Question 66
Alberto, to celebrate Barbara's birthday, proposes to play the following game: given the set of numbers $0, 1, \ldots, 1024$, Barbara removes $2^{9}$ numbers from this set. At the next step Alberto removes $2^{8}$ of the remaining numbers. It is Barbara's turn again, who removes $2^{7}$ of the remaining ones, and so on, until only 2 numbers $a$ and $b$ remain. At this point Alberto has to pay Barbara $|a-b|$ euros.
Determine the maximum amount of euros that Barbara is sure to collect, regardless of the strategy adopted by Alberto.
Determine the maximum amount of euros that Barbara is sure to collect, regardless of the strategy adopted by Alberto.