Question 136
The number $10^{2007}$ is written on a blackboard. Anne and Berit play a game in which the players move in turn and each move is one of two operations:
(i) Replace a number $x$ on the blackboard by two integers $a$ and $b$ greater than $1$ such that $x = ab$;
(ii) Erase one or both of two equal numbers on the blackboard.
The player who is not able to make her move loses the game. Who has a winning strategy?
(i) Replace a number $x$ on the blackboard by two integers $a$ and $b$ greater than $1$ such that $x = ab$;
(ii) Erase one or both of two equal numbers on the blackboard.
The player who is not able to make her move loses the game. Who has a winning strategy?