The Tower of Hanoi (Recursive Formula and Proof by Induction)

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  • Опубліковано 25 лис 2024

КОМЕНТАРІ • 63

  • @ricericericericericerice
    @ricericericericericerice 4 роки тому +38

    i was ready to give up until i saw this. thank you so much you explained this 100% perfectly

    • @flolu
      @flolu  4 роки тому +5

      haha, i am so glad i was able to help! :)

    • @YokoYokoOneTwo
      @YokoYokoOneTwo 3 роки тому +1

      @@flolu You made me little bit smarter

    • @What_is_an_alias
      @What_is_an_alias Рік тому

      yes fr it was a horrible journey

  • @bathoreon3203
    @bathoreon3203 11 місяців тому +1

    Best explanation video for Towers of Hanoi problem!
    I’ve watched 5 other videos (and mind you, 3 of them are around 20 minutes long each) and rewatched them multiple times but the answer just wouldn’t click for me but I watched this one video and understood the solution right away. Thank you so much!

  • @Nope-eu9rx
    @Nope-eu9rx 3 місяці тому +1

    I’ve understood so much better Thankyou

  • @franciscocarneiro
    @franciscocarneiro 2 роки тому +4

    Excellent explanation :-) The best of the 5 explanations I have watched this afternoon.

  • @Harsh-xy5em
    @Harsh-xy5em 2 роки тому +1

    I cant thank you enough, have to submit the assignment tomorrow with the restricted tower of hanoi problem, knew the equation 3(number of previous moves)+2, but didnt know how it worked. Thanks so much

  • @beelzebub3920
    @beelzebub3920 2 місяці тому

    Ich deklariere hierbei dass du mich gerettet hast und mir die Motivation Mathe zu lernen wiedererstatten konntest danke bruder

  • @admirali.a.6175
    @admirali.a.6175 2 роки тому +1

    Dude this is one of the best ones out there. Why is it so hard to find?

  • @ahmetresatdemir3216
    @ahmetresatdemir3216 2 роки тому

    You are my savior. Thank you

  • @littleefecik383
    @littleefecik383 4 місяці тому

    best explanation i've seen! very good video thank you.

  • @davidlandivar7710
    @davidlandivar7710 Рік тому

    thank you sir! without fancy graphics its completely understood.

  • @grantmccotter8779
    @grantmccotter8779 3 місяці тому

    This is an excellent explanation and has helped me a lot. I suggest Just one minor adjustment. at 8:46 I suggest you explain that T(k+1) = 2 x T(k)+1 because the recursive formula states T(n) = 2 x T(n - 1) +1. Therefore T(k+1) = 2 x T(k+1-1)+1 = 2 x T(k) +1.
    I was stumped for a while before I worked that out

  • @monthihan
    @monthihan Рік тому

    very intuitive explanation of the solution. thank you!

  • @MsSebaastian
    @MsSebaastian 3 роки тому +1

    Thanks for the video you explained it better than anyone else ive seen!

    • @flolu
      @flolu  3 роки тому

      I really appreciate those words, thanks!

  • @leihan2670
    @leihan2670 10 місяців тому

    Best explanation so far

    • @flolu
      @flolu  10 місяців тому

      Glad you think so!

  • @richardcoterie8091
    @richardcoterie8091 2 роки тому

    Thanks bro You save my life

  • @nonentity168
    @nonentity168 Рік тому

    Great explanation. Thank you

  • @asher4312
    @asher4312 2 роки тому

    Excellent explanation!!
    the best video on this topic cause I've watched several and couldn't understand until now

  • @bishwajeetpandey1570
    @bishwajeetpandey1570 3 роки тому

    Thank u so much , it helps me lot .
    Love from India❤️

  • @awesomegamedev
    @awesomegamedev 3 роки тому +12

    I just made some Tower of Hanoi animations for my channel, went to see what other videos are out there on the topic, found your channel and ... wow, you've made so many math videos:) that only received few views:(
    You usually cover more advanced stuff than most math UA-camrs, but it still seems like it would be better to select some interesting/intriguing bigger topic (e.g. Godel incompleteness theorem, Basics of math logic) and introduce/explain concepts (proof by contradiction, proof by induction) that come along the way (kind of like Mathologer/3Blue1Brown style), instead of covering various questions in isolation.

    • @flolu
      @flolu  3 роки тому +1

      Thank you! And congratulations for creating such wonderful animations!
      And you are absolutely right. Broader topics would be more interesting. I've actually created this content to prepare for my own exams.

    • @awesomegamedev
      @awesomegamedev 3 роки тому

      @@flolu
      Thanks you too:)
      > I've actually created this content to prepare for my own exams.
      That's a nice strategy!
      Hope your channel grows!

