Talk:Tower of Hanoi

Rewrite please

Someone really needs to rewrite the algorithm-oriented sections of the article. To begin with, the definitions of variables (n, h, t, f, etc) and other symbolic terms are lost in the text, and ought to be listed in some sort of glossary. Also, redundancies should be removed (e.g. whether pegs are to be labelled A/B/C or source/spare/target). 202.91.199.36 (talk) 06:51, 14 March 2021 (UTC)

Mersenne numbers

Jasper Deng: what is the relevance of the word "Mersenne number" to the Towers of Hanoi? Mersenne numbers are studied in connection with Mersenne primes, but as far as I know that has nothing to do with the source of this number in the solution to the Towers of Hanoi problem, which is basically from a recursive algorithm. CapitalSasha ~ talk 14:51, 25 September 2021 (UTC)

I don't know why it's of interest that the sequence happens to be of the same form as the Mersenne numbers, except that the Mersenne numbers are restricted to those where the exponent to be prime. A source is provided that implies that the term "Mersenne numbers" is sometimes used to refer to numbers of this form without the primality restriction, but that just might mean the sometimes the term is used sloppily. Either way, I don't see any point in mentioning it; the word "precisely" certainly doesn't belong given that we're using the term "Mersenne numbers" ambiguously. Largoplazo (talk) 16:05, 25 September 2021 (UTC)

See also https://mathworld.wolfram.com/MersenneNumber.html: "A Mersenne number is a number of the form $M_{n}\equiv 2^{n}-1$ where n is an integer." So, broadly speaking, they are not necessarily prime (though I agree that much interest has traditionally been focused on the prime ones). OEIS.org confirms there is a connection between Mersenne (not necessarily prime) numbers and the solution to the Towers of Hanoi problem. Now, explaining why there is that connection could be a whole different kettle of fish 😀 —Mᵒdᵘlᵃtᵒ.📩 22:48, 25 September 2021 (UTC)

@CapitalSasha: From that, any learned mathematician would infer that the number of steps to complete the puzzle always has the special properties inherent of Mersenne numbers, particularly factorization. @Modulato: has added a source making the connection. Mathematical coincidences are often remarkable in their own right (Monstrous moonshine).--Jasper Deng (talk) 20:13, 25 September 2021 (UTC)

The sequence 2^n-1 is given by such a simple formula that it is not at all surprising that it comes up in different parts of math. I'll grant that we now have a source so this is not pure original synthesis. As a mathematician I feel that OEIS is full of a lot of minutia (being as it is a compendium of all integer sequences anyone has ever heard of) not all of which needs to be included in the relevant Wikipedia articles unless someone can provide a source with an actual mathematical reason why this connection is interesting or surprising. CapitalSasha ~ talk 04:43, 26 September 2021 (UTC)

I agree that OEIS.org has a myriad of notes, quotes and links, not all of which are relevant or interesting (although being relevant or interesting is subjective most of the time). However, in the case of a non-technical reader, I see no harm in saying that the sequence 2ⁿ-1 is also called "Mersenne numbers" — assuming we don't mean the Mersenne primes, of course. —Mᵒdᵘlᵃtᵒ.📩 13:35, 26 September 2021 (UTC)

Bill Gates came up with some solution in college?

I believe this game is one where Bill Gates, studying math, impressed his professors with a solution or some novel idea about this game. Perhaps worth adding to article. 50.230.251.244 (talk) 07:12, 12 February 2023 (UTC)

Why is it known as the "Tower(s) of Hanoi"?

An explanation in this article is lacking but it's the main reason I looked it up in the first place. Breezin2022 (talk) 03:14, 25 November 2023 (UTC)

Simpler statement of iterative solution does not work

The "Simpler statement of iterative solution" described ends up in a loop for some puzzle configurations. It also doesn't make sense that a solution would exist that works irrespective of the size of the loop being moved. 145.108.231.16 (talk) 18:00, 21 January 2024 (UTC)