What Is The Most Complicated Lock Pattern?

A journey through patterns, logic and intuition with a mad patternologist.
An entry to #SoME1.
● 𝗔𝗱𝗱𝗶𝘁𝗶𝗼𝗻𝗮𝗹 𝗰𝗼𝗻𝘁𝗲𝗻𝘁
· Python code that counts max-complexity patterns:
github.com/zz-zye/patterns
· Full process of finding all max-complexity patterns in a 3×3 grid:
drive.google.com/drive/folder...
● 𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲
· 3Blue1Brown, 𝘞𝘩𝘺 𝘪𝘴 𝘱𝘪 𝘩𝘦𝘳𝘦? 𝘈𝘯𝘥 𝘸𝘩𝘺 𝘪𝘴 𝘪𝘵 𝘴𝘲𝘶𝘢𝘳𝘦𝘥? 𝘈 𝘨𝘦𝘰𝘮𝘦𝘵𝘳𝘪𝘤 𝘢𝘯𝘴𝘸𝘦𝘳 𝘵𝘰 𝘵𝘩𝘦 𝘉𝘢𝘴𝘦𝘭 𝘱𝘳𝘰𝘣𝘭𝘦𝘮,
• Why is pi here? And w...
· Mathologer, 𝘌𝘶𝘭𝘦𝘳’𝘴 𝘗𝘪 𝘗𝘳𝘪𝘮𝘦 𝘗𝘳𝘰𝘥𝘶𝘤𝘵 𝘢𝘯𝘥 𝘙𝘪𝘦𝘮𝘢𝘯𝘯’𝘴 𝘡𝘦𝘵𝘢 𝘍𝘶𝘯𝘤𝘵𝘪𝘰𝘯,
• Euler’s Pi Prime Produ...
· Paulo Coelho, 𝘛𝘩𝘦 𝘈𝘭𝘤𝘩𝘦𝘮𝘪𝘴𝘵
· Zoltan Puskas(sinustrom), 𝘈𝘯𝘥𝘳𝘰𝘪𝘥 𝘶𝘯𝘭𝘰𝘤𝘬 𝘱𝘢𝘵𝘵𝘦𝘳𝘯 𝘴𝘦𝘤𝘶𝘳𝘪𝘵𝘺 𝘢𝘯𝘢𝘭𝘺𝘴𝘪𝘴,
sinustrom.info/2012/05/21/and...
· Summoning Salt's videos, / summoningsalt
· jan Misali's videos, / hbmmaster8472
· The patterns of this video were animated with Manim! It's a python library for math animations. Check it on www.manim.community/
● 𝗠𝘂𝘀𝗶𝗰
(𝗦𝗼𝗿𝘁𝗲𝗱 𝗯𝘆 𝘁𝗵𝗲 𝗳𝗶𝗿𝘀𝘁 𝗮𝗽𝗽𝗲𝗮𝗿𝗮𝗻𝗰𝗲 𝗼𝗳 𝗲𝗮𝗰𝗵 𝗺𝘂𝘀𝗶𝗰 𝗶𝗻 𝘁𝗵𝗲 𝘃𝗶𝗱𝗲𝗼)
Home - We're Finally Landing (00:00)
Asher Fulero - Lukewarm Hazy (00:57)
Home - Pyxis (01:27)
Toby Fox - Can You Really Call This A Hotel, I Didn't Receive A Mint On My Pillow Or Anything (02:35)
Toby Fox - Hotel (04:06 and all the Try It Yourselfs)
Home - Nosebleed (05:22)
C418 - Beton (06:57)
Toby Fox - Snowdin Town (08:46)
Cheel - Soft Feeling (18:49)
Home - Before The Night (20:44)
C418 - AMS (21:58)
● Try It Yourself! #3 HINT : sǝɯıɹdoɔ
● There was a mistake in 2:53, the written definition only applies to 3x3 patterns because it only checks if there exists a dot in the 'middle' of the current dot and the next dot. The correct way would be to check if there are any dots in the line segment of the current dot and the next dot.
● 𝗧𝗶𝗺𝗲𝗹𝗶𝗻𝗲
00:00 - Intro
01:22 - 1. Define
02:58 - 2. Find It
06:07 - 3. Find All
09:23 - 4. Generalize
15:17 - 5. Number Theory
20:41 - 6. Find Everywhere

[@DrZye]

와!!!!!!!!!! Turns out, this video was selected as one of the winners of SoME1!!!! THANK YOU for enjoying this so much! I'll be uploading videos from time to time, the topic may not be about math and just anything I want to study. (I'll start when my univ projects are over) Here's a pi for celebration ──────────▄▄▄────▄▄▄──────▄▄▄ █▀▄──────█▄█─█──█▄█─█───▄▄▀─█ ▀▄─▀▀▀▀▄▄█▄▄▄█▄▄█▄▄▄█▄▀▀▀───█ ─▀▄─────────▄▄▄▄▄▄─────────█─ ───▀▀▄▄▄▄▄───▀▀▀▀─────▄▄▄▀▀── ──────────█──█▀▀▀▀█──█─────── ──────────█──█────█───█────── ──────────█──█────▀█───█───── ──────────█──█─────▀▄──▀▄──── ─────────▄▀──█──────█───█──── ─────────█───█──────▀▄───█─── ────────█────█───────█────█── ───────▄▀────█───────▀▄────█─ ───────█────█─────────▀▄───█─ ───────▀▄▄▄▄▀──────────▀▄▄▄▀─

[@walangid]

Congrats :D

[@BestKorean144]

축하!

