Any algorithm for "Flip all" (Light Out) game? [duplicate]

Question

in this game: http://www.mathsisfun.com/games/allout.html The solve function can solve any case, no matter how you "abuse" the original board. Please tell me the algorithm for solving this game. I have tried to think for days but still found no clue to solve all cases.

OK, after read some answers and comments (and have a quick look at Light out game), I expand my question:

Will the game different if I expand the size of the grid (like to 25x25)? Still any possible algorithm to solve any case, in acceptable time (< 2s)?

Answer 1

This game is more commonly known as Lights Out, and has a number of elegant solutions, all based in some standard but somewhat advanced mathematics. I won't describe them all here but if you Google a bit you can find all kinds of explanations varying from straightforward procedures to transformations into linear algebra or group theory. A few links:

http://www.hamusutaa.com/pilot/solution.html

http://www.ripon.edu/academics/macs/summation/2010/articles/M.%20Madsen%20-%20Lights%20Out.pdf

http://people.math.sfu.ca/~jtmulhol/math302/notes/24-Lights-Out.pdf

Edit: Re: your second question. The algorithm presented in the second link I posted can solve an n x n board in O(n^6) time, meaning you should be able to quickly solve a 25 x 25 board.