MathDB
2019 Saint Petersburg Grade 11 P3

Source:

April 14, 2019
combinatorics

Problem Statement

Kid and Karlsson play a game. Initially they have a square piece of chocolate 2019×20192019\times 2019 grid with 1×11\times 1 cells . On every turn Kid divides an arbitrary piece of chololate into three rectanglular pieces by cells, and then Karlsson chooses one of them and eats it. The game finishes when it's impossible to make a legal move. Kid wins if there was made an even number of moves, Karlsson wins if there was made an odd number of moves. Who has the winning strategy?
(Д. Ширяев)
Thanks to the user Vlados021 for translating the problem.