Thanks, Matthew, for \\( 2^{\aleph_0} \\) solutions to Puzzle 71.

In layman's language: if we have two points \\(x\\) and \\(y\\) on the plane, we can decree that \\(x \le y\\) if \\(x\\) is no further _north_ than \\(y\\), or no further _southwest_.... or no further in _any_ chosen direction on the compass.

This will get along with vector addition, meaning

\[ x \le x' \textrm{ and } y \le y' \textrm{ imply } x + y \le x' + y' \]

for all points \\(x,x',y,y'\\) in the plane.

But believe it or not, these are not all the solutions to Puzzle 71!

In layman's language: if we have two points \\(x\\) and \\(y\\) on the plane, we can decree that \\(x \le y\\) if \\(x\\) is no further _north_ than \\(y\\), or no further _southwest_.... or no further in _any_ chosen direction on the compass.

This will get along with vector addition, meaning

\[ x \le x' \textrm{ and } y \le y' \textrm{ imply } x + y \le x' + y' \]

for all points \\(x,x',y,y'\\) in the plane.

But believe it or not, these are not all the solutions to Puzzle 71!