Date of Submission

Spring 2023

Academic Program


Project Advisor 1

Steven Simon

Abstract/Artist's Statement

In the puzzle game Flow Free, the player is given a n x n grid with a number of colored point pairings. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project examines pairs of points in triangular grid graphs obtained by hexagons for which Hamiltonian paths exist in order to identify which point configurations have solutions. We show that n ≥ 5, any pairs of endpoints admit a Hamiltonian path as they do not surround a corner. This is a solution when n=2 fails when n=3 or 4.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
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Mathematics Commons