7 problems

Let $P$ denote the set of ${\cal P}$-positions in single-hop Peg Duotaire. A language is context-free if it is generated by a context-free grammar. Single-hop context-freeness conj…

A position in single-hop Peg Duotaire has a nim-value, namely the Grundy value of the associated impartial game position. Unbounded-nim-value conjecture. There are positions in sin…

Let $P$ and $N$ denote the sets of ${\cal P}$-positions and ${\cal N}$-positions, respectively, in single-hop Peg Duotaire. A language is regular if it is recognized by a finite-st…

Earlier fool's solitaire conjecture. The inequality

Let $A$ and $A'$ be points of a peg-solitaire board, and let $I$ be an initial position. Define $\operatorname{Height}(A,I)$ as the minimum number of legal moves needed to put a pe…

Let $\mathfrak{S}$ be a peg-solitaire board, let $\mathscr{D}(\mathfrak{S})$ be its set of legal-move vectors, and let $\mathcal{B}\subset\mathscr{D}(\mathfrak{S})$ be a basis of…

Let $\mathfrak{S}$ be the set of points of a peg-solitaire board. Let $V(\mathfrak{S},\mathbb{Z})$ be the integer span of legal-move vectors and let $V^+(\mathfrak{S},\mathbb{Q})$…