A page containing the puzzle, variations, and solutions.

Wikipedia describes The Towers of Hanoi as a mathematical puzzle that has
become a popular example of the concept of recursion. On this page, we have provided the puzzle,
several options used to create variations of it, a method of playing these
games manually, and solutions to many of the combinations. We made this
program to educate, entertain, and strive for the best solutions to these
variations. You can view the project on
GitHub if
you have feedback or contributions. Thanks for visiting.

A disk must be moved onto either an empty tower or a bigger disk.

To win, following these rules, transfer all of the disks to the tower
farthest to the right in size order. Even in this basic case, this may
prove to be much more difficult than expected, and the number of moves
it takes to finish grows exponentially as you increase the number of
disks.

How to Use this Page

This page provides several ways to play. These methods can be put into
two categories: manual and automatic ones. You can play manually by
clicking a tower to take off the top disk and clicking another tower to
place it. In addition, you can do the same thing by using the number
keys to indicate the tower you want to move to or from, although this
doesn't work for towers greater than 9.

For the automatic methods, depending on what options you have provided,
there might be a built-in Solution that you can watch. To see if
we have implemented a solution for this setup, check the Minimum
Moves field; if it shows something other than "Unsolved", click
Start to begin the solution and Stop to stop it.
Also, if you have come up with your own solution and want to save the
moves you made, check Export Moves, copy the contents of the
box that appears, check Import Moves, paste the contents into
the box that appears, and press Start. It will then execute the moves
you did previously. The program will use this method as long as you
keep the Import Moves box open and it contains moves. For both of these
automatic methods, you can adjust the Delay field to change
the number of milliseconds the the program will wait in between moves.
What happens when the program finishes making the moves depends on the
selected Mode: selecting "Wait" will make it await further
input, "Repeat" will restart the solution with the same options
selected, and "Increase" will restart the solution with one additional
disk.

We have also provided some additional information fields in the
Solution fieldset that deserve mentioning:

Moves shows the number of moves that have been made.

Log shows the moves made. You can show them by checking
the checkbox.

Minimum Moves shows the smallest number of moves it takes
to finish a given configuration known. In other words, it shows how
many moves the built-in solution takes to complete, if this number
can be calculated (It shows "N/A" if the puzzle can be solved, but
it has no method of calculating the number of moves it would take).
This means you can get a solution in less moves than those
provided, as few of these configurations have a solution that has
been proven optimal.

Once you get a hang of playing the game, you might want to change up
the Settings. Most programs like this one only have you adjust
the number of disks, whereas this one provides many other settings that
deserve explaining:

Towers per Stack adjusts how many towers each stack can
use. Although increasing this number usually greatly reduces the
number of moves needed to win, it also makes the solution much
harder to prove optimal.

Stacks adjusts how many different colored stacks get
placed on the towers. In the default case, making this number more
than one changes the layout of the puzzle so that each stack has
its own game, and the games interlock. This introduces a new rule:
No disk of a given stack can go on a tower that has a
different colored base and peg. This still allows disk of the same
color but a different shade, though. Under this configuration,
rotate the colored stacks clockwise to win.

Checking Antwerp changes the layout of a game with
multiple stacks. Instead of placing towers in between the different
stacks, the program places them all next to each other, and each
stack can go on any tower. Again, to win, you must rotate the
colored stacks clockwise. To enable this, you must also enable
Disks of the same size can be placed on each other in the
restrictions section.

The Shades option adjusts how many shades each stack has,
the Alternate option makes the shades of the disks
alternate on the stacks, and the Change option makes the
shade of a disk change when moved. These settings only matter when
you enable certain restrictions.

The Random option randomly places disks on the towers,
while the Shuffle option shuffles the order of the disks.
These options might create initial setups that break rules for the
given variation. However, in many cases, it's still possible to
solve the puzzle if you don't make any illegal moves from that
point on. That said, we're still working on these features, so
there might be some cases in which they create unsolvable puzzles.

Lastly, you can enable several Restrictions. These restrictions
have been labeled in an obvious way, so we won't explain what each of
them does. However, if you enable any of the restrictions regarding
shade, and you have enabled Change, two additional settings
appear:

Top Shade states what shade the top disk of each
stack must be to complete the puzzle. This value can either be
"Any" or a number. Initially, top disk has the shade 1. If you have
set Shades to more than 1, then the color that disk
changes to upon moving would be shade 2, and so on.

If you check the Home option, then to win, all the stacks
must return to where they started with the top disk having a
different shade than it originally had. For this reason, when you
check this option, there must be at least two Shades, and
the Top Shade can't be "Any" nor 1.

If you don't set any additional restrictions, you can also select
Star Towers. To make a tower a star tower, check the checkbox
on top of it. If you have selected star towers, moves must either be
from or to them.

Finally, if you want to share the options you have set, copy the
URL for this configuration.

In order to use this page, you must enable Javascript.

Special thanks to Fred Lunnon for his Java implementation I
based this page on, Victor Mascolo for inventing the original
Multistack Hanoi puzzle and models (U.S. patent number 7,566,057), Paul
Stockmeyer and Steve Minsker for their papers on several variations as well
as other contributions, Alex Munroe for his example of a custom built
generator as well as other assistance, Chris Santiago for design help,
James Rhodes, Ian Rahimi, and Samuel Sieb for support, and my sister,
Lindsay Evans, for proposing an alternative solution to the Classic
multiple stacks problem, and for being supportive with all of my endeavors.