2 problems

Let $\mathbb{G}_n$ be the regular board, let $(B,W)$ denote a peaceful battle on it, and call a battle optimal when it maximizes the relevant objective. Let $d\in\mathbb{N}$ and…

Let $n\in\mathbb{N}$ be even, and let $(B,W)$ be an $(a,b)$-plaid on the torus $\mathbb{T}_n$ for which $\min\{|B|,|W|\}$ is maximum. Even-torus conjecture. Then … The conjecture f…