MathDB

Andriy and Olesya take turns (Andriy starts) in a

2 \times 1

rectangle, drawing horizontal segments of length

2

or vertical segments of length

1

, as shown in the figure below.
https://i.ibb.co/qWqWxgh/Kyiv-MO-2021-Round-1-7-2.png
After each move, the value

P

is calculated - the total perimeter of all small rectangles that are formed (i.e., those inside which no other segment passes). The winner is the one after whose move

P

is divisible by

2021

for the first time. Who has a winning strategy?
Proposed by Bogdan Rublov

Problem Statement