MathNet 2016-part-07 — 182 problems (EN–VI) Question 54

Let $R$ be the rectangle in the Cartesian plane with vertices at $(0,0)$, $(2,0)$, $(2,1)$, and $(0,1)$. $R$ can be divided into two unit squares, as shown; the resulting figure has seven edges.

How many subsets of these seven edges form a connected figure?
Proposed by: Joy Zheng