Alice and Bob play the following game on a square grid with $2024 \times 2024$ unit squares. They take turns covering unit squares with stickers including their names. Alice plays the odd-numbered turns, and Bob plays the even-numbered turns. On the $k$-th turn, let $n_k$ be the least integer such that $n_k\geqslant\tfrac{k}{2024}$. If there is at least one square without a sticker, then the player taking the turn: selects at most $n_k$ unit squares on the grid such that at least one of the chosen unit squares does not have a sticker. covers each of the selected unit squares with a sticker that has their name on it. If a selected square already has a sticker on it, then that sticker is removed first. At the end of their turn, a player wins if there exist $123$ unit squares containing stickers with that player's name that are placed on horizontally, vertically, or diagonally consecutive unit squares. We consider the game to be a draw if all of the unit squares are covered but no player has won yet. Does Alice have a winning strategy? Proposed by Erik Paemurru, Estonia
Problem
Source: IMSC 2024 Day 1 Problem 3
Tags: combinatorics, combinatorics proposed, game, game strategy