[@user-jw1mo1yq2e]

Congrats man! I saw the 3b1b thumbnail and knew it was your video on it!

[@Lulzinh]

seriously? CONGRATS MAN! how long did this video took to make? (from idea to posting)

[@user-qo3pq2lj7q]

샌즈!!!!!!!

[@Higgsinophysics]

I'm calling it right now: this is one of the winners

[@DrZye]

I'm flattered, but there have been really great videos coming this summer! so I'm not expecting much :p

[@skelet8337]

Not it isn't bcs now everyone watching knows it so it will be priority from ppl trying to unlock phones

[@sunlooker9392]

@@skelet8337 The video is "What Is The Most Complicated Lock Pattern". It's breaking it down with math to construct a complicated lock, not the most obscure and safe lock.

[@skelet8337]

@@sunlooker9392 I was making a joke ik it wasn't good one and you are right

[@hobanm45]

Take your 1000th like.

[@JustAGiraffe]

Ironically, if someone uses a high completely pattern to make their phone more secure, they're actually _less_ secure if the attacker knows they're using one of the 296 max-complexity patterns.

[@dickurkel6910]

Hackers will try the most obvious ones first though, especially the least complex ones such as the example that was shown in the beginning (the one with only 2 slopes). If the hackers were aware of these max-complexity patterns, it seems the most secure would be the ones that are in-between, with around 4-5 slopes. Edit: Actually, thinking about this again, if they were aware of only the max-complexity slopes, the most secure would be the patterns containing 7 slopes, as those would be the most complex while them still not knowing about them. Additionally, you could even try to have less than 8 lines if they test all the ones with 8 lines first.

[@smashingstargamer]

then try a 295 complexity pattern B)

[@jesterokami]

@@smashingstargamer and if you wanna be extra safe 294 complexity pattern

[@TheJacklikesvideos]

Even if the brute force wasn't naive, it would still be a slower execution to break starting from most complex than your average under a forwards attack, because high complexity keys are slower to input.

[@espenhellesnes]

If they do unlock my phone doing that i think they are worthy of having it

[@PsRohrbaugh]

The visual proof at around 25:00 was one of the best visualizations I've ever seen and gave me shivers

[@yashphirke3609]

Yeah true! I think the music also had to do something with it, the cosmic vibe that it gave was mindblowing. Loved it!

[@LuisGmoDeLosMonteros]

that shit was like blending into the 4th dimension

[@pridepotato314]

More precisely 24:43

[@PsRohrbaugh]

@@pridepotato314 24:42 for symmetry 😋

[@petterlarsson7257]

yeah

[@LookingGlassUniverse]

There’s so many things I loved about this I may as well make a list: 1. The comedy and the characters 2. The fact that this was a problem you got obsessed over (it shows!) 3. That you somehow solved this?!? And then kept generalising anyway?? 4. Even though the problem was so tough, your intuitions about how to do it where very helpful 5. Your sense of (comedic) timing and (pedagogical) pacing was impressive! 6. The moral of the story about the role of intuition was so well embodied in the video 7. The very affectionate cat. Please make more!

[@DrZye]

Thank you so much! Yep, I'm looking forward to making more math videos!!

[@adityakhanna113]

Hi! Nice seeing you here!

[@kameronpeterson3601]

There are the same number of patterns that use 8 dots are there are 9 dots so you don't gain complexity by using using the ninth btw

[@SR_Joseph]

anyone please get this madlad back to hospital GOSH THAT'S INSANE

[@SR_Joseph]

@@DrZye legends have said that he is still drawing patterns till this day.

[@pewpewlesay1345]

"Is this a serious video?" "Yes,...look at the lenght" dayum

[@megadaddysean]

damn

[@lyricsassam]

@@megadaddysean DAYYUUM

[@Hankathan]

Can I just say I love this soundtrack? The Summoning Salt music during the visual proof was genius. I solved the proof by induction and it felt like I just took a step in The History of Math World Records.

[@nate-thegrate]

Loved the Undertale songs & samples too :D

[@garrettsmith6549]

Yes sir! Working on it right now hahahaha

[@andremrh7690]

HOME - We're Finally Landing, for anyone interested.

[@Ferrichrome]

HOME is to thank :)

[@DrRan617]

EDIt the can to ca then again edit the ca to can pls

[@cavemann_]

I wanted to know this for many years, and finally someone crazy enough has provided me the answer. Thank you Dr. Zye, you deserve a Nobel Prize!

