Imagine you have a $8 \times 8$ completely white field of squares on your screen. Now you can click on any square. When you do this, all the squares in that column and line (including the one you clicked on it) will change their color (if it's white it will be black and vice versa). How many steps at least would it take to create a standard chessboard?
I tried it manually but it got too complicated and I lost track of the situation. But if I could tell my problem to Mathematica it could be very easy. Is there a way to write code to calculate this? Or even a formula to do this manually without any program?
Best Answer
Hint: Try to convert your problem into solving a $64 \times 64$ system of linear equations over $\mathbb{F}_2$.