About a year and a half ago I ask this question regarding $P=NP$. The answers have helped me understand the problem tremendously and since then I've dabbled further into the topic.
With that stated, it is my understanding that $NP-Complete$ problems are such that if a solution for $P=NP$ were found for that specific problem, then all $NP$ problems could be solved using the same rules for resolving $NP$.
With that stated, what is the simplest $P=NP$ problem outlined to date that is %NP-Complete$?
In other words, what is the most basic of problems that one could test a theoretical $P=NP$ solution against? I'm aware of many of the examples such as the Traveling Salesman or Knapsack problems but I assume there could be even simpler scenarios where all properties of the $P=NP$ or $P≠NP$ dilemma are present.