Goal: Turn off all the lights by clicking a sequence of boxes. Clicking a box will toggle the light plus any light to the left, right, above, and below. You can generate a solution at any time.
The solution is generated by solving a system of equations modulo 2. For example, a 3x3 grid will require you to row reduce a 9x10 matrix to find the solution. A 5x5 requires a 25x26, 6x6 requires a 36x37. In general, a nxn grid requires row reducing a n^2 x n^2+1 matrix modulo 2.