The Square-Sum Problem - Numberphile

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Recommends Geerten Verweij · 2018-04 · Stack Overflow · on “Symmetric(or undirected) Hamiltonian Cycle data sets”

Check this video: [this video] Also check the in depth sequel to the video. You can determine yourself how many nodes you want to add to the graph. It does require you to construct the data yourself, which should be deable. One note: the problem is about a path, not a cycle, but you can overcome this by connecting the start and end node.

Cites Simo Ryu · 2018-01 · Mathematics Stack Exchange · on “numberphiles's square-sum problem”

[this video] I do not know any details or anything, but it seems like this very interesting conjecture doesn't have a name or something, I could not search it. Does anyone know more about this problem? For those who didn't watch the video, here is the conjecture. "For large enough $N$, there exists some permutation of $\{1,2,...,N\}$ such that for every pair of adjacent number, the sum is always square." My guess is that they discovered this problem themselves, but it's sure interesting! I'm asking if this problem has a name, or was noted by a mathematical organization or by a journal, or mathematician. It seems like since there is OEIS dedicated to such possible N there must be some recognition

Cites Alexander Day · 2018-01 · Mathematics Stack Exchange · on “constraints to the hamiltonian path: can one tell if a path is hamiltonian by looking at it?”

A few days ago, the channel Numberphile [LINK] released this video [this video] on the square-sum problem. The show later released this follow-up [LINK] video on how they proved that every number from 25 to 91 can have themselves and all the preceding numbers be ordered so the sum of any two adjacent numbers add up to a square. (confused? check out the video!) Anyway, I wanted to see if I could get, say $100$ somehow, but the lines linking the numbers on a graph are way too complex for me to tell where a line goes. So I'm doing it the hard way... First, I made a table from $1-100$ dictating what numbers would be added to said number to get a square number, like $100$ or $4$. To keep this question

Cites Mark S. · 2018-03 · Mathematics Stack Exchange · on “What is the name of the conjecture related to what Matt Parker has called "The Square-Sum Problem"?”

On the OEIS sequence for counterexamples [LINK] , R.K.Guy [LINK] claims that "the problem originated (for n = 15) with Bernardo Recamán Santos [LINK] of Colombia.", but does not give a name for the problem. On a Numberphile episode [this video] , Matt Parker himself has given this problem the name "The Square-Sum Problem". I have not evaluated the proof myself, but there is what amounts to a program and description (a preprint?) purporting to prove this conjecture at this mersenneforum post [LINK] (and the preceding posts help for context) by Robert Gerbicz [LINK] . For the same problem but requiring the numbers to make a loop (so that the first and last numbers sum to a square as well), the numb

Cites Dutchottie · 2018-11 · Stack Overflow · on “Speed up N(P) problem search - Sum-Square Problem”

Speed up N(P) problem search - Sum-Square Problem I was wondering if anyone could help me figuring out ways to speed up a small programm I was working on. The problem is a math exercise called the Sum-Square Problem ( [this video] ). So you take a list of continuous integers starting at 1 to N and see if you can reorder them so that the sum of each pair makes a square. So for example: 1-3-6-10-15- or 1-15-10-6-3-13-12-4-5-11-14-2-7-9- The trick is to use all the numbers in the domain [1,N]. Obviously you can either find just one solution proving that there is a solution for [1,N] or you can show all the solutions for that domain. In the latter case you will get a reverse solution for each solutio

Cites Artem Vladimirov · 2019-05 · Mathematics Stack Exchange · on “The square-sum problem v2.0”

My question concerns the problem of 'the square-sum problem' which is described in details in this video: [this video] On this video is told that a series of sequential numbers from 1 to 15 we can rearrange in such a way that the sum of two neighboring ones will be an perfect square. Here is a solution {9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8}. That is not the only number with this property. The question goes like 'does there exist the biggest N with these properties. If there is not, how to prove it?'. P.s. excuse for my not-inteligence on this comment, i'm not a student, i'm just a scholar who spent his time dealing with math and thus i don't have a perfect english and i may translate

Cites Grey · 2019-07 · Mathematics Stack Exchange · on “Efficient hamiltonian path through neighboring squares”

My knowledge of Number/Graph theory is very limited. I'm sorry if someone can find this answer posted elsewhere quickly, I spent some time searching but don't know enough to know what to search. The following video describes exactly the problem I am trying to solve. [this video] ex: for N = 15 the solution would be 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9 However, I have a twist. I've written some code to solve this via brute force, for anything below 30 it is plenty fast, anything above takes more time than I'm allowed. My question is, instead of generating a list of all pairs that would cooperate together, and mucking with it until it works. Is there an extremely fast way to find the s

Cites sweatspaghettios · 2020-08 · Stack Overflow · on “Hamiltonian path function returns empty path unexpectedly”

The assignment I'm struggling with is based around a problem called the knight's tour and this Numberphile video: [this video] Basically, what I'm trying to do here is to write a helper function that recursively computes a Hamiltonian path in a given graph (V, E). It should return a list of the elements in V in the order of that path, or nil if no such path exists. But it only returns an empty list for the path P. My attempt so far (further down): (and formatting is a bit weird) (defn- H' ;; ;; "This is the helper function for computing the Hamiltonian path. ;; E is the relation, i.e. the graph, we are looking for a path in. ;; a is the current node. ;; S is the set of nodes we haven't visited ye

Cites volcanrb · 2020-11 · Mathematics Stack Exchange · on “Diameter of graph where $V = \mathbb{N}$ and two vertices are connected if they sum to a square”

After watching the Numberphile video The Square Sum Problem [this video] , I explored the idea further and came up with this conjecture. Let $G$ be a graph where $V(G)=\mathbb{N}$ and $E(G)=\{(a,b)\in\mathbb{N}:a+b \space$ is a perfect square $\}$ . The diameter of $G$ is $3$ . Exploring finite subgraphs of this with Mathematica seems to suggest the conjecture is true. For example, the shortest path between $1$ and $2$ is $(1,15,34,2)$ , and I can confirm that the maximum distance between any two integers $\le 100$ is $3$ . I can also rephrase the conjecture in number-theoretic terms: $\forall n,m\in\mathbb{N}, \exists x,y\in\mathbb{N}:n+x,x+y,$ and $y+m$ are all perfect squares. This would imply

Cites Prasun Biswas · 2021-12 · Mathematics Stack Exchange · on “Proving the number circle internet meme, where sum of each adjacent numbers is a perfect square”

A bit of searching informed me that this conjecture was proved in 2018 by Robert Gerbicz (there is a Hamiltonian cycle for the square-sum chain for all $n\ge 32$) (see this Mersenneforum post [LINK] ). Related OEIS sequences: 1 [LINK] , 2 [LINK] and a few others you can find linked there. There's also some Numberphile videos on YouTube on this, see here [this video] and here [LINK] .