Tower of Hanoi, 8 disks. Only 255 moves requires to solve it.

The famous Towers of Hanoi puzzle, invented by French mathematician Édouard Lucas in 1883. I will show easy trick which helps to solve the puzzle with minimum steps.

If you have 7 disks version, you have to make 127 moves.
If you have 9 disks version, you have to make 511 moves.

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[babbarutkarsh]

Any computer science student here! Recursion is the key.

[michalsadovski]

In order to win with 255 moves (2^8 - 1) do following steps:
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 5 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 4 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 6 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 4 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 5 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 7 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 4 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 5 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 4 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 6 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 5 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 4 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 8 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 4 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 5 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 6 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 4 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 5 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 4 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 7 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 5 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 4 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 6 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 4 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 3 from tower C to tower A
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 5 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 3 from tower A to tower B
Move disk 1 from tower C to tower A
Move disk 2 from tower C to tower B
Move disk 1 from tower A to tower B
Move disk 4 from tower A to tower C
Move disk 1 from tower B to tower C
Move disk 2 from tower B to tower A
Move disk 1 from tower C to tower A
Move disk 3 from tower B to tower C
Move disk 1 from tower A to tower B
Move disk 2 from tower A to tower C
Move disk 1 from tower B to tower C
Done !

[SweetSagan]

I used to play with this at school when I was about 8. I got so fast at solving it. I loved it. I started thinking about that game today but I couldn't remember what it was called. I loved it! Thanks for posting!

[Zyugo]

Solving the Tower of Hanoi is very trivial once you know the secret of how to solve them.
2^n - 1 = T(n) = optimal moves, n = number of discs.
Odd: towards the goal
Even: away from the goal

[AliceDiableaux]

Awesome, I was reading up on this puzzle but this video really showed and made me understand why it is an iterative process I couldn't grasp from just reading about.

[marcozini]

For the Tower of Hanoi, I propose a simple and mnemonic solution. The rule is as follows:
- move the smallest disk, circularly, clockwise, in two different ways:
˗ for even numbered discs (2, 4, 6, 8…): a -> b -> c -> a ->…
˗ for odd numbered discs (1, 3, 5, 7, 9…): a -> c -> b -> a ...
- move the smaller disc, of the two left, on the major, it is the only possible operation,
- in the next move, move the smaller disk again in a circular way, as seen above
- in the next move, move the disc in the only way possible ...
and so on, until all the disks from the initial stake "a" to the final destination stake "c" are brought.
I hope I have been clear, thanks for your attention and enjoy.

[ivanjones]

formula for least amount of moves required to solve for N number of discs. (2^N) -1 in this case N=8 and 2^8=2x2x2x2x2x2x2x2=256.
256-1=255.

[keer-stin]

I've never seen a channel take a puzzle route! I really love your videos! 👏💖

[adtdn]

*HELLO I'M VIETNAMESE AND I'M FROM HANOI*

[everythingisconnected]

for those who are looking for C code to solve this

#include<stdio.h>
void hanoi(int n, char a, char b, char c);
int main(){
int n;

char a='A';
char b='B';
char c='C';
printf("entre numbers of rings\n");
scanf("%d", &n);

hanoi(n, a, b, c);
printf("\n%f steps are taken ", (pow(2, n))-1);

}
void hanoi(int n, char a, char b, char c){
if(n==1){
printf("move disc %d from %c to %c\n", n, a, c);
}
else{
hanoi(n-1, a, c, b);
printf("move disc %d from %c to %c \n", n, a, c);
hanoi(n-1, b, a, c);
}

}

[sallaklamhayyen]

Excellent job thank you so much we need more

[onyx_vii]

🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨
An easier method I found out for myself is to use the left right method. If all my rings are in column A, then column B would be left, and Column C would be Right. If I want all my rings to go to the 'right' column but dont know which column to start in, I name each ring top to bottom using Right left. Start at right, then next ring will be left, then next ring will be right, etc. The last ring you stop on will start your first move at the right or left Column.
5 rings

Right
Left
Right
Left
Right <---- Move top ring here
A B C

If you want the rings in the 'Left' column, you start counting Left then right instead.

Once thats done, since a big piece cant go on a little ring, put the second ring in column B. Then move the small ring on to Column B as well; giving you space to put the 3rd ring in column C. Your goal now is to move all the pieces in column B to column C as well. Once you do that you'll have room for the 4th ring to go to column B.

[Dzz]

Bro I'm here 2024 and
I need this so much 🙏
Because we have a competition for math ..
And the choices were : Sudoku, tower of Hanoi, ruibix cube and I think that's all
Thank you so much 🙏

[maheshkanojiya]

It was created much earlier in a temple in India TOWER OF BRAMHA

[davidwinokur]

I've had this puzzle for decades and counted the moves. My result was always 262. My mother gave me the puzzle and I solved it in about 30 minutes.

[sajidmanzoor]

Solve the following puzzle for Tower of Hanoi

· If puzzle can be accomplished in 3 moves with two discs. Use this to work out how many moves would be needed with three discs?

· If puzzle can be completed in 15 moves with four discs. Use this to work out how many moves would be needed with five discs?

· In general, describe a way of working out how many moves are needed when one extra disc is added?

ye kese hoga

[byronsmothers]

Not only does the top ring only jump 1>2>3>1, but the 2nd ring only jumps 1<2<3<1 whenever top ring isn't on top of it, and never naturally goes above the top ring

[aki]

I finished all 3 to 10 disks in least possible moves in just 1 night with sleep of course. It's not that hard. It just need to take a lot of time to finish. By the way, the 10 disks has 1023 least possible moves optimal solution.

[u.u.u]

I like how you dont have to think about the other moves besides 1, 2, 3 because all the b other moves are just follow the rules.

[bikoteedesigns]

Hi! Please how do I draw a DFD from a flowchart of hanoi tower?

Do you have any tutorial on that?