* segments. (unfortunately, Google does not allow me to provide the link)
ua-cam.com/video/Hh62HAmFZAc/v-deo.html
@@RichSmith77 fair point! I stand corrected.
Extremely fun and satisfying to solve! 48:28
40:42. Feel like I made hard work of this. Time to watch Simon's solve to see what I missed!
I have now tried 3 sudokus featured on ctc and everytime i work on them for about 2-3 hours (yes the approachable ones) and get very proud when i discover or realize a mechanic only to find that it breaks when i near the finish. This has happened to me all 3 times ive done sudokus. All. 3. Times.
Im dumb :))))))))))))))
nice puzzle, and a very nice logical approach to the solve. very impressed. but wish you had stuck only to colours, eliminating those that couldnt work (thus easily having enough colours). those "arrow tips" were very confusing and made the grid messy
I was solver #2967 -- it seems this is already a very popular puzzle, and rightfully so! My time was 16:59.
Got it in 16:14 and was the 37th person to solve it in this software. Short, sweet and fun puzzle.
Very elegant puzzle. I nearly called shenanigans over the app timing, because I raced through this - no faffing around with colours, and the positions were mostly forced, so I didn't waste time trying to mark where they went, yet I still ended up a minute slower than you. Then I realised I'd got a drink and fixed my supper after loading it, and had forgotten to restart when I returned.
I missed this when it first posted, fun and beautiful puzzle, took me only 10 mins ...once I solved the break in "3in-A-row" digits😊
22:51 Saw the logic right away then it was just keeping track of everything. Very rare for me to solve with no help from the video!
Solve counter 137
Nice idea. Reminds me of one of my puzzles that was tackled by Mark a couple of years back: Ten Triples.
Thank you for the rules update. I read the original wording five times and didn't even begin to understand what it's supposed to mean.
First time doing something like this, so it took me a while (55 minutes). The thing that gave it away for me was the 2, 3, and 4 in rows 3 and 4, because they removed a few possible spots to place the triple same-digit lines. And wouldn't you know it, there were only 9 remaining spots to place those lines, perfect as the puzzle required doing it (at least) once for 1 to 9. Beautiful!!!
EDIT: Just watched Simon's solve. We concluded the same thing!!! (though he started with triple 8s and 7s, and for some ungodly reason I started with the triple 4s)
I just solved it in about 90 minutes 😅
And now I watch how a pro does it 👍🏻
Well basically I did the same conclusions but waaaayyyyyy slower 😂
I assumed I couldn’t do it so I just messed around shoving triples anywhere… then when it broke my brain finally kicked in. Restarted and got it in 33:53 🎉
19:45 for me. I'm pretty sure I overcomplicated this one a lot, but I don't quite know how exactly. Time to watch the video!!
After letting Simon interpret the rules for me, I was able to get going and finished it in a reasonable time, only 35m.
13:04 for me. I saw this kind of puzzle on the channel a while back. Once you know where the triples can go, there are far too many given digits. Still, not a bad puzzle to revisit this ruleset.
~31mins for me. Very approachable. cool stuff ❤
A lovely puzzle. I didn't understood that there had to be straight line of adjacent same-digit cells /for each digit/ so at first I was like ??? But very much enjoyed Simon's solve.
25:15 - "Have we got any easy wins?" Simon wonders just after having put a nine in r4c1 and an eight-nine pair in r3c1 just above it. Although the very idea of doing sudoku in a sudoku puzzle is frankly preposterous. :P
One of the first puzzles I ever completed from the channel had this same ruleset! "Catching Criminals with Sudoku", November 11th 2020!
26:58 ... two more seconds and my time would have been exactly '9 x rt(9)' minutes
A most interesting puzzle!
100 minutes for me. It was tough, but still pleased that I solved it!
18:41 for me! Great puzzle!
17:32 for me. Nice little puzzle once you work out where the lines can go. 👍🏻
30 minutes (once I saw what the rules were).
Each of Simon's possibilities has to be one of each (I don't know why he didn't say that - and get rid of that non-possibility line up top).
[[Edit: if he had done that -- he would have seen there were only 9 possibilities counting them - and been able to continue]]
30 mins, though.
Nice one.
15:10 was my time (conflict checker off), but I will admit I had to bifurcate once (which ended up being the wrong path, so needed to back up). Still a really cool puzzle!
I’d say this was nice and easy, but I managed to make two false starts before I really got the logical principle solid enough to show the option I was overlooking. 41:31. It’s a really nice principle, though.
After you solve the puzzle, double-click the 3s and change them all to 0. Then double-click the 4s and change them to 3s and you get two parties in the corner at the same time.
What a beautiful and funny puzzle.
I'm surprised you didn't notice that you could have taken out a good part of the top squares at 25:03
You had "possible 8 or 9" in r3c1, with a 9 on r4c1
You would then put 9 on r3c9, 8 on r5c2 r9c3 and r1c9, 2 on r5c1 and r4c9, 4 on r4c7, and so on
Otherwise, a very nice puzzle and solution, good job!
I FOUND IT. Seeing the geometry was easy for me, but then I went more by instinct rather than deduction. However, my instincts were correct.
How I solved this! To find out where the 2/9 triples are, consider the R5C6,R4C5,R3C6 triple diagonal. If that was 9, then where does 9 go in box 4? that Eliminates 9 from R3C6, so it is a 3. This allows you to solve a bunch of sudokus.
31:50 for me -- watching Simon's solve I can see how I could have shaved off some time early on. Coloring with too many different colors throws off my scanning, so was trying to limit that ... but might've helped me in this case.
