How many ways are there to walk across a room?

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

ความคิดเห็น • 168

  • @iantoys4193
    @iantoys4193 2 ปีที่แล้ว +207

    I’m the guy from Batman who fart

    • @yellowmarkers
      @yellowmarkers  2 ปีที่แล้ว +48

      This is the truest comment I've ever had

    • @chasejohnson8326
      @chasejohnson8326 2 ปีที่แล้ว

      have stroke 💀

    • @mike10240
      @mike10240 2 ปีที่แล้ว +9

      the hero we needed but didn't deserve

    • @burrdid
      @burrdid 2 หลายเดือนก่อน +3

      why so serious?

    • @mekaindo
      @mekaindo 2 หลายเดือนก่อน +1

      I don't get anything.

  • @adiaphoros6842
    @adiaphoros6842 2 ปีที่แล้ว +441

    You can still allow for left and down movements while still having a finite number of paths. Just don’t count paths that intersect itself.

    • @kyyzh12
      @kyyzh12 3 หลายเดือนก่อน +6

      Genius

    • @brandonmack111
      @brandonmack111 3 หลายเดือนก่อน +80

      Or, in other words, don't add the direction rule, instead add a rule that you cannot pass over a previously visited square.

    • @kylesnotepic
      @kylesnotepic 2 หลายเดือนก่อน +7

      snake

    • @KevinLivian
      @KevinLivian 2 หลายเดือนก่อน +5

      @@brandonmack111 yes. I don’t see the issue

    • @Negreb25
      @Negreb25 หลายเดือนก่อน +2

      I was literally thinking the same

  • @Dannii_1
    @Dannii_1 หลายเดือนก่อน +36

    1:39 “Does this look familiar?”
    My dumbass: Hehe yeah it’s minesweeper

  • @daper1015
    @daper1015 หลายเดือนก่อน +89

    The best math videos begin with "Have you ever wondered x? No? But I did, here's what I found."

    • @EliteCameraBuddy
      @EliteCameraBuddy 25 วันที่ผ่านมา +2

      the best video is the one that starts with”have you wondered x? No? well i did so here what i found”

    • @Steve_Bloks
      @Steve_Bloks 13 วันที่ผ่านมา +1

      @EliteCameraBuddy yes that's literally the comment you replied to idiot

    • @baconheadhair6938
      @baconheadhair6938 11 วันที่ผ่านมา

      the best video is the one that starts with “have you wondered x? No? i did though so here’s what i found”

    • @Leenomacino
      @Leenomacino 5 วันที่ผ่านมา +1

      the video is the one that starts with “have you wondered x? I did here is what I found.”

  • @syllabusgames2681
    @syllabusgames2681 2 ปีที่แล้ว +74

    That was an enjoyable mess. I was expecting this to turn into an analysis of A Star, but I’m glad to see you stayed on the math side instead. While building a multi-input function to solve some problem comes up a lot in programming, I don’t think I have ever seen it done in this manner: where the function ends up being a single mathematical structure.
    Out of the video I have seen this year, this might be the one I learned the most from since this is the first time I have seen someone build a summation series to solve a problem rather than to complete some proof where they already knew the answer ahead of time. This is probably a process I will end up using at some point, so thanks for that.
    A few notes:
    It sounds like you keep changing the distance you are from the microphone. I have a habit of doing that. My only fix was wedging my chair against my desk so I couldn’t move too far from the mic while recording. Not the best solution.
    2:40 It’s hard to read vertical text. Instead, write the text out to the side and add a leader line.
    6:17 I enjoyed the series of different applications for the path algorithm. I can tell you were messing with this problem for a while.
    12:20 The music is a bit loud in this section.
    I appreciate you just saying “this” instead of reading off a bunch of variables/equations.
    Over all, this was a pretty enjoyable video. Thanks for making it.

    • @yellowmarkers
      @yellowmarkers  2 ปีที่แล้ว +9

      I find it unorthodox that you learned more from this video than from videos made by people with actual mathematics education because I had practically no idea what I was doing here.
      About A*, I hadn't actually heard of it before you made this comment, but it appears to have applications related to which traversing method is the fastest, rather than finding every possible method. In most lattices described in this video, every path would have the same number of moves.

