The Nine Dots Puzzle Extended to Nxnx…xn Points
Marco Ripà, Pablo Remirez · 2013
Abstract. 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.