8 problems

Consider a position of Version C with $a_i$ piles of size $i$, for $1\leq i\leq n$, where … Exclude the position with $1,1,2,2,3,3,3$ as its piles, equivalently…

Eventual parity conjecture. The outcome class of the position is determined solely by the parities of $a_1,a_2,\ldots,a_{n-1}$. The source reports preliminary calculations for smal…

Consider a position with $k\geq 3$ piles of tokens, and let … Assume that every pile has more than $m$ tokens. Parity-pattern conjecture. The position is a $\mathcal{P}$-position p…

Let $\mathscr{A}$ be a closed set of games with the evil twin property. A pair $(\mathscr{A},\mathscr{K})$, where $\mathscr{K}\subseteq\mathscr{A}$ is a kernel, is evilly normal if…

Let $\mathbb{SG}_{\mathrm{King}}(\mathcal{S}_{r,r}^{k})$ denote the Sprague–Grundy value of the impartial chess game with the king move rule on the generalized staircase determined…

Classification conjecture. The P-positions in ${\rm SCN}(6,4)$ are classified into one of the following categories:

Consider the exact slow game NIM$(n,n-1)$ for $\ell$ players: a position is a non-negative $n$-vector, players move cyclically, and on each move a player keeps one entry unchanged…

Let $k$ be a positive integer, and let $(x,y,z)$ denote a position in the triangular chocolate bar game, with $x,y,z\in Z_{\geq 0}$. A position is a P-position if the next player h…