MathDB

Oleksii and Solomiya play the following game on a square

6n\times 6n

, where

n

is a positive integer. Oleksii in his turn places a piece of type

F

, consisting of three cells, on the board. Solomia, in turn, after each move of Oleksii, places the numbers

0, 1, 2

in the cells of the figure that Oleksii has just placed, using each of the numbers exactly once. If two of Oleksii's pieces intersect at any moment (have a common square), he immediately loses.
Once the square is completely filled with numbers, the game stops. In this case, if the sum of the numbers in each row and each column is divisible by

3

, Solomiya wins, and otherwise Oleksii wins. Who can win this game if the figure of type

F

is: a) a rectangle ; b) a corner of three cells?
Proposed by Oleksii Masalitin

Problem Statement