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The smallest value of N for the 2nd player to win

Source: Baltic Way 2002

November 13, 2010
combinatorics proposedcombinatorics

Problem Statement

Let NN be a positive integer. Two persons play the following game. The first player writes a list of positive integers not greater than 2525, not necessarily different, such that their sum is at least 200200. The second player wins if he can select some of these numbers so that their sum SS satisfies the condition 200−N≤S≤200+N200-N\le S\le 200+N. What is the smallest value of NN for which the second player has a winning strategy?
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