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Use these hints if you're stuck. Try solving on your own first.
Think of the final answer as a sum of weights with + or - sign symbols infront of each weight. Actually, all sums with 1 of each sign symbol are possible.
Use dynamic programming: for every possible sum with N stones, those sums +x or -x is possible with N+1 stones, where x is the value of the newest stone. (This overcounts sums that are all positive or all negative, but those don't matter.)