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

[@ricericericericericerice]

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

[@flolu]

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

[@YokoYokoOneTwo]

@@flolu You made me little bit smarter

[@What_is_an_alias]

yes fr it was a horrible journey

[@iqraafzal517]

SAME I was frustrated until I saw this video

[@grantmccotter8779]

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

[@shrek95372q]

no

[@bathoreon3203]

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!

[@franciscocarneiro]

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

[@Harsh-xy5em]

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]

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

[@Nope-eu9rx]

I’ve understood so much better Thankyou

[@admirali.a.6175]

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

[@MsSebaastian]

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

[@flolu]

I really appreciate those words, thanks!

[@littleefecik383]

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

[@davidlandivar7710]

thank you sir! without fancy graphics its completely understood.

[@leihan2670]

Best explanation so far

[@flolu]

Glad you think so!

[@monthihan]

very intuitive explanation of the solution. thank you!

[@asher4312]

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

[@ahmetresatdemir3216]

You are my savior. Thank you

[@sallaklamhayyen9876]

Superb explanation thank you so much. Please continue

[@flolu]

Glad I could help!

[@sallaklamhayyen9876]

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

[@flolu]

@@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]

@@flolu Ok thank you again

[@richardcoterie8091]

Thanks bro You save my life

[@nonentity168]

Great explanation. Thank you

[@bishwajeetpandey1570]

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

[@sepehrzali4512]

That was a great explanation thank you so much ❤

[@flolu]

Glad it was helpful!

[@onasr2534]

brilliant explaination !!

[@_Atmika_]

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

[@luiz_ed76]

Awesome! Thanks a lot.

[@flolu]

I appreciate, that I was able to help :)

[@MahmoudSY-f3s]

Thank you you are the best

[@awesomegamedev]

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 KZbinrs, 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]

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]

@@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!

[@Kuchenklau]

bester Mann, rekursive Programmieraufgabe erledigt 👌

[@flolu]

Das freut mich 💪😅

[@bieelzzin]

Perfect video

[@kerohanna]

Amazing... Thank you

[@flolu]

I'm glad I could help you :)

[@lianchuanglee7139]

excellent thank you

[@서원빈-u2x]

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?

[@procrastination3560]

really good :) thanks

[@ashique.e1900]

Thank you bro♥️♥️♥️

[@flolu]

Glad that I've could help :)

[@bibekdhkl]

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

[@flolu]

Thank you, I appreciate your comment!

[@Albano030]

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]

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

[@karimhakki1942]

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

[@flolu]

That's definetly possible

[@neilmehra_]

tysm

[@universeexpansioninkoran1466]

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

[@universeexpansioninkoran1466]

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

[@universeexpansioninkoran1466]

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

[@flolu]

@@universeexpansioninkoran1466 Das schaffst du schon. Viel Glück

[@purelove9571]

❤

[@xavier3153]

R u german?

[@flolu]

Yes I am