  • @SusDoctor
    @SusDoctor 28 วันที่ผ่านมา +13

    I sometimes think im crazy, but then i see a video like this and I remember im not insane.

    • @EliteCameraBuddy
      @EliteCameraBuddy 25 วันที่ผ่านมา +2

      sometimes i think im sane and then click on this videk and remember im insane

  • @Amy-qv3oq
    @Amy-qv3oq หลายเดือนก่อน +22

    This music is making me feel like I'm on a surreal point-and-click adventure.

  • @Iwontusethis255
    @Iwontusethis255 หลายเดือนก่อน +8

    "Its 3 am, i should probably sleep"
    TH-cam recommended:

  • @Kavukamari
    @Kavukamari 2 หลายเดือนก่อน +118

    it's just 1, the correct way. what is that way you ask? look inside your heart, the answer was inside you all along.

    • @manjuegazos4672
      @manjuegazos4672 หลายเดือนก่อน +14

      Just go in a straight line instead of frickin' zigzagging

    • @thegoldengood4725
      @thegoldengood4725 หลายเดือนก่อน +1

      “the answer is left to the reader”

    • @drhabit
      @drhabit 27 วันที่ผ่านมา +3

      answer inside me

    • @cristianpajaro8323
      @cristianpajaro8323 18 วันที่ผ่านมา +1

      Pause

    • @Mag3.1415
      @Mag3.1415 15 วันที่ผ่านมา +2

      I can’t look inside my heart my ribcage is in the way

  • @jackfrederiksen7979
    @jackfrederiksen7979 2 ปีที่แล้ว +13

    Finally, I have found another who uses a dodecahedron in their profile picture! My search is at last complete.

    • @qwerty_qwerty
      @qwerty_qwerty 25 วันที่ผ่านมา

      dodecahedrons r w

  • @qoekeur
    @qoekeur 2 ปีที่แล้ว +16

    the graphics on this are really nice. great job sir

  • @qKitti
    @qKitti 2 ปีที่แล้ว +14

    Hey YM, it's been a while since we've talked but I just wanted to say your videos are amazing! I love the editing, transitions, special effects, and all the research that goes into them as well :) Even the music, especially the one that started at 10:01 were really good! GL on the contest :D

  • @GrimblyGoo
    @GrimblyGoo หลายเดือนก่อน +3

    14:00 how come, in the irregular grid, that 20 quadrilateral can move ⬇️ to the 32 one? It seems like that move only takes you further from the exit.

    • @mrzd3756
      @mrzd3756 26 วันที่ผ่านมา

      It can be argued that the center of the figure is closer to the end figure, specially since they shared a side that goes diagonally and it brings the figures closer when going down

  • @frendogel_1115
    @frendogel_1115 หลายเดือนก่อน +7

    Why Am I Watching This At 1 Am

  • @DeoIgnition
    @DeoIgnition 2 ปีที่แล้ว +6

    Great video Quinn! You should really look into doing the CCC next year as I think you would do great at it (probably better than me lol) as most of the problems are similar to this and you already intuitively have a good understanding of how to solve these problems. Keep up the good work as well, this video was very well made, one of these will go viral I am telling you!

  • @miguelcerna7406
    @miguelcerna7406 2 ปีที่แล้ว +6

    This is rough but in general it is correct and I hope it helps with your intuition.
    Suppose we have n numbers as: a_1,a_2, a_3, ..., a_k, a_(k+1), ... n and we want to choose k numbers out of these.
    We know that the total possible ways of ordering is n!
    And note that the total possible orderings of a_1, a_2, ...a_k, a_(k+1),...n is exactly k! What is left over is (n-k)! (n_choose_k)
    Conclusively. we have n! = k!(n-k)! (n_choose_k) ==> n!/k!(n-k)! = (n_choose_k)
    Cool video. Make more. =)

  • @ArtTheGamer
    @ArtTheGamer 3 หลายเดือนก่อน +7

    I just sat through a math lecture... and enjoyed it...

