Baltic Way 2023 Shortlist

(a) Let $n=8$. Determine whether there exists a labelling of an $8\times 8$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $65$.

(b) Let $n=10$. Determine whether there exists a labelling of a $10\times 10$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $101$.