[@Majimba_Enjoyer]

Imagine having this as your Pattern you forget it turn on yiur pc and watch this video for the answer or all of the sudden everyone gets acces to your phone XD

[@nikk-named]

@@Majimba_Enjoyer This pattern now is both super secure and insecure at the same time and it's kinda funny

[@leandro8897]

Nobel Prize for peace

[@kiyotakaayanokoji6950]

@@Majimba_Enjoyer plot twist: u cant watch it because u only have the phone

[@msrikavya9651]

No, he deserves the parody version of it

[@LordWhiteWolf06]

wow, what a great video. calling it now, here before this blows up insanely hard. currently at 7k views at the time of writing this.

[@kingofkoalas6923]

Lol your comment probably led me to this video. Thank you. This was a really cool video

[@vixogarces6829]

Ragnir video when?

[@gabrieldouaihy4893]

Omg it you gi

[@gabrieldouaihy4893]

Hi**

[@inxphy]

almost 10k views rn

[@TehSnaH]

You forgot about one feature of a pattern that I would consider complexity. I will try my best to explain the pattern complexity feature that I would call "fake skipping". It is whenever a pattern goes back over an already drawn edge (e.g. a pattern that includes the sequence: 2, 1, 3). If a person is shown a drawing of a pattern that includes a fake skip they would not know the order of the drawn edges and therefore the pattern would have multiple ways to be drawn, but only one correct way. I would consider patterns with fake skips to be more secure against an attacker that somehow has an image of your pattern, since there are extra possible ways to draw the pattern.

[@fuuryuuSKK]

With Zye's definition of complexity, there can only be one line of each slope, and fake skips necessitate two lines of the same slope. The pattern would also have to begin or end on the fake-skip doubleback, since otherwise the pattern can be identified even more easily, since its order can only include the middle point before the others, accessed by a line to the middle, then the fake skip is performed, and the direction it is performed in is clearly identifiable due to the leaving line. Even then, the only unclarity would be, in the case of a starting fake skip, whether it is a fake skip, a regular line or a regular line at the end of the pattern (assuming the other end is not a fake skip, as that would dictate the direction), or in the case of an ending fake skip whether it goes in one direction or the other. Thus it is possible to have a pattern, featuring a starting fakeskip and an ending fake skip, that cannot be guaranteed to be guessed even if the attacker knows the shape of the code, since both ends' fake skips obfuscate which direction they are performed in and as such the attacker has a 25% chance, assuming equal probability of each pattern, to be locked out of the phone. For an example pattern demonstrating what I am talking about, 58231 could well be 85231, 58213 or 85213 as well. However, this is now a fully different matter of complexity as compared to the problem posited by Zye.

[@banger5283]

1+1 is 2

[@Corn0nTheCobb]

@@fuuryuuSKK tl;dr

[@fuuryuuSKK]

@@Corn0nTheCobb doublebacks make an attacker that only knows what lines exist, but not their direction, guess which way the individual lines go. For example, 213 and 123 look the same at the start of a pattern, while 213 and 231 look the same at the end of a pattern.

[@banger5283]

1+4 is 5

[@Stablezin]

I was literally studying this exact subject until 2am yesterday, and swore I never wanted to lay my eyes upon this again. I've just watched a nearly 30 minutes video about it, and found it amusing. I don't know what to think of this.

[@DrZye]

*To everyone visiting this video,* 𝓦𝓔𝓛𝓒𝓞𝓜𝓔! This is the first of videos where I try to investigate random stuff in unorthodox ways. It was very very hastily made for the SoME1 event, but I'm...okay about how it turned out? *My To-Do List* -Timelines- ■ -Subtitles- ■ -Korean Subtitles- ■ -Python code- ■ -Full document of proofs- ■ All done!

[@R4ffir]

maybe pin 📌 your comment ❤️

[@psychoduck4264]

Why korean subtitles? lol

[@nijiiro2134]

how do you succeed with the 3blue1brown thing again? did you? I don't remember the original video by them anymore but this was great

[@amazuri3069]

@@psychoduck4264 Because he knows korean?

[@simon9734]

Are you going to add a generalization to higher dimensions to your to do list?

[@kietcan4799]

Everyone: *admiring this guy's knowledge* Me: damn this guy has good music taste.

[@audiohacker5298]

Yeeeees

[@tijmenwubben7817]

Whats the 1st song name

[@robertserban2422]

Undertale music always slaps

[@Wojciechgc]

@@robertserban2422 and sfx

[@yourcerealguy]

@TheGekey77 broooooo, home is underrated af.

[@HBMmaster]

great video!

[@olliehug1132]

👀

[@blower5]

oh hey it's the "how many seximal heavenlangs are there" guy

[@rust3152]

hey look its the person who made the best warioware fanfiction on ao3

[@mopishlynx2323]

@@rust3152 this person is known for many things apparently

[@rust3152]

@@mopishlynx2323 i only remember when they very kindly showed me that Scooby Doo teaches us that humans are the real monsters and if that's not deep I don't know what is

[@aquilazyy1125]

24:40 I did it, after 1 hour’s worth of thinking. Can’t imagine what if you didn’t have the luck to find the exact pattern that can be this easily expanded as your first pattern (or did you actually have tried a lot of them and failed?). I think I’ll try expanding some of the other patterns to see if they also have such property.

