Spring 2020 Team Round Problem 13
Source:
January 3, 2021
Problem Statement
In the game of Flow, a path is drawn through a grid of squares obeying the following rules:
i A path is continuous with no breaks (it can be drawn without lifting a pencil).
ii A path that spans multiple squares can only be drawn between colored squares that share a side.
iii A path cannot go through a square more than once.
Compute the number of ways to color a positive number of squares on the grid such that a valid path can be drawn.
An example of one such coloring and a valid path is shown below.
[Insert Diagram]
Proposed by Alex Li