Question

Help needed with a rather difficult math question. It is challenging and fun!

Answer 1

first, consider what can occupy what space. note that a plank has two orientations on the XZ plane (fundamentally), so you can cover an entire column even if the k-1th column is occupied. what we're looking for is the combinatorial structure of something that has two classifications; and, within those two classifications, the amount of space it can occupy. this is kinda difficult but i might see a way into it.
the poisoner is a parity case, so as long as he goes second then you have parity (or is it vice versa?)

Answer 2

if n is odd then you have vertical parity

Answer 3

Mind elaborating, a little bit more?

Answer 4

wait a second, when you place a cover, can you cover the poison or just prevent open spaces from being poisoned?

Answer 5

You just cover the poison. Basically, the poisoner tries to place his planks in such a way that there is some pit left uncovered. But to counter that, I, the protagonist have to place the planks in such a way so that NO pit is uncovered and al get covered up!

I am pretty sure you knew that but that is all I know in this question, I am clueless about the derivation of a formula from the clues in the question. :|

Answer 6

ok well our strategy for a first move is definitely to put the plank horizontally

Answer 7

the poisoner always goes first, miracrown.