[@coltyn2003]

By finding the most complicated lock pattern, doesn't that make it the least secure?

[@joobin814]

Security and complexity isn't necessarily equivalent

[@jimmyh2137]

No, because the basic L shape pattern and most other basic patterns would be less secure anyway. Not to mention there are a bunch of "most complex patterns" and a random guesser doesn't know which one is right.

[@9nikolai]

The thing about "most complex" is that when someone looks over your shoulder it's much harder to memorise than an L or a V or some square.

[@ZelenoJabko]

His choice of definition of complexity is completely arbitrary. I would define complexity as the maximum length of the line. This video has no real mathematical value.

[@scmiller]

@@ZelenoJabko I think that’s going too far. It has little value to choosing a good lock pattern. It has entertainment value, it has mathematical insight and so also value, and has math-promotional value.

[@llamaz6731]

This felt like a very very scary man broke into my room, and started reading advanced math concepts, and now I'm cowering in the corner, screaming every time I think it's going to end, but he just keeps on going, and I love it

[@hihello3372]

With all those "DUN DUN" sounds and the background music it looks like we got an undertale fan on our hands. Its great to see another man of great culture

[@cyancookie1937]

Well my man drew an entire pi person from deltarune in a comment so I guess you're right

[@rayzhang3246]

Guess what was in my list of videos to watch when watching this LOL kzbin.info/www/bejne/hHqsqWadorGXpqM&ab_channel=ThatGuyGlen

[@PrimerBlobs]

Very nice. I sent you a discord friend request.

[@XanderAnimations]

Very nice. I sent you a pipe bomb.

[@ruhaiddoesnothing]

Hopes he accepts

[@TramNguyen-pk2ht]

rare comment of primer

[@boredyoutubeuser]

Very nice. I sent a jar of salted peanuts.

[@Sciencedoneright]

This... this is surprisingly pure and beautiful. It starts with a simple happy go merry start, but converges to a great math lesson that just shows what mathematical thinking is. Loved it

[@Lifeslayer8]

zye: doesn't wanna study for exam also zye: "so this is my research paper for developing an algorithm / formula in order to find the most complex phone grid patterns" it's amazing the length people will go just so they can avoid studying for exams xD

[@RamiSlicer]

I bet this was way more interesting than the exam.

[@daesmua]

Is a genius

[@Leonardo_H.]

almost everything can become fun if you aren't forced to do it and almost everything can become boring if you're forced to do it

[@UntarLaManteca]

@@Leonardo_H. Correction: Literally everything can become boring if you are forced to do it

[@user-ox7yi1it9u]

Relateable lol

[@aioia3885]

"if you're pausing and reading this please don't" I'm dying

[@johnnysaurus04]

Nice pfp

[@aioia3885]

@@johnnysaurus04 thanks!

[@marcusdudebro9426]

at least you're not pausing

[@kjt9589]

im pausing

[@user-um3jv7xt5c]

브라보! 초등학생도 이해할 수 있는 문제에서 시작해 정수론의 여러 공식들이 사용되어 문제를 결국 해결하는 이 스토리는 그 자체로도 상당히 아름답지만, 하나의 완벽한 논문을 보는 아름다움도 느낄 수 있었습니다. 30분 내내 화면에서 눈을 떼지 못했네요. 감사합니다.

[@lodevijk]

I love your style, the music you used, the jokes and emojis, everything is on point. You have earned all of the attention with impressive work. You even credited all the music in the description, so I can find more of it. You're the best.

[@dropnight4549]

“Anything’s more fun then studying before exams” So… did you pass the exam?

[@SuperShredder2003]

Yes, I want to know to

[@DrZye]

👍

[@dropnight4549]

@@DrZye :D

[@Eric0_0]

Damn its 12:00 am and morning's my exam Cant relate more

[@kronos4890]

@@Eric0_0 i'm also studying for an exam, good luck!

[@jordanlin4437]

This is possibly the best recommended video I’ve had for a while. You reminded me of why I fell in love with math in the first place. I will definitely be rooting for you to win :P Kudos! Edit: And you did win! Congrats!

[@randomlittleidot]

to win what

[@jordanlin4437]

@@randomlittleidot It's a competition called #SoME1, which was started by 3Blue1Brown, and it is essentially a competition about who can make the best math explainer video :)

[@randomlittleidot]

@@jordanlin4437 explains alot

[@Someone-tc6ig]

@@jordanlin4437 damn now im a competition?

[@triplespamlegend]

@@Someone-tc6ig damn lucky

[@poutiflet1227]

And that, that's the type of math videos I enjoy the most and find the most interesting.The perfect mix of humour, math, vulgarisation, emotion, and nerdness . Excellent job man, pls make more vids like these. Merci.

