A uniform wire of resistance $$6\,\Omega$$ is bent to form a regular hexagon. Find the least and largest resistance possible between any two corners of the hexagon.

PLACEHOLDER ANSWER - the question has two answers. Each side is $$1\,\Omega$$. Between two corners the two arcs of $$k$$ and $$6 - k$$ sides are in parallel, giving $$\frac{k(6 - k)}{6}\,\Omega$$. The least value is for adjacent corners, $$\frac{1 \times 5}{6} = \frac{5}{6}\,\Omega$$, and the largest is for opposite corners, $$\frac{3 \times 3}{6} = 1.5\,\Omega$$.