Carlos and Yue play the following game: First Carlos writes a + sign or a − sign in front of each of the 50 numbers 1,2,⋯,50.
Then, in turns, each one chooses a number from the sequence obtained; Start by choosing Yue. If the absolute value of the sum of the 25 numbers that Carlos chose is greater than or equal to the absolute value of the sum of the 25 numbers that Yue chose, Carlos wins. In the other case, Yue wins.
Determine which of the two players can develop a strategy that will ensure victory, no matter how well their opponent plays, and describe said strategy. algebracombinatoricsnumber theory