Nine dots puzzle

In 1867, in the French chess journal Le Sphinx, an intellectual precursor to the nine dots puzzle appeared credited to Sam Loyd.

The phrase thinking outside the box, used by management consultants in the 1970s and 1980s, is a restatement of the solution strategy.

According to Daniel Kies, the puzzle seems hard because we commonly imagine a boundary around the edge of the dot array.

For instance, if the dots are assumed to have some finite size, rather than to be infinitesimally-small mathematical grid points, then it is possible to connect them with only three slightly slanted lines.

Or, in mathematical terminology, the minimum-segment unicursal polygonal path covering an n × n array of dots.

[20] Moreover, the further constraint that the closed path remain within the convex hull of the array of dots can be satisfied for all n > 5.