# Binary, Hanoi and Sierpinski, part 1

Binary counting can solve the towers of Hanoi puzzle, and if this isn’t surprising enough, it can lead to a method for finding a curve that fills Sierpinski’s triangle (which I get to in part 2).

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Ojalá fuera un vídeo de física para que mi ahora ex novio me hubiese puesto atención 😔😔😔

There are 111 types of people in the world, those who understand binary, those who don't, and those who understand unary.

5:10 is the

exactmoment I realized where this was heading.8:17 I can't unsee disc 3 making a duckface.

Amazing video

cột cờ Hà Nội

When you reach 16 you will get something like 1 0000

In java: recursively

Import java.util.Scanner;

Public class ToH{

Public static void main (String args[]){

Scanner s=new Scanner(System.in);

int disks=s.nextInt();

int disk

Char source='A';

Char auxilary='B';

Char destination='C';

towerOfHanoi(disks,source,auxilary,destination);//ofcourse this is method

}

Public static void towerOfHanoi(int disks,char source,char auxiliary,char destination){

if(disks==0){

Return ;

}towerOfHanoi(disk-1,source,destination,auxilary);

System.out.print(source+""+destination);

towerOfHanoi(disks-1,auxiliary,source,destination);

}

}// np

This is a whole new way to look at numbers

Men, that means 64 disks will be solved in 18 446 744 073 709 551 616 moves, phef.. good luck with that 😀

a(1) = 1 & a(n) = 2·a(n – 1) + 1 imply a(n) = 2[2·a(n – 2) + 1] + 1 = 2^2·a(n – 2) + 2 + 1 = 2^m·a(n – m) + 2^m – 1 = 2^(n – 1)·a(1) + 2^(n – 1) – 1 = 2^(n – 1) + 2^(n – 1) – 1 = 2^n – 1. Therefore, a(n) = 2^n – 1.

exactly at 2:14 my mind fucks up

6:11

you're in contact with desmos! ask them to integrate the triangle thing for log, pow, root in their graphing calculator! that would be a huge step for getting more people to using it (hopefully) – btw i love these videos thank you so much for all of this. i have learned so so so much from you and i really appreciate the way you explain things

Zelda !

Do you think that the puzzle can be solved using factorials?

Does the 3Blue1Brown logo have a fractal form?

Hol up. So, you can go from tower 1 to 3? Always tought you chould only go to agacent towers

I remember when I programmed this for the first time, it was one of my first times programming as well. They never explained us anything about the problem, I got to understand that it was recursive (although I didn't know that term formally), but didn't understand it completely, so I looked up for the flow diagram and implemented it.

They didn't believe that I solved it, they were right, although an explanation like this could've helped me.

me as a child: layer cake is a fun game

me as an adult in CS course: towers of ha—HEY

I have been struggling with finding the best strategy for this game and you revealed it!!! :O

My blow was minded

Menger Triforce

My friend: Solve towers of Hanoi for 8 disks!

Me: Okay, but lemme count up to 255 in binary k?

OM NAMAH SHIVAYoMNS oMNS OMNS

which software are you using?

美丽的数学啊！