Comments on: Solving the Tower of Hanoi

By: Konrad

Konrad — Tue, 20 Jun 2023 03:41:11 +0000

In reply to Steve Becker. I noticed what Steve Baker mentioned too.

By: Steve Becker

Steve Becker — Fri, 11 Nov 2022 02:59:18 +0000

This is a very helpful article… thanks!!! I have one editorial suggestion: The 4-disk graph just underneath the 3-disk solution appears to be labeled incorrectly – it is full of invalid transitions from one vertex to the next, i.e., transitions that involve moving more than one disk at a time. (Perhaps it is intended to represent something other than the Tower of Hanoi puzzle, but it is not clear what that something other might be.) The article goes on to introduce fractals, and the 4-disk graph is then shown again, this time with vertex labels that indicate valid transitions per the Hanoi puzzle.

By: Admin

Admin — Tue, 07 Jun 2022 08:16:59 +0000

In reply to christian ray l marshburn.

Hi Christian,

Thank you for your message. We cannot ask Dan to do your homework for you and therefore suggest that you ask your teacher for help with this. If you read Dan’s article, you will be able to explain the Tower of Hanoi in simple terms.

Wishing you all the very best,

The Futurum team

By: christian ray l marshburn

christian ray l marshburn — Fri, 03 Jun 2022 10:01:20 +0000

Answer the following questions: You may use bullets in organizing your answers.
Instruction: With the Recurrence Relations topic, it consists of 3 modeling namely: Fibonacci Numbers, The Tower of Hanoi and Counting Problem. Discuss each in a simplest way and give at least one (1) example each with proper explanation.

PLEASE HELP!!!

By: Dan Romik

Dan Romik — Thu, 04 Nov 2021 17:01:48 +0000

Yes it can be solved, but not specifically using permutations and combinations as far as I’m aware. The book The Tower of Hanoi — Maths and Myths, by Hinz, Klavzar, Milutinovic and Petr is a good reference if you want to know what’s been done.

By: Gyuri Palomo

Gyuri Palomo — Thu, 28 Oct 2021 13:32:58 +0000

Dear Professor Romik,

Is there a way to solve the Tower of Hanoi puzzle using permutations and combinations? I’ve been trying to research whether or not it can be solved and I have not had much luck. Do you have any ideas?

By: Dan Romik

Dan Romik — Thu, 23 Sep 2021 16:56:42 +0000

Dear Yoko,

Thank you for the nice feedback about the article. It’s fantastic that you and your group are making Tower of Hanoi kits out of recycled materials! About your question, the article was published by Futurum with the same kind of recyclability in mind, so everyone is free to use or even adapt the materials, subject only to mild conditions of attribution of the source and noncommercial use. Specifically, if you’ll look at the bottom of this web page you should see a notice that “All Futurum content is produced, created and published under the Creative Commons license: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0).” The link to the license if you want to learn more is https://creativecommons.org/licenses/by-nc/4.0/ . So, quoting with appropriate credit is certainly fine.

Hope this helps!
–Dan

By: Yoko Wakiya

Yoko Wakiya — Wed, 22 Sep 2021 22:50:56 +0000

Dear Professor Romik,

I have just enjoyed reading your article about the Tower of Hanoi.

I am coordinator of a non-profit group named Upcycling Club 1 in Palmerston North, New Zealand. Under the slogan of “Creative Conservation” we aim to make and play with items made out of pre-loved and recycled materials. We offer regular free arts and craft workshops at our city museum, Museum of Arts, Science and History.

One of the most popular activities we do is the Tower of Hanoi. We make kits of Tower of Hanoi using hard covers of unwanted books from Red Cross book sales for bases, and bottle tops/jar lids for discs. We make bags out of fabric remnants and recycled clothing.

We are now working on instruction sheets to accompany the kits. They will be 2 pages long, but on request a 6 page (or so) version will be sent on request separately. Further a modified version will be submitted to the online publisher Frontiers in the near future.

Here is the reason why I am writing this mail to you. Would you give us your permission to quote your “Pathway from school to mathematician”, please? Main readers of my paper for Frontiers will be older children, so your statement is
just spot on. On another occasion I would also like to write about scholars whose interests in their chosen fields began when they were children.

Thank you and kind regards, Yoko Wakiya