Hi, I checked the forum rules and homework / coursework is not allowed so I am not sure if this is appropriate or not. Feel free to guide me through appropriate forum and/or lock this thread if such questions are not allowed. The question I have is mostly related with my research and since I am not good at physics, I stumbled upon a problem which I couldn't solve. The problem seemed more like a physical problem rather than an optimization problem so here I am. Anyway here is the story. Info: Assume that there is a square grid plate with cells having same dimensions. Plate has no weight. Each cell has its own associated weight and weights located at symmetrical positions are equal. Now, I randomly remove some weights from cells and this may shift the center of mass from central cell. Here is an image http://imgur.com/13338Lf What I want to do is that, on a given "plate system", recalibrate remaining weights in a such way that the center of mass should be on central cell (or center of the plate). But there is a restriction - While recalibrating, I do not want drastic changes on remaining weights. Assigning symmetrical weights to 0 would balance the system but that's not what I want. The reclibration should be reflected to many weights instead of focusing on just 1. As suggested on the image I uploaded. We could increase the weights at some side, or decrease from otherside. Or both of them for a more evenly distributed weight change. Now, this is some sort of optimization/graph-search problem and can be solved with AI algorithms. However, that's not what I want for various irrelevant reasons. Question: Is it possible to achieve such recalibration with trivial functions (linear etc.)? If so, can you give me some information or insight about the solution.