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 29 numbers, then Alberto erases 28 numbers, then Barbara 27 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. linear algebramatrixcombinatorics proposedcombinatorics