Nearly a century ago, the classic nine dots problem appeared in Samuel Loyd’s Cyclopedia of Puzzles. The challenge was as follows: “…draw a continuous line through the center of all the eggs so as to mark them off in the fewest number of strokes”.

The Rectangular Spiral Solution

A generalization of Ripà’s square spiral solution for the nXnX…Xn points upper bound problem. Additionally, we provide a non-trivial lower bound for the k-dimensional n₁ Xn₂ X…Xn_k points problem. In this way, we can build a range in which, with certainty, all the best possible solutions to the problem we are considering will fall. Finally, we provide a few characteristic numerical examples in order to appreciate the fineness of the result arising from the particular approach we have chosen.