    • @yellowmarkers
      @yellowmarkers  3 หลายเดือนก่อน +2

      Thanks, I'll be making more of these and I'll be trying to make them even more entertaining

  • @KrasBadan
    @KrasBadan 2 ปีที่แล้ว +5

    You could allow moving backwards as long as it doesn't repeat. For example, if you stand on some square and go up, then the moment you return to that square you can't go up anymore.

  • @kotowskiGames
    @kotowskiGames หลายเดือนก่อน +1

    When I saw the title, I was like "Dynamic programming maybe?", and I was right

  • @tunafllsh
    @tunafllsh 2 ปีที่แล้ว +10

    All problems related to computational geometry are fun to watch. Because you can always have nice visualizations

  • @ba-it3xz
    @ba-it3xz หลายเดือนก่อน +1

    I got recommended this video a week ago and watched a third of it... I only stopped watching it because I realized that it related to my discrete structures course... I am now watching it through because it might be able to help me with a 15 point problem on my assignment in my discrete structures course.

    • @ba-it3xz
      @ba-it3xz หลายเดือนก่อน

      Update: I'm curled up in a little ball on my bed.

  • @QuantenMagier
    @QuantenMagier 2 ปีที่แล้ว +3

    Here is a nice followup question:
    How many shortest ways are there to move through a gridded rectangular room if you allow diagonal movements with a cost greater-equal one and less than two: 1=cost_horizontal=cost_vertical≤cost_diagonal

  • @truejeffanderson
    @truejeffanderson 2 ปีที่แล้ว +3

    @5:45 the numerator is (l-w-2), but on the next slide it shows (7+4-2). Perhaps the negative width in the first slide is a typo?

    • @Numa369
      @Numa369 2 ปีที่แล้ว

      It's a typo that was dragged the whole video sadly, making the final función actually wrong

    • @yellowmarkers
      @yellowmarkers  2 ปีที่แล้ว +2

      I apologise for that typo, I will make a correction in the description to avoid getting more people misinformed. Thank you for letting me know about it

  • @redpepper74
    @redpepper74 หลายเดือนก่อน +6

    You can transform this problem into another more general problem: How many ways are there to travel across an acyclic directed graph? Here the graph’s vertices correspond to the floor cells, and an edge exists between any two adjacent cells, in the direction that you are allowed to go in.

  • @brillum
    @brillum หลายเดือนก่อน +2

    the beepbox music really puts this all together

    • @Koimond
      @Koimond 24 วันที่ผ่านมา

      It makes it genuinely terrifying

  • @elunedssong8909
    @elunedssong8909 16 วันที่ผ่านมา

    Great video bro. The intro was amazing. Instantly made me laugh, and then consider.

  • @sledzik1235
    @sledzik1235 2 ปีที่แล้ว +6

    Umm you forgot that center of mass can sometimes be outside of humans body so you inaccesible yelow squares are invalid at the corners becouse I could banana myself around the corner and my center of mass is in the wall

  • @greatfate
    @greatfate 2 ปีที่แล้ว +3

    OMG I literally came across this problem in Project Euler!!!! I ended up solving it by realizing that the progression of the number of ways forms a pascal triangle and I already knew its relationship to binomial coefficients😅I'm so glad somebody made a vid about it!!!! Cool explanation btw ♥♥

  • @StarlitWitchy
    @StarlitWitchy หลายเดือนก่อน

    For the first problem my intuition is basically that you'll be making 3 up moves and 6 right moves guaranteed. These moves can be arranged in 9! Different combinations with each up and right move being unique, and you can un-unique the up moves from each other by divinding by 3! And same for right moves by 6!
    A general solution for getting from one corner to the other in an X by Y rectangle is
    (X-1+Y-1)! /( (X-1)! (Y-1)! )
    This is the same as the pick 3 from 9 unordered equation which does make sense. If you put notes numbered 1-9 in a bag and pull out three and put all the up movements on the three numbers you pulled and the right movements on all the rest, thatX's mathematically equivalent ig?