[@sujals7108]

This is the most beautiful math video I've seen and in fact it's better than a 3b1b (Grant's videos are still amazing)! This was completely mind blowing and it's one of the first videos I've seen which actually shows the whole problem solving process!

[@KHariram]

There are actually 3 kinds of symmetries here: rotation, reflection and order reversal. None of the patterns in the 296 have rotation or reflection symmetry so you could just divide by 8 to get 37. But 16 of them occur in 8 pairs with order reversed. Using this as well, the number of distinct patterns can be shrunk down to 29. The only criterion which prevents a pattern from being order reversible is the 4th rule of android lock pattern.

[@DrZye]

Yes, this is correct! I thought about getting rid of the reversed patterns, but I couldn't find a prettier way to present the two categories(reversible and not reversible) together.

[@mrosskne]

what's the 4th rule?

[@lfb6087]

@@mrosskne 1:08

[@s.j7423]

just, the editing, use of sound effects, music, the presentation is perfect . you have a real knack for this, and we appreciate it greatly !!! cannot wait to see if you create more media:]

[@tomdoritos3568]

I honestly thought he had atleast 1m subs , this is quality editing

[@petarlandeka9278]

Yeah Undertale sound effects and music fit in everything

[@NasTheGod215]

Its just EZScapes editing style copy and pasted lol

[@Akotski-ys9rr]

Because he’s copying summoning salt

[@s.j7423]

@@Akotski-ys9rr apart from the intro which was just an homage or reference to summingsalt's work, the rest is just clean editing. it's a similar style to a lot of video creators, doesn't mean they're all copying each other

[@user-by7bb2yz9m]

진짜 새벽 5시에 우연히 보게된 영상입니다. 매우 졸린상태였는데 영상을 보고나니 5시까지 자지 않은 내자신 칭찬합니다. 너무 좋은 영상입니다. 40분간 풀집중하면서 시청했네요 정말 대단하십니다

[@SlowerCuber]

A well made and inspiring video that I cannot I appreciate enough!! This reminds us the reason why people develops math and shows the original form of it. BTW glad to see another summoningsalt lover :D

[@rysea9855]

Undertale sound effects and music are always a good time

[@Krunschy]

13:55 That's gotta be the best way I've ever seen someone sell the concept of putting problems in mathmatical terms. To the uninitiated it always seems so superfluous, but when you see how it allows you to tap into all the incredible work that has already been done on your problem without you even knowing, that's when you can start to appreciate the power of this approach.

[@user-kv6bo8rp8y]

와 중간에 한국인이셨다는게 제일 놀라웠어요. 흥미로운 주제에 이끌려 왔는데 완벽한 한국어 자막이 달려있어서 감동했는데, 반전이 있었네요

[@TrandusNinja]

One of the best video I've seen on KZbin. The music, the references, the math. Before you showed where your ideas came from, I could already feel the references of the four minds in your video. Simply amazing

[@mazda9624]

This is one of the most expertly crafted videos to ever grace the internet.

[@sanderbos4243]

I actually pogged when you said there was a max-complexity pattern, this is such a cool video!

[@DrZye]

Pog

[@cr_lucky7906]

Ch

[@Strychuu]

Choggers

[@NxVernxual]

Poggers

[@silly_on_]

Pog

[@LostMekkaSoft]

Now THATS a very salty intro. And the rest of the video is great too! I can deeply relate to this story about being obsessed with some random thing, spending way more time with it than anyone would approve of, and getting a beautiful insight from it in the end. Rebellious curiosity

[@paydirt4996]

I sincerely hope you create more. The pacing, humor, explanations. All of it was amazing. Great work!

[@bzavacado]

I know math is my strong suit but damn, this is a process you learned and found through HIGH SCHOOL and expanded upon it in the event. I’m not as smart as I used to be but seeing your process with all of this was a roller coaster for me. I tried to do all the try it yourself stuff but it just stumped me. Still love the video the same. Thank you recommended home page, oh and I just subscribed too!

[@truthseeker7815]

Go forward

[@ilovecovid]

Right now im kinda depressed about how my math career is going, i feel like an absolute failure, but this video show me once again why i choosed maths. Probably one of the best videos about a problem that is pretty intuitive and i think than a lot of kids have thought of. Thank you for this wonderful video.

[@jacobsiehler8750]

Congratulations on producing this (and the deserved recognition in the contest). To me, it's less about lock patterns than it is about ... how mathematicians work and what mathematical curiosity and research is like. This is a video I'd use to explain my subject to people who don't really know what it's about.

[@ROBOSapiens7]

Now I want the most complex pattern in three dimensions (x,y,z)!

[@jatloe]

:O that’s interesting, maybe this can be generalized for all dimensions.

