Combinatorics and Graph Theory


The Nine Dots Puzzle Extended to Nxnx…xn Points

Authors: Marco Ripà, Pablo Remirez

The classic thinking problem, the “Nine Dots Puzzle”, is widely used in courses on creativity and appears in a lot of games magazines. One of the earliest appearances is in “Cyclopedia of Puzzles” by Sam Loyd in 1914. Here is a review of the generic solution of the problem of the 9 points spread to n^2 points. Basing it on a specific pattern, we show that any nxn (for n ≥ 5) points puzzle can also be solved ‘Inside the Box’, using only 2∙n − 2 straight lines (connected at their end-points), through the square spiral method. The same pattern is also useful to “bound above” the minimal number of straight lines we need to connect n^k points in a k-dimensional space, while to “bound below” the solution of the nxnx…xn puzzle we start from a very basic consideration.

Comments: 11 Pages. This is the second version of the paper in Italian that I already submitted a few months ago. It has been entirely written in English.

Download: PDF

Submission history

[v1] 2013-07-04 10:04:35
[v2] 2013-07-08 18:48:41
[v3] 2013-07-30 15:01:36
[v4] 2013-09-05 19:08:16

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