  • @LeoStaley
    @LeoStaley 2 ปีที่แล้ว +3

    Gosh I am loving browsing this tag.

  • @joshuathomasbird
    @joshuathomasbird หลายเดือนก่อน +8

    if we define walking across a room as entering a specific door and leaving through a specific door, then the route doesn't matter, and there's only one way to walk across a room.

  • @EliteCameraBuddy
    @EliteCameraBuddy 25 วันที่ผ่านมา +1

    if you are walking in a straight 1D line there are 2 ways to walk
    Forward and Backwards

  • @thesketch1794
    @thesketch1794 2 ปีที่แล้ว +5

    I liked the part where you walked across a room

  • @lexinwonderland5741
    @lexinwonderland5741 2 ปีที่แล้ว +1

    i just started the video but i already love the music

  • @ten-faced-carrot
    @ten-faced-carrot หลายเดือนก่อน +1

    Me rn (Middle of the night, 2 exams coming up): *interesting*

  • @mrsharpie7899
    @mrsharpie7899 หลายเดือนก่อน

    You sound like a younger, less gritty J.C. Denton in this, and I am here for it lol

  • @ayushanand_9a502
    @ayushanand_9a502 2 ปีที่แล้ว +2

    What if we can go left or down but not go to an already visited square

  • @thedra9ongod
    @thedra9ongod หลายเดือนก่อน +1

    it’s that one bitburner contract

  • @kbeazy_3050
    @kbeazy_3050 หลายเดือนก่อน +1

    5:42 I think the formula here has a typo

    • @annanay007
      @annanay007 29 วันที่ผ่านมา

      What?

  • @thacuber2a03
    @thacuber2a03 หลายเดือนก่อน

    I thought you'd also try piecewise functions and recursion for the formula derivation

  • @cycloneentertainmentofficial
    @cycloneentertainmentofficial 26 วันที่ผ่านมา

    it turns out the real only path was the friends we made along the way.

  • @janmae
    @janmae 2 ปีที่แล้ว +1

    Hey man, very clean, interesting and professional. Good sNice tutorialt.

  • @CoulterKawaja
    @CoulterKawaja หลายเดือนก่อน

    5:44 where are the absolute value signs?

  • @truejeffanderson
    @truejeffanderson 2 ปีที่แล้ว +3

    You could say that each step in the walk must be closer to the destination. A more general statement where right and up are used for example.
    Also, I wonder how hard it would be to try this rule: can not walk into a square which was previously occupied.

    • @truejeffanderson
      @truejeffanderson 2 ปีที่แล้ว

      What if there were no walls? You just had a source square and a destination square and you found the probability of steps to get from here to there. And then put no limit on the direction of travel.

  • @jotadiolynedicci3361
    @jotadiolynedicci3361 หลายเดือนก่อน

    It was really cool video ! I loved it ! Although, i thought you might extend it to a probability question : what's the probability of going to door using those restriction ?

  • @LittleCloveredElf
    @LittleCloveredElf หลายเดือนก่อน

    Dam I actually enjoyed this even with beforehand knowledge amazing soundtrack you earned a sub

  • @elrikcourtemanche2281
    @elrikcourtemanche2281 หลายเดือนก่อน

    How about if we don't use a square grid and limit the angle that the path ça follow to be between 0 and 90 degrees?

    • @hakurou4620
      @hakurou4620 หลายเดือนก่อน

      Thats an infinite amount of paths, similarly to if you kept splitting the square grid into smaller and smaller square grids (which approaches infinity, even if it has a discrete answer for any given grid)

    • @elrikcourtemanche2281
      @elrikcourtemanche2281 หลายเดือนก่อน

      @hakurou4620 yes, it's an infinite amount of paths. I didn't think this through all the way but felt like there would be something to do there with calculus

  • @moo4boy
    @moo4boy 2 ปีที่แล้ว +1

    Another way to solve would be with a recursive formula, it would be described as following assuming l and w are integers.
    f(l,w)=f(l-1,w)+f(l,w-1) l>1&w>1, 1 otherwise.

