Once this realization came to light, it actually made a lot of sense. Our brains are designed to read patterns, and when something breaks that pattern a red flag goes off in our heads. By breaking the grids up into quadrants based on symmetry, we are easily able to distinguish which quadrant is the most problematic.
In the example above, you can clearly see that the bottom left quadrant is the most incorrect in comparison to the answer key. In fact, it is the exact inverse, so we can be reasonably sure that the tile we want to click is one of those four (it's the second column, third row ;) ). Because of this discovery, I divided the puzzles in each grid size into bins by symmetry and added this consideration to the puzzle generation algorithm.
This was a very useful discovery, especially for puzzle games! When making a game that involves patterns of any sort, whether it's pieces of a puzzle or ships flying at you, it's worth considering the symmetry of your design!