7 problems

Consider the three-dimensional Wythoff's game with move vectors … A position is a triple of nonnegative integers, and a $\mathcal{P}$-position is a position from which the previous…

Eventual tail conjecture. For every $a>0$, there exist integers $c_0>b_0>a$ such that

Heavy-handed Twyst-off conjecture. Heavy-handed Twyst-off has the same $P$ positions as Twyst-off on three stacks.

Let $\mathcal{G}_{\mathcal{E}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in E-Wythoff. E-Wythoff row-value conjecture. For integers $a\geq 4$ and…

Let $\mathcal{G}_{\mathcal{E}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in E-Wythoff. E-Wythoff diagonal conjecture. For integers $r\geq 0$ and $a\geq 2r$, … T…

Fix a nonnegative integer $a$, and let $\{\mathcal{G}_{\mathcal{R}}(a,i)\}_{i\geq 0}$ be the sequence of Sprague–Grundy values along the row with first coordinate $a$. A sequence…

Let $a$ and $b$ be integers with $4\leq a\leq b$, and let $\mathcal{G}_{\mathcal{R}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in R-Wythoff. R-Wythoff bounds co…