augustin_p wrote: Sasha has $10$ cards with numbers $1, 2, 4, 8,\ldots, 512$. He writes the number $0$ on the board and invites Dima to play a game. Dima tells the integer $0 < p < 10, p$ can vary from round to round. Sasha chooses $p$ cards before which he puts a “$+$” sign, and before the other cards he puts a “$-$" sign. The obtained number is calculated and added to the number on the board. Find the greatest absolute value of the number on the board can Dima get after several rounds regardless Sasha’s moves. whAt is this all about???

Aha4525 wrote: augustin_p wrote: Sasha has $10$ cards with numbers $1, 2, 4, 8,\ldots, 512$. He writes the number $0$ on the board and invites Dima to play a game. Dima tells the integer $0 < p < 10, p$ can vary from round to round. Sasha chooses $p$ cards before which he puts a “$+$” sign, and before the other cards he puts a “$-$" sign. The obtained number is calculated and added to the number on the board. Find the greatest absolute value of the number on the board can Dima get after several rounds regardless Sasha’s moves. whAt is this all about??? you dont understand the statement?

I think the statement is not clear enough, and the following is the version what I understand. Correct me if there is anything wrong. Sasha has $10$ cards with numbers $1, 2, \dots, 512$. Initially, he writes a $0$ on the board and invites Dima to play a game. In each round, Dima chooses an integer $p$ where $0<p<10$, and then Sasha chooses $p$ cards among the $10$ cards. They add the number on the board by the sum of the numbers on the $p$ cards and then subtract it by the sum of the numbers on the rest $10-p$ cards. Find the greatest absolute value of the number on the board Dima can get after finitely many rounds regardless of Sasha's moves.

heck, I can not understand the question anyway