    • @MrHenryG123
      @MrHenryG123 หลายเดือนก่อน +1

      Nice, that is the essence of how this is solved via Dynamic Programming

  • @ameliasteynberg5841
    @ameliasteynberg5841 2 ปีที่แล้ว +1

    Really well-made video.

  • @petrxs
    @petrxs 14 วันที่ผ่านมา

    5:28 isn't the top supposed to be (n + k - 2)! ??

  • @LeoStaley
    @LeoStaley 2 ปีที่แล้ว +4

    I wish you would has extended it to getting accross a 3d lattice room.

    • @yellowmarkers
      @yellowmarkers  2 ปีที่แล้ว +3

      A 3d lattice would follow Pascal's pyramid instead of Pascal's triangle, and its formula would be (l + w + h - 3)!/((l - 1)!(w - 1)!(h - 1)!)
      Also, I recognise you from comments on some of David Pitcher's videos.

    • @LeoStaley
      @LeoStaley 2 ปีที่แล้ว +2

      @@yellowmarkers wooo! Niche nerdy youtube crew checking in!

  • @Phantotree
    @Phantotree 24 วันที่ผ่านมา

    this is a great video to eat to, i dont understand half of things he's saying but its cool

  • @der.Schtefan
    @der.Schtefan 2 ปีที่แล้ว +1

    Have you considered submitting this as #SaME2 ?

  • @zacknattack
    @zacknattack หลายเดือนก่อน

    was that stranded lullaby

  • @danielcajas7983
    @danielcajas7983 หลายเดือนก่อน

    This is actually an interview question asked by google. Its quite hard to figure out in 30 minutes but yeah, its pretty much just dp

  • @ZedUndSonstNichts
    @ZedUndSonstNichts 2 ปีที่แล้ว +1

    And then you realize that the doors might not be on opposite walls but on the walls next to each other...

  • @blockshift758
    @blockshift758 หลายเดือนก่อน +1

    I was sure i have watched this before. And then the circle appeared

  • @maurozambruno1394
    @maurozambruno1394 15 วันที่ผ่านมา +1

    6:57 24 + 13 + 24 = 37 ????

    • @yellowmarkers
      @yellowmarkers  15 วันที่ผ่านมา +1

      Today I learned I made a Hopeless Mistake, 2.5 years ago

  • @EricMcCarty-ej7lf
    @EricMcCarty-ej7lf 23 วันที่ผ่านมา

    Was the music in the beginning made with beep box?

  • @chasejohnson8326
    @chasejohnson8326 2 ปีที่แล้ว +1

    Please make more of these

  • @sriramn1809
    @sriramn1809 หลายเดือนก่อน

    Removing down and left movements kinda make it too simple.
    Just make it so u can only pass through 1 tile once. That wud be a better question to answer

  • @truthseeker7815
    @truthseeker7815 2 ปีที่แล้ว +2

    "A human body has thickness"
    -some rule34 artist, probably

  • @James2210
    @James2210 2 ปีที่แล้ว

    Definitely feels like a descent into madness meme

  • @be78hk
    @be78hk หลายเดือนก่อน

    6:49 did nobody else notice that going to the top path would be longer than the bottom path

  • @Bozitico
    @Bozitico หลายเดือนก่อน

    Please link the music! I enjoyed it, it wasn't bad.

  • @jayrony69
    @jayrony69 หลายเดือนก่อน +1

    Make the grid in planck lengths

  • @chrisk6637
    @chrisk6637 หลายเดือนก่อน

    KEEP NOTES GUYS! YOU NEVER KNOW WHEN NITENDO WILL PATTEN NEXT

  • @PretzelBS
    @PretzelBS หลายเดือนก่อน

    Everyone loves square and hexagonal tiling, but why doesn’t triangular tiling get any love??

  • @rgc-exists
    @rgc-exists หลายเดือนก่อน +1

    Jonas Tyroller.

    • @rgc-exists
      @rgc-exists หลายเดือนก่อน

      (This is an inside joke that this person may or may not understand depending on if they are the same YellowMarkers I “interacted” with a long time ago)

    • @yellowmarkers
      @yellowmarkers  หลายเดือนก่อน

      @@rgc-exists I am indeed the same person.

