MathDB

Given a positive integer

k

, a pigeon and a seagull play a game on an

n\times n

board. The pigeon goes first, and they take turns doing the operations. The pigeon will choose

m

grids and lay an egg in each grid he chooses. The seagull will choose a

k\times k

grids and eat all the eggs inside them. If at any point every grid in the

n\times n

board has an egg in it, then the pigeon wins. Else, the seagull wins. For every integer

n\geq k

, find all

m

such that the pigeon wins.
Proposed by amano_hina

C1