MathDB

Two people take turns writing natural numbers from

1

1000

. On the first move, the first player writes the number

1

on the board. Then with your next move you can write either the number

2a

or the number

a+1

on the board if number

a

is already written on the board. In this case, it is forbidden to write down numbers that are already written on the board. The one who writes out wins the number

1000

on the board. Who wins if played correctly?

Problem Statement