Lights Out on Different Sized Grids

There doesn't seem to be any particular reason that Tiger chose to base Lights out on a grid of 5x5 buttons, except perhaps that any smaller size makes for quite a simple game! Lights Out can easily be generalized to play on any size grid, from 2x2 upwards - and indeed if you can get hold of Lights Out Deluxe, you can play on a 6x6 grid.

In fact, the choice of 5x5 grid for Lights Out causes some problems, since not all configurations of lights are solvable. In fact, only a quarter of all possible puzzles can be solved. But what about other sizes? Well, if you know the maths you can obtain the following table

So, from the above table, you can see that the 6x6 choice of grid for Lights Out Deluxe was a very sensible one, whereas a 19x19 grid would be awful (not that it wouldn't be anyway!)

But why stop at square grids? Lights Out can just as easily be played on rectangular grids (e.g. 4x5). I've calculated the results in the following table for these grids

I'm sure by now you're gagging to play Lights Out on a bigger (or smaller) grid. So here are some links

On-line Lights Out on Different Sized Grids

Jaap's Puzzle Page Javascript Lights Out that can play on any size grid (square or rectangular) from 2x2 to 10x10. The game is good, and the page is worth visiting anyway!
Eric Fuglister`s Java Lights Out Plays Lights Out on any board size from 2x2 to 24x36. However, there is only one puzzle available for each board (all lights are on at the start)