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

This is the first video in the "Discrete Mathematics" series. We will cover how to create a recursive formula for the Tower of Hanoi issue. After we've found it, I'll show how to find a closed formula and proof it with the help of induction.

⏰ Timeline
00:00 Explanations
00:40 Finding recursive formula
05:46 Creating closed formula
07:39 Proof by induction

🔢 Recursive formula
T(n) = 2 * T(n) + 1
T(1) = 1

🔢 Closed formula
T(n) = 2^n - 1

📜 All Discrete Mathematics Exercises

📜 All Linear Algebra Exercises

🖼️ Thumbnail icon credits

[ricericericericericerice]

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

[bathoreon]

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-xyem]

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

[beelzebub]

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

[grantmccotter]

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

[admirali.a.]

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

[Nope-eurx]

I’ve understood so much better Thankyou

[MsSebaastian]

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

[littleefecik]

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

[davidlandivar]

thank you sir! without fancy graphics its completely understood.

[monthihan]

very intuitive explanation of the solution. thank you!

[asher]

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

[sallaklamhayyen]

Superb explanation thank you so much. Please continue

[bishwajeetpandey]

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

[sepehrzali]

That was a great explanation thank you so much ❤

[_Atmika_]

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

[Kuchenklau]

bester Mann, rekursive Programmieraufgabe erledigt
👌

[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 YouTubers, 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.

[bibekdhkl]

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