What's the catch? Clicking a cell will not only flip its color, but also that of all cells sharing the same row or column as it.

To me, this game feels like playing with a Rubik's cube --- every time you think you are fixing one cell, you mess up its neighbors!

There are many ways to arrive at a solution... some mathematical (linear algebra, or combinatorics), others more logical,... and yet others which are brute force.

Try it out and let me know how you do!