how did you derive this solution?

thanks, it is approved

interesting kata, i was able to solve it quickly with brute force in python, don't know if that's intended.
Here is a great explaination how a more efficient algorithm works.
https://math.stackexchange.com/a/2804461/186763

one of the few solutions that optimize performance by stopping as soon as the element is found

Added the hint about the origin. Thanks for the suggestion!

thanks for your interst in the kata.
Maybe i misunderstand something. The solution in the description for the complex case works. clicking it through on the sketch you provided solves the puzzle, and it is accepted by the solution checker in the test cases. Maybe you confused x and y axis?

regarding the test output, yes it indeed seems there was a mistake there, since the check_solution function modified the grid. fixed, thanks!
As for your solution, it seems to be indeed false. I created a fork of the interactive version to display this grid: https://openprocessing.org/sketch/1540470, the issue should become clear then.

I am not testing for a certain solution, i just verify if the given solution works.
Here's what's in preloaded:

def _cross_indices(x, y, w, h):
        return {(i, y) for i in range(w)}.union({(x, i) for i in range(h)})
def _toggle(grid, x, y):
    for ix, iy in _cross_indices(x, y, len(grid[0]), len(grid)):
        grid[iy][ix] ^= 1
def check_solution(grid, solution):
    grid = copy.deepcopy(grid)
    for x, y in solution:
        _toggle(grid, x, y)
    return all(all(val == 1 for val in row) for row in grid)

not fully specified and insufficiently enforced.
my solution to just replace all duplicates in a loop passed after a few tries.

Added sample tests. How do i enable Node 12?