My first complete solve, without hints, in under 100 minutes 🎉🎉
Rules at 1:55! Even though rules and puzzle start are the most important marks in these videos, I guess the mark got lost somewhere in the editing. At least the birthday presentations mark, of people I didn't know exist and will never meet is there. Awesome!
41:35 for me, that became a bit tougher at a point, when I had to prove some inferences I wasn't ready to feel confident on.
36:03 for me this time around. I went about it a different way than I think I did before, since I used much more logical and provable inferences. But I didn't save as much time as I'd expected.
Such an easy puzzle
For those confused and dont want to watch the video first...picture the solution to Knights move variant....these line strings are abundant in that variant
Not too tricky but a lot of fun. Just under 20 minutes for me.
Absolutely NO IDEA! Well done everyone for getting the puzzle....but , narrrrrgh, not for me😏😏 I need at least 25 numbers to start with! lol .....
69:10 I got hung up on the 29 pairs in the bottom right and missed the "A" deduction that Simon got, instead waffling over a 29 pair in column 7 that eliminated 9 from r4c7 for about 20 minutes.
I really think that Simon and Mark should play through at least the first game of the series. They should get a kick out of the final puzzle.
I've definitely considered trying to get that petition going, but I'm afraid that there is a fair amount of blood and violence which would be a tough sell for a channel as wholesome and family-friendly as Cracking the Cryptic. It's also quite a bit longer than anything else they've played, as far as I know. Moreover, [SPOILERS FOR 999 BELOW!]
the final puzzle is a sudoku only in the DS version, the remaster replaced it with a completely different puzzle that is in equal parts inane and obtuse. So you'd have the extra deliberation of whether you want Simon and Mark to have an easier time (and not be accused of piracy) by playing the remaster, or whether you want them to experience the story and the finale in its full glory but have them go through the extra hassle of either getting a DS or an emulator and setting up screen capture for it.
@@botaku12721 harsh...
It took me considerably longer than the video, 75:22 to be exact, but I finally broke the code. The concept was fairly easy to work out, but deducing the exact layout was considerably harder for me. Solve #7212.
And come to think of it, I stopped halfway and got some sleep before finishing, so it probably did take me somewhere in the area of nine hours to do.
21.35 for me, happy to get the logic straight away
It took me way too long to realize that the 16 3-cell sequences only allowed for 9 total, so I wasn't able to get the 8 and the seven so easily. Simon didn't notice that the three cell sequences can only happen at corner intersections, which was the other way of quickly drawing all 16 lines.
It allows for 10 total, but one of them is ruled out by givens. The fact it allows for 10 total means you could have the same restriction for each digit, but use the digits 0-9 and include schrodinger cells.
Simon, I don't know if you have some alternate color scheme, but why don't you use the colors corresponding to the numbers? You have 3s marked with 4's color (green) and 4s marked with 9's color (blue). All of the color keyboard shortcuts are their numbers on the keypad, so if you highlight the 8s and press 8, it will color them yellow, but you've colored the 7s as yellow, and 7's color is red.
great and simple!
When people usually hear about straight lines, especially when you mention them, they think about rows and columns, not diagonals.
That's quite a weird interpretation. Most people know that a straight line can have any possible orientation in 2D space. Horizontal, vertical, oblique.
67:34 for me, completely unaided by Simon!
21:36 for me. Lovely puzzle!
Very strange and simplistic rule set(esp if u enjoy Knight move rule)....wonder if the methodoloy of this variant allows you to cheat at Knights move variant.
strangely even if u break open this puzzle you can get stuck on a 2nd stage while trying to race the vsimon.
Fun puzzle
42:14 for me. nasty puzzle- very lovely!
I love it when Simon colors the whole grid.
31:55 for me. No idea if I solved it the "right way" (haven't watched the vid yet) but a solve is a solve.
So, at 28:30,... why is the sequence of 1s set? What gives away that the two lines in the South-East can not in fact also be sequences of 1s? Was this an oversight and luck, or am I missing something?
The nintendo game was a really fun mystery point and click style game
It was a great puzzle. I only understood the rules because our great gas setter Bill gave us one of this kind recently.
Found it!!!!! 30:53
32:43 for me. Solve no. 777 😎
❤❤❤this one!!!
As usual...it 🧡🩷❤️💛s you..😀
@@davidrattner9 ❤️
Are you guys going to expand the sudoku pad to Mac OS as well at some point?
I'm obviously feeling a little slow today, but at 12:30 when Simon deduces that the 8's go on "red", could they not have gone on "orange"? I know he deduces later on, that the outside colors needed to be 3,5 & 6, but he hadn't got to that stage yet.
The reds are all the same digit. And 8 is in a red box, so reds are 8.
@@djyarnsworth No. The reds have the oppotunity to be the same digit, its not a given. There are 16 chances to fill 9 triplets. I posted a comment, I think he accidentally lucked out on the 7s and 8s because they had a bunch of other spots where they could have gone.
That's exactly where I am confused, and I looked in the comments for validation. The rules state that the sequence can be somewhere in the grid, but the fact that the 7 in r5c7 falls in a possible sequence doesn't mean that has to be its sequence, as 7s are also possible in r6c5/r7c4/r8c3 at this stage of his solving. Others have commented that only 9 of the 16 three-digit sequences are possible, but I must be missing something because I cannot see that yet.
I concluded correctly to use the line tool but entered all the possible lines. Then unfortunately got hung up on the rule stating at "least" one set of each digit. ie there could be more.
Watching Simon do the solve had me asking why has he dismissed that possibility and of course asking myself why did I accept it as the only possible one?
Simon did explain why only 3 of his arrows would work, 4 of the outside colors, and so he needed 2 (not 1) on the inside colors to obtain 9 triples. I got hung up on "at least" too, but didn't immediately see the constraints that he explained which gave a max of 9 options.