[@gudmundurjonsson4357]

try it yourself#1 you get the desired pattern after the 18349 sequence (at 3:47) with 7526. 17 gives the 0-slope, 75 the 1-slope, 52 the inf-slope, and finally 26 would give the -1 slope. #2, after seeing the initial reasoning for the -2 slope: similar reasoning can be made to conclude that the -0.5 slope has to be 94, with similar reasoning again we conclude that the -1 slope will only ever fit in 48 again the +2 slope will only fit in 83, inf-slope only fits in 36, from there the +0.5 and +1 are trivial and 67 , 75 respectively. #3: done without hint for an NxN grid any combination of integers a,b less than N will give a valid slope. Considering the no crossing points rule, this constrains us to the reduced fractions of a/b as the slopes. This then means that: The number of slopes is defined by all the coprime pairs a,b less than N. for an MxN grid, where N>M, the same coprime logic holds, but one of the numbers must be less that M. correction after seeing video: this only counts the positive slopes #4 for k=2 there are 2*2+2 = 6 slopes which is not less than 2*3=6. for k=3 a single extra posetive slope is added, which would require two points to fit into a pattern, but 3 points are added so the inequality shifts to 3*2+2 = 8 < 9 = 3 * 3. And for k=4, two slopes are added along 3 points, the two slopes require 4 points, so they use the extra point added at k=3 to make it such that 4*2+4 = 3*4, and so the pattern continues forever. #5 tried a few patterns and could do it, i'm sadly not an avid enough lock patternoligist to keep trying to solve this one. Great video!

[@user-vr4tp1qm2d]

선이 교차하는 점의 개수가 가장 많은 패턴이 제일 복잡해보인다고 생각했는데, 확실히 기울기가 수학적이군요.

[@user-wo6ol7he8h]

나도 들어오기 전까지 이생각함..

[@rudrodeepchatterjee]

This was by far the best maths class I ever had. Also your video arrangement and proving methods are amazing.

[@MaloriMakes]

Honestly, it was such a beautiful video, you did such a good job! You're really talented, and the way you explained everything, on top of the stellar editing. It did a really good job of keeping the viewers attention, and giving digestible information without being overwhelming. Seriously, outstanding work!

[@Areian-vn1qt]

선생님... 아무 생각 없이 영상을 보며 또 많고 많은 천재 미국인 중 한명이 시청자들의 수준을 고려하지 않고 봉인된 힘을 개방하는 그런 영상이라고 생각했습니다... 그러다 한국인에 심지어 고2때 이러한 도전을 했다는 점에서 정말 말문이 턱 막히며 존경심을 뛰어넘는 경외심까지 들었습니다... 부디 하시는 일, 하고 싶으신 일 모두 승승장구 하시길 바라며 자랑스러운 한국인이 되어주시길 바라며 구독 박고 갑니다!!!

[@monarque_]

말 진짜 재밌게 하시네요ㅋㅋ웃고갑니다

[@schishne7546]

Ah yes, the one guy that answers a english video with another language than english

[@jangeunjo1437]

@@schishne7546 vid owner is korean btw?

[@schishne7546]

@@jangeunjo1437 bruh, didnt know that

[@hatsu_haru]

@@schishne7546 0:20 "잠금해제 패턴을 그리세요" Is that english?

[@SteveMcKeon]

I've become similarly obsessed with a problem before - mine was trying to come up with an improved algorithm for determining optimal golomb rulers. I had 5 or 6 different algorithms and was attempting to parallelize them to run on my GPU. Took me many hours to prove that it was inherently an unparallelizable problem. Good times. Max respect for you, not just for you work in the proofs, but in this extremely well made and animated video. For your effort I hope this video blows up!

[@hi__im_zack4890]

The induction problem at the end was a fun challenge that I'm proud to admit I was able to solve. Good video! You've earned a new sub. Also, congratulations on the SoME1 win.

[@hg1986]

몇시간전 3b1b 채널 영상이 떠서 보다가 찾아왔어요 축하드립니다! 내용 조직도 그렇지만 애니메이션 급이 정말 대단하세요... 제가 고2때는 코흘리개 꼬맹이던거밖에 기억이 안나는데 ㄷㄷ 이런 영상들때문에 중학생부터 지금까지 토나오는 공학부 공부에도 아직도 수학을 놓거나 재미없어하지 않게된거같습니다. 열심히 살아가는 천재분들께 감사드립니다

[@greggregoryst7126]

I was sure i'd see something like 3 million views here, heh. Great stuff my man, really proud of your obsession with -stupid- math problems, and your abillity to solve them. This was fun to watch, good to hear due to decent hardware and overral loved it! Cant ask for more videos like that, because people dont come up with those problems daily, and neither do they solve them fast, but damn I would love to see more ;p

[@DrZye]

Thank you so much! I'm trying to balance content creating and univ studying right now, can't promise many videos but I'm working on more ideas!

[@darthmath1071]

@@NottoScales wtf ?

[@NottoScales]

​@@darthmath1071 Oops, I just realized that it was I poor choice of words. The comment has been deleted now.

[@user-wandererRed]

이건 '이과 망했으면' 드립으로 넘어가기엔 너무나 정성들인 영상이군. 문과 이과 이전에 수학을 배웠던 학생으로서 경의를 표합니다.

