MathDB

Players

A

and

B

play a game on a blackboard that initially contains 2020 copies of the number 1 . In every round, player

A

erases two numbers

x

and

y

from the blackboard, and then player

B

writes one of the numbers

x+y

and

|x-y|

on the blackboard. The game terminates as soon as, at the end of some round, one of the following holds:
[*]

(1)

one of the numbers on the blackboard is larger than the sum of all other numbers; [*]

(2)

there are only zeros on the blackboard.
Player

B

must then give as many cookies to player

A

as there are numbers on the blackboard. Player

A

wants to get as many cookies as possible, whereas player

B

wants to give as few as possible. Determine the number of cookies that

A

receives if both players play optimally.

Problem Statement