3 problems

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 $V^+(\mathfrak{S},\mathbb{Q})$…