MathDB

Let

n\geq 2

be an integer. Players

A

and

B

play a game using

n\times 2021

grid of square unit cells. Firstly,

A

paints each cell either black of white.

B

places a piece in one of the cells in the uppermost row, and designates one of the cells in the lowermost row as the goal. Then,

A

repeats the following operation

n-1

times: ・When the cell with the piece is painted white,

A

moves the piece to the cell one below. ・Otherwise,

A

moves the piece to the next cell on the left or right, and then to the cell one below. Find the minimum possible value of

n

such that

A

can always move a piece to the goal, regardless of

B

's choice.

Problem Statement