[@weaselfranklin7478]

The amount of love & dedication. It seeps out of the video I can feel the hard work

[@Oscar1618033]

So, the first time I saw this video in my recommended videos I wasn't very interested in the question, so I skipped it. Now I gave it a try, and I cannot underestimate how much I was wrong! It's amazing! Simple question leads to complex generalization, beautiful math, description of the math-creating and intuition process, humor, great explanation. Awesome!

[@DeLittleCat]

WOW... That was by far the best YT recommendation ever. Nice work, I really enjoyed the proof visualization at the end. Doing ALG2 and also having watched one of those videos before this helped me understand some of chapter 5 so it was cool seeing that being used.

[@needlegood]

Bro, i found this video suddenly in recommendations and it's excellent ! I think it deserves at least couple hundreds of thousands views

[@DrZye]

Thank you!! It's an honor!

[@candramarshall101]

Wow, this is super enjoyable. I love how interactive you made this video is. And I appreciated how you made it easy to understand.

[@makareno12]

Congrats on surpassing 10,000 subs! It's to be admired that you got so much support with a single video :)

[@ShefsofProblemSolving]

This was absolutely stunning! I love how you took us step by step and didn't take leaps of logic which were too large. Most things seemed motivated which many math explainers miss. Hope you continue making more! Subbed!

[@gehteuchnichtsan7911]

The summoning salt vibe hahaha. Imagine a competitive scene for lockpatterns.

[@nikk-named]

The song in the beginning, yes

[@turtle_mike]

@@nikk-named name?

[@Rohishimoto]

@@turtle_mike Home- We're Finally Landing

[@DarnYeet]

Easily one of the most engaging math videos I've seen :)

[@panzerkampfwagentigerausfb6378]

YOU WON MY GUY , YOU WON! YOU DID IT , DESERVED, im so proud og you zye. Hope you make more quality content.

[@newspaper0169]

외국 영상인줄 알고 들어왔는데 한국인이라니... 이렇게 좋은 주제를 영상으로 만들어주셔서 감사드려요 ㅠㅠ 수학 좋아하는 고딩으로서 한국에서도 이런 컨텐츠가 나왔다는 게 너무 기뻐요 ㅠㅠㅠ

[@kaustubhgupta46]

What an amazing video! Really enjoyed, especially the try yourself problems. The connection between different aspects of Mathematics always fascinates me, in this case it's geometry and number theory. Fascinating to say the least!

[@qprx]

You present the topic in such an interesting way 🤩 the information is very memorable due to that! I hope to see more videos like this from you!

[@ZedaZ80]

I'm still watching this and it keeps getting better, nice work!

[@user-bt2zu8ls4e]

그저 놀랍다 진짜 생각만 하고 넘어간 주제를 이렇게.. 평소에 수학을 좋아해서 이런 영상이 뜬것 같은데 너무 좋다..

[@calciumfree9626]

이런 별 것 없어보이는 주제로 이런 경이로운 이야기를 풀어내신 게 정말 멋져요... 잘 봤습니다... 많이 해주세요.

[@_random-person]

정말 멋지십니다. 한 달에 한번씩은 정기적으로 보러 오는데, 올 때마다 그 감회가 새롭네요.

[@DrZye]

감사합니다!!

[@theolabbate1611]

That last proof was amazing and so satisfying visually, awesome video !

[@ClaTronix]

I’m still halfway through algebra 1 so 85% of this made absolutely 0 sense to me but the parts I could understand were pretty interesting and cool! Good job!

[@crosselsmith776]

Try learning basic of number theory and combinatorics. You'll understand

[@phoenixrafael08]

이런 대단한 영상은 도대체 어떻게 만든 것이죠.. 정말 제가 본 수학 영상중 원탑입니다 진짜...

[@DrZye]

감사합니다!!

[@sandorrclegane2307]

I love your visualizization, choice of music, and narration! Great video

[@crazy1azy]

It's never easy to make advanced mathematics engaging and fun, somehow, you did it. I have never been more focused in a KZbin video, you sir have not only entertained me in an educational way, you also changed my mind about math, you made me more interested in it. All thanks to you for this lovely analysis, you have educated a high schooler and opened his mind.

[@DoeNyang0122]

정말 수포자에게도 수학의 아름다움을 보여주는 영상이었다고 생각합니다...

[@user-jh5is2so2b]

ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ

[@user-qm1vg6hq5k]

ㅋㅋㅋ

[@ZelenoJabko]

I wish I could understand these Chinese characters

[@DoeNyang0122]

@@ZelenoJabko it's not chinese!! it's korean

[@chillicrab17]

@@ZelenoJabko Koreans really hate hearing that they are Chinese.

[@Tramontano_T]

DAMN THIS INTRO LMAO Big summoning salt inspiration. I love It ❤️

[@littlenarwhal3914]

Absolutely wonderful this video really captures some of the essence of problem solving without trying to explicitly ring it out, it's genius!

[@lordvipul]

What a great video! So much knowledge, details explained so well in under 30 minutes. Amazing.

