Question 43
Let $N$ be a positive integer. Two persons play the following game. The first player writes a list of positive integers not greater than $25$, not necessarily different, such that their sum is at least $200$. The second player wins if he can select some of these numbers so that their sum $S$ satisfies the condition $200-N \leqslant S \leqslant 200+N$. What is the smallest value of $N$ for which the second player has a winning strategy?