There is a variety of popular puzzles having a goal of reducing an arbitrary binary matrix to either all “0” or “1” matrix. In this paper we study methods for solving “Flip-Flop” like puzzles of dimensions 3x3, 3x4, 4x4 applying tools of logical analysis of situations, combinatorics and discrete mathematics. We found that applying the method of sequential analysis of each combination that works well for 3x3 matrices is cumbersome and inefficient for matrices of 4x4 and higher dimensionalities. Therefore, we discovered and analyzed algorithms named trait selection method, stream method and snake method which work better. We concluded that in order to find an optimized solution it is helpful to check if each current combination matches one of the pre-final ones, or to swap «0»s with «1»s and vise versa.