8 problems

Golden-ratio formulas. For every $n\geq 1$,

Wythoff's losing-state characterization. The states $langle p(n),q(n)\rangle$ for $n\geq 1$ characterize all losing states of Wythoff's game.

Consider the Wythoff variation formed by the basis … Let $(x,y)$ denote a P-position in the $(a,a)$ game. Grid conjecture. There are exactly $a^2$ P-positions satisfying … This is…

Consider the three-dimensional Wythoff's Game with three piles and move vectors … A P-position is a losing position under these moves. Sierpinski Sponge conjecture. The set of P-po…

For the Wythoff variation with basis … let the parameter $a$ tend to infinity. Large-parameter Nim-limit conjecture. As $a$ grows increasingly large, the game approaches standard N…

Consider Wythoff-game variations formed by the basis … The paper establishes an algorithm for the cases $a=2^i$ with $i\in\mathbb N$. Nonexistence conjecture for cyclic games. Apar…

In the generalized $(b,b)$ game, players may make Nim moves or remove $kb$ stones from each pile, where $b$ is fixed. A game formed by the basis $\left\{(1,0),(0,1),(a,a)\right\}$…

Diagonal uniqueness conjecture. For all nonnegative integers $a$ and $g$, there exists a unique integer $b$ such that