You&#x27;re confusing solving an instance of subset-sum with solving subset-sum.<p>If you solve subset-sum, yes, you&#x27;ve solved all NP-complete problems.<p>If you solve an instance of subset-sum, you&#x27;ve only solved that instance of subset-sum.<p>The issue here is that to show you&#x27;ve solved subset sum, you need to show that you&#x27;ve solved it for _all possible inputs_.<p>Subset sum is &quot;given a set (or multiset) of integers, is there a non-empty subset whose sum is zero?&quot;.<p>If I give you the set {-2, -1, 0,  1, 2}, you can tell me in O(n) time that a subset of this sums to zero.<p>That doesn&#x27;t mean you&#x27;ve solved subset sum, it means you&#x27;ve solved an instance of subset sum. To solve subset sum, you need to provide a proof showing that you have an algorithm that works for ANY set.<p>The work here gets results for a specific configuration. To show it solving subset-sum, it would need to be shown to work for all possible sets.