MathDB

Today is Barbara's birthday, and Alberto wants to give her a gift playing the following game. The numbers 0,1,2,...,1024 are written on a blackboard. First Barbara erases

2^{9}

numbers, then Alberto erases

2^{8}

numbers, then Barbara

2^{7}

and so on, until there are only two numbers a,b left. Now Barbara earns

|a-b|

euro. Find the maximum number of euro that Barbara can always win, independently of Alberto's strategy.

Problem Statement