6 problems

Solvability conjecture.

Let $T$ be a strong starter of odd order $p\geq 7$ coprime with $3$, let $\hat{T}$ be the set of pair sums of $T$, and let $t\in\mathbb{Z}_n^*\setminus\hat{T}$. Modular Sudoku solv…

Let an unavoidable set be a set of Sudoku clues whose removal makes the puzzle non-unique. Nonexistence conjecture. No Sudoku instance has an unavoidable set of size $5$ or size…

Let $k$ be the parameter in the construction $(M_n)$ of the higher-order-$k^2$ pandiagonal super-sudoku squares, and call the resulting panmagic square natural when it has no dupli…

A Knut Vik sudoku square (also called a Latin pandiagonal sudoku square) is a sudoku square satisfying the Knut Vik, or Latin pandiagonal, condition. Ollerenshaw's conjecture. Ther…

Let a partial $p \times q$ Sudoku square have big cells that are either empty or completely filled, and interpret completion as filling the remaining big cells to obtain a complete…