Let n≥3 be an odd integer. We denote by [\minus{}n,n] the set of all integers greater or equal than \minus{}n and less or equal than n.
Player A chooses an arbitrary positive integer k, then player B picks a subset of k (distinct) elements from [\minus{}n,n]. Let this subset be S.
If all numbers in [\minus{}n,n] can be written as the sum of exactly n distinct elements of S, then player A wins the game. If not, B wins.
Find the least value of k such that player A can always win the game. combinatorics unsolvedcombinatorics