  • @lawrdtv
    @lawrdtv 2 ปีที่แล้ว +1

    I started making soft recently, I was wondering if you wanna do any features.

  • @Yutaro-Yoshii
    @Yutaro-Yoshii 2 ปีที่แล้ว +2

    now try version with all four moves but path can't collide with itself

  • @Zcon18
    @Zcon18 หลายเดือนก่อน

    1:19 Omgr Combinatorics

  • @coolroblox12
    @coolroblox12 หลายเดือนก่อน

    What about going over the room

  • @joshuabarqueesimeth4530
    @joshuabarqueesimeth4530 หลายเดือนก่อน

    how many ways can you walk across the room, without any of the paths intersecting?

  • @johnchessant3012
    @johnchessant3012 2 ปีที่แล้ว +1

    very cool

  • @Akawump
    @Akawump 17 วันที่ผ่านมา

    The tired math teacher:

  • @kuznechiks
    @kuznechiks หลายเดือนก่อน

    now find how many ways there are to walk across a room with different pentagons inside of it

  • @Ultimaximus
    @Ultimaximus หลายเดือนก่อน

    This music is great, it feels like a descent into madness just like the video itself

  • @rismosch
    @rismosch 2 หลายเดือนก่อน

    when i saw the thumbnail i immediately thought pascals triangle

  • @shappp1
    @shappp1 หลายเดือนก่อน

    make the squares each a Planck length long to get the true number

  • @eWosMrV
    @eWosMrV หลายเดือนก่อน

    Thinking is finited when you only think inside a box.
    Process to walk on the wall to walk out of the room with no roof to make it a 3d space*

  • @MoroccanSpace-s1y
    @MoroccanSpace-s1y 11 วันที่ผ่านมา

    Infinite ways (before I watched the video)

  • @Tmayhem
    @Tmayhem 2 หลายเดือนก่อน

    do i hear beepbox in the background?!?

  • @Ed1414One
    @Ed1414One 26 วันที่ผ่านมา

    Just do 2^(n+k-2)

  • @Jacko_hedgehog
    @Jacko_hedgehog หลายเดือนก่อน

    Sounds like beepbox in the background

  • @Enderguy57
    @Enderguy57 หลายเดือนก่อน

    it's one way, diagonally

  • @Jc27uhh4h4h4
    @Jc27uhh4h4h4 4 วันที่ผ่านมา

    Professor Layton himself made this video

  • @jakethewolfie119
    @jakethewolfie119 2 ปีที่แล้ว

    jan Misali would approve

  • @jamez6398
    @jamez6398 2 ปีที่แล้ว +1

    Infinite.

  • @Bald1_Bas1cs
    @Bald1_Bas1cs หลายเดือนก่อน

    Infinite

  • @Albaraa
    @Albaraa หลายเดือนก่อน

    The area of the room

  • @strawberryjim
    @strawberryjim 29 วันที่ผ่านมา

    this is my autism interpreted into a youtube video

  • @hello_hi1
    @hello_hi1 20 วันที่ผ่านมา

    The music sounds beepboxy

  • @krzysztofmiller3557
    @krzysztofmiller3557 2 ปีที่แล้ว +1

    nice

  • @glitchy9613
    @glitchy9613 11 วันที่ผ่านมา

    I'm the guy from Spiderman who piss

    • @yellowmarkers
      @yellowmarkers  11 วันที่ผ่านมา +1

      This is the falsest comment I've ever had

  • @nataliexists
    @nataliexists 12 วันที่ผ่านมา

    mmmm yummy math

  • @chalkosis9739
    @chalkosis9739 2 ปีที่แล้ว +1

    Hi ym UwU

  • @JustBlack4
    @JustBlack4 หลายเดือนก่อน

    a lot-
    edit: -of ways to get across a room

  • @rigel7252
    @rigel7252 2 ปีที่แล้ว +1

    6th

  • @charl10439
    @charl10439 หลายเดือนก่อน

    23