3 problems

Consider impartial Tak played on an $n\times n$ board, with the first player seeking a winning strategy. Odd-board first-player conjecture. If $n>5$ is odd, then the first player h…

Let $L(n)$ denote the quantity measuring the size of a minimal snake diagram. Quadratic lower-bound conjecture. For all $n$, … for some constants $a$ and $b$. This conjecture asser…

Let $n\geq 6$. Write $M_n$ for the value given by Proposition, and let $x$ satisfy … A penult is a position on an $n\times n$ board with the stated token count from which the relev…