Question 23
Carlos and Yue play the following game: First Carlos writes a $+$ sign or a $-$ sign in front of each of the $50$ numbers $1$, $2$, $\ldots$, $50$. 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.