6 problems

Let $\mathcal{M}_{10}\subseteq\mathcal{M}$ be the class of mazes whose destination is at distance $10$ from the origin. The $k=10$ conjecture. Conjecture that there exists a $k$ fo…

Let $\mathcal{M}$ be the class of all mazes, and let $\mathcal{N}_3\subset\mathcal{M}$ be the set of mazes for which the only horizontal edges removed between the pairs of columns…

For each $k$, let $\mathcal{M}_k\subseteq\mathcal{M}$ be the set of mazes whose destination is at distance $k$ from the origin. Fixed-distance nonsolvability conjecture. There exis…

Let $\mathcal{M}$ denote the class of all mazes under consideration. All-maze nonsolvability conjecture. There is no algorithm that solves the class $\mathcal{M}$ of all mazes. The…

Let $\mathcal{N}$ be the subset of square-lattice mazes in which the connected component of the origin is a simple, possibly infinite, path. Path-component maze solvability conject…

Let HNEs and VNEs denote horizontal and vertical edges removed from the square lattice maze, respectively. Consider mazes with arbitrarily many HNEs and arbitrarily many VNEs in on…