Two people take turns writing natural numbers from 1 to 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? number theorycombinatorics