4 problems

Let $\mathcal{C}$ be a cut set satisfying … and suppose that $\mathcal{C}\neq\{1,2\}$. This is Family C. Family C arithmetic-periodicity conjecture. The nim-sequence for every game…

Family B partial conjecture. If $3x<y$, then

Family A arithmetic-periodicity conjecture. The nim-sequence for every game of textsc{cut} in this family is precisely $(0,1)^c (+2)$. This concerns one of the families whose nim-s…

Arithmetic periodicity conjecture. Every instance $\mathcal C$ of $\operatorname{CUT}$ for which $\{1,2\}\not\subset \mathcal C$ is ultimately arithmetic-periodic.