MathDB

Two players write alternatively some integers on the blackboard. The rules are the following : - The first player write

1

. - At each of the other turns, the player has to write

a+1

2a

where

a

is any number already wrote in the blackboard and

2a \leq 1000.

- One cannot write a number which has already been written, and no number is erased. - The player who writes

1000

is the winner. Determine which player has a winning strategy. Pierre.

3