MathDB

Let

{n}

be a fixed positive integer.

{A}

and

{B}

play the following game:

2023

coins marked

1, 2, \dots, 2023

lie on a circle (the marks are considered in module

2023

) and each coin has two sides. Initially, all coins are head up and

{A}

's goal is to make as many coins with tail up. In each operation,

{A}

choose two coins marked

{k}

and

k+3

with head up (if

{A}

can't choose, the game ends) and

{B}

choose a coin marked

k+1

k+2

and flip it. If at some moment there are

{n}

coins with tail up,

{A}

wins. Find the largest

{n}

such that

{A}

has a winning strategy.

Problem Statement