NP Complete 3rd Grade Math Problems (2018)
Is there any proof that the solution must have an iterative approach?<p>For instance, say there was some extremely clever way of depicting the relationships that allowed a &quot;single pass&quot; computation in a way that abstractly solves it that can be  reduced to the valid combinations without ever having to &quot;guess&quot; or backtrack or do some variation of a permutation map wherein you reduce a set of candidate solutions.<p>This novel method would solve it like say, one does with the process of algebra. Of course this would be in some rules and abstractions perhaps invented and defined solely for this problem - perhaps discarding all of arithmetic in the process.<p>I can imagine a proof could exist showing such an approach isn&#x27;t possible and I realize coming up with such a novel system for this problem is so unlikely the inventor would be put in the league of Gauss and Maxwell, the question is setting that aside, has it been shown to be a futile effort?