[@alexanderreynolds7638]

Awesome video! I wonder what other definitions there are for "max complexity" which also map to our intuition. In the 3x3 case, it seems to produce patterns that certainly look complex. But the fact that "max complexity" patterns don't exist in certain sized grids acts like a litmus to me that the definition is not ideal: complex patterns of course exist within those grids, so it stands that there are some patterns which are "maximally complex" for those grids. One simple reformulation would just be to use the maximum possible number of slopes, rather than enforcing that it must use all slopes. One of the features of the 3x3 grids you showed was number of polygons created, which is a pretty interesting metric, and there will be a maximum for any size grid. Another metric which you didn't mention (but probably have thought about) is number of crossings

[@DrZye]

Yes, there can be better candidates for the definition! I just came up with this one because it seemed easiest to tackle.

[@caramelcupcakes]

Nerdy stuff? Great voice? Great editing? "Unnecessary" but intriguing concept? Humor? Undertale Music? Other music that fits perfectly? Damn, this video is made for me.

[@BlightCosmos]

This video is amazing. It has great plot, great backstory and great explanaitions!

[@aliasziken7847]

“The beauty of intuition is just like the beauty of complex patterns” Wuhu! So great and inspiring!

[@ray_math]

이렇게 수학과 수학교육의 모든면에서 아름다운 영상을 제작해주셔서 정말 감사합니다. 제가 지금껏 만들었던 영상들이 다 쓰레기처럼 느껴질만큼 너무나 큰 충격을 먹었습니다. 정말 수학을 전공해서 이 영상의 아름다움을 남들 보다 더 느낄 수 있음에 행복했습니다.^^

[@l00won565]

헐 ㄷㄷ

[@user-qo3pq2lj7q]

오..

[@heejunsong3942]

Ray 님 영상도 너무 잘 보고 있습니다! 저한테는 엄청난 동기부여도 되었고 말입니다. 그런 느낌이 드셨다니 제 마음이 아픕니다... 파이팅입니다!

[@k5m_]

ee

[@sandy0.047]

와..

[@vicomi999]

I once had an bug where you could basically skip points like going from the upper right corner strait to the lower left corner without using the middle point when you where really carefull nobody could get even close to unlock my screen

[@nossahalf119]

I'm actually speechless. Thank you for this video. I laughed so hard at some parts I had to pause, I legit paused just to sink in all the information with so much joy. Thank you.

[@ArcZH]

미쳤다 진짜 마지막에 패턴 시각화 하는거 보고 어떻게 저렇게 아름다울 수 있는지... 정말 감동이네요 ㅠㅠㅠ

[@juanpa732]

Tiene toda la razón

[@nobody9292s]

That was the most interested I’ve ever been in math! Didn’t even skip any of the chapters!! Amazing video!!

[@Cawub_]

nice pfp lol

[@eyitsaperson]

pfp source?

[@Cawub_]

@@eyitsaperson from the game Oneshot. 10/10 would cry again

[@johnnysaurus04]

Sup homies. This is the Kool Kidz Club.

[@tung-hsinliu861]

This is beautiful! Especially when you visualize the general solution at the end of the video, it's heart touching tbh. Imagine the sweat and frustration before getting that beautiful result. We can clearly hear his enthusiasm in this video!

[@lost.clouds5400]

I cannot tell you in words how much I enjoyed this video! I'm looking forward for more:)

[@jovangerbscheid4619]

I made the mistake of trying the last problem myself, without the hints. It took me my whole afternoon, but in the end it was really cool to see that my solution was the same as yours (but upside down) (btw I have a gold IMO medal from last year)

[@teeweezeven]

This inspires me to start sharing my own mathematical findings!

[@thundert4566]

wow... this is one of those videos that keep you interested even if you're not good in math. the video was amazing and definitely a winner!

[@mugetsu3509]

you right

[@igornowik7377]

mate, that's some amazing top tier content! loved everything about this video (from cool starting idea and ingenious explanation to great sense of humour and really good music taste) and can't wait to see more from you :))

[@pokelij]

The math in this video is wildly above my head but 8:13 is genuinely one of the most satisfying to watch pieces of video I have ever seen.

[@DatSwif]

This was like, the best math video I've ever seen! Even though I saw tons of them! Everything about it is just so perfect! And I just can't comperhend how memorable this will be...

[@mh944]

This was on whole another level! Well made, beautifully visually explained and easily graspable! Amazing work. Needs hella lot views. One of the best recommended videos ever! Keep up and kudos to you on working so hard on this.

[@tmunt08]

지나가던 중1입니다 유튭 알고리즘에 이끌려 숙제는 제치고 영상에 몰두하였는데요 중간에 수학 공식들이 좔좔 나올 때 이해가 잘 안 되는 부분도 있었지만, 매우 흥미롭고 자세히 설명해주어 재밌게 보았습니다 정말.. 감탄이 절로 나오더군요! 그런고로 바로 좋아요 구독 바로 눌러 드렸습니다 ㅎㅎ Dr.Zye님을 응원합니다!

[@nachochips8090]

That 24:46 bit just blew my mind! That was a beautiful demonstration!

[@Coco-kt6mt]

What's the music title?