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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That was 256 moves

Can u do 255 disks with only 8 moves? Jk 😂✌🏽

Nice video 👌

Are you native speaker? 🤔

some corrections: it was invented by ancient Hindu god Lord Brahma and it is called tower of Brahma problem, originally these towers are situated in Kashi : ancient city with 64 disks. later on it moved to Vietnam by some east Asian scholars. and as it was french colony at that time, it moved to Europe by some guy named Lucas.

Interesting that it takes 255 moves for 8 disks, considering 2^8 – 1 = 255. I wonder if this pattern of movement exists for all disc amounts

🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨

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.

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.

That’s pretty cool but can you do a 32 disk Tower of Hanoi?

If the number of disks are n then the least number of moves required to solve is 2^n-1. It can be proved using combinatorics.

Awesome video…thank you so much.

Wrong. The name is Towers of Hanoi.

Any computer science student here! Recursion is the key.

Vietnam = Hanoi

Hanoi = Tower of Hanoi

Vietnamese flag = Red

Red = Hecc

Tower of Hanoi = ToH

ToH = Tower of Hecc

I had 2 ideas, and u did one of them

I never noticed the top disk, that's cool. For me,

**SPOLIER ALERT**Here's how I eventually thought when doing the same 8 disk one of these, and I think it is the most naturally actively brain-teasing way (most fun) for me — because I just asked as a series of questions to myself to figure it out, trying not to think about patterns, so I could always head toward the end from wherever I was if I made a mistake. (Here I will call the disks by numbers, but I didn't think in numbers when doing the puzzle — Numbers I think make it easier to write clearly) I will call the big bottom disk, "8" and count up to the small top disk, "1":

So I started with the obvious question, then went on:

"How do I get the tower over on the far side?"

– "I need the bottom disk (8) there first, so I can build the rest of the tower on it"

"How do I get the bottom disk to the far pole with the least moves?"

– "Get the rest of the disks (7-1) on the middle pole with the least moves, so the far pole is open, and the big disk is free to move there"

"How do I get the rest of the disks on the middle pole with the least moves?"

– "Get the bottom of

thosedisks, (disk 7) on the middle pole so I can stack the rest (6-1) on it"—- I just kept asking that back and forth, with the next thing being disk 6 on the far pole, disk 5 on the middle pole, disk 4 on the far pole… etc.

Things naturally built from there, figuring out what ideas I had to remember and what information I could forget about as I went along.

Not going to spoil any of the set of fun ways I found to only have to remember the general idea and not much information, just that if I got lost — I didn't make any moves, and asked myself the questions again starting at disk 8. The ones I did were also different colours, so it probably would've been harder without that, and if they all looked the same colour I would probably have tried to number them in my head based on bigger size means bigger number, like I used now to write the questions.

(Also, this way with the questions it was possible to keep going if I made a mistake, which I did once or twice the first time, making me only get it in 259 moves instead of 255. It makes me really happy to do a puzzle where if I lose patience or focus, all I have to do is forget everything I was thinking, breathe, and start thinking about the original questions. It can take a minute to move forward from the mistake, but I don't have to think about the mistake — just where my pieces are, and where I want them to be)

Reminds me of the Kotor puzzle in the sith tomb for that sword of Naga shadow. Except its simplified

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.

HELLO I'M VIETNAMESE AND I'M FROM HANOINote:if you have an odd number of disks and you have to move the disk on the bottom to the moved disk, Always Move the smallest disk on the moved disk. If even then the other peg.

Note2: If You Are Trying To Solve An Even N Of disks the always place the smallest one in the middle. If odd, then the peg that is the finishing peg.

Edit: in Note 1 i am talking about the amount of disks. I am saying the amount of perfectly decreasing order from the very top with the smallest disk.

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.

After watching video , I can say that YOU ARE LEGEND

Wow that is great. Thank you

Great

Any Ha Noi people here ??

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.

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 !

2^n – 1

please solve with 64 disks

here is a challenge do the same thing but you can not jump to the 3rd "stick" you have to go to the 2nd one and then the 3rd one its doable

keep up!!! using this for discrete structure

Online towers of hanoi:

https://www.mathsisfun.com/games/towerofhanoi.html

Send me the Towers Of Hanoi in 1 week.

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!

I never would have thought that the smallest disk dictates the most efficient move pattern. this is really interesting.

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