  • @onasr2534
    @onasr2534 2 роки тому

    brilliant explaination !!

  • @MahmoudSY-f3s
    @MahmoudSY-f3s 3 роки тому +1

    Thank you
    you are the best

  • @bieelzzin
    @bieelzzin 7 місяців тому

    Perfect video

  • @_Atmika_
    @_Atmika_ 11 місяців тому

    Thank you so much. It helped me a lot :)

  • @sallaklamhayyen9876
    @sallaklamhayyen9876 2 роки тому +1

    Superb explanation thank you so much. Please continue

    • @flolu
      @flolu  2 роки тому +1

      Glad I could help!

    • @sallaklamhayyen9876
      @sallaklamhayyen9876 2 роки тому

      @@flolu what best course or book or any resource or strategy to learn discrete math for a beginner?

    • @flolu
      @flolu  2 роки тому +1

      @@sallaklamhayyen9876 Honestly, I'm not sure, because I'm a beginner myself. I've just created those videos as a preparation for my exam. Doing a lot of different exercises will definitely help.

    • @sallaklamhayyen9876
      @sallaklamhayyen9876 2 роки тому

      @@flolu Ok thank you again

  • @sepehrzali4512
    @sepehrzali4512 8 місяців тому

    That was a great explanation thank you so much ❤

    • @flolu
      @flolu  8 місяців тому

      Glad it was helpful!

  • @Kuchenklau
    @Kuchenklau 4 роки тому

    bester Mann, rekursive Programmieraufgabe erledigt
    👌

    • @flolu
      @flolu  4 роки тому +1

      Das freut mich 💪😅

  • @luiz_ed76
    @luiz_ed76 4 роки тому +2

    Awesome! Thanks a lot.

    • @flolu
      @flolu  4 роки тому

      I appreciate, that I was able to help :)

  • @lianchuanglee7139
    @lianchuanglee7139 2 місяці тому

    excellent thank you

  • @서원빈-u2x
    @서원빈-u2x Рік тому

    I don't know if I can ask you this question, but after you move the N-1 disk to the second row
    Number of times all disks have been moved to the third column
    Why is it the least?
    I can understand if I study while drawing the Hanoi Tower
    But I can't explain it in words
    How can I prove it?

  • @kerohanna
    @kerohanna 4 роки тому +1

    Amazing... Thank you

    • @flolu
      @flolu  4 роки тому

      I'm glad I could help you :)

  • @bibekdhkl
    @bibekdhkl 4 роки тому

    Sorry that you are underrated 🥺
    Keep up
    Btw you have different style of writing one😁

    • @flolu
      @flolu  4 роки тому

      Thank you, I appreciate your comment!

  • @procrastination3560
    @procrastination3560 2 роки тому

    really good :) thanks

  • @karimhakki1942
    @karimhakki1942 4 роки тому +1

    Could proof by Induction be completed with 4 poles instead of 3 for The Tower of Hanoi?

    • @flolu
      @flolu  2 роки тому

      That's definetly possible

  • @Albano030
    @Albano030 11 місяців тому

    I don't understand the step with T(3), because if I use the explicit formula I've 2^n - 1 and that's 2^3 - 1 = 8 but if I use your recursive formula I've 2T(n - 1) + 1 I get 2 * 3 + 1= 7 so that's not equal so how is that working? or am I just missing smth?

    • @seeraft
      @seeraft 9 днів тому

      You miscalculated. 2^3 - 1 = 2 * 2 * 2 - 1 = 7.

  • @ashique.e1900
    @ashique.e1900 4 роки тому

    Thank you bro♥️♥️♥️

    • @flolu
      @flolu  4 роки тому +1

      Glad that I've could help :)

  • @neilmehra_
    @neilmehra_ Рік тому

    tysm

  • @purelove9571
    @purelove9571 11 місяців тому

  • @universeexpansioninkoran1466
    @universeexpansioninkoran1466 2 роки тому

    @Florian Ludewig und ich wollte eigentlich einen Algorithmus finden, mit dem ich das spiel spielen kann.

    • @universeexpansioninkoran1466
      @universeexpansioninkoran1466 2 роки тому

      Quasi als anleitung, Damit ich in der minimalen anzahl von zügen jeden Schwierigkeitsgrad schaffe.

    • @universeexpansioninkoran1466
      @universeexpansioninkoran1466 2 роки тому

      In dem Algorithmus fehlt nur die info, wann ich welche scheibe auf welchen turm ablege

    • @flolu
      @flolu  2 роки тому

      @@universeexpansioninkoran1466 Das schaffst du schon. Viel Glück

  • @xavier3153
    @xavier3153 3 роки тому

    R u german?

    • @flolu
      @flolu  3 роки тому +1

      Yes I am