My Lights Out app is based on the 1995 handheld electronic game by Tiger Electronics of the same name. In the 1995 version, the game board consists of a 5x5 grid of lights, and then when game starts, a seemingly random pattern of lights is presented to the player. The player's objective is to toggle lights to turn all the lights off with button presses, preferably in as few presses as possible.
When a light is pressed, the on/off state of the pressed light and all directly adjacent lights are toggled.
Although similar handheld games and apps already exists. There are two things that I believe make my app unique: variable board sizes, and mathematical optimization.
Variable Board Sizes
Many of the apps available today only feature a single board size, usually the classic 5x5. This makes the app less challenging once the user finds a reliable method for solving the single board size and limits the number of possible scrambles. For the 5x5 board, there are 223=8388608 distinct ways to create a scramble. However, there are at least 4 different ways to create any given scramble, leaving at most 219=524288 unique scrambles. All of these scrambles can be solved in at most 15 button presses.
My app allows user to play any board size from the trivial 1x1 to the daunting 10x10, providing orders of magnitude more unique scrambles than the 5x5 alone. I would have allowed even larges sizes, but the buttons were getting too small to reliably press.
In fact, just the 10x10 size has 2100, over 1 nonillion unique scrambles. For comparison, if each unique board were printed on a sheet of paper 0.1 mm thick, the stack of paper would reach to the edge of the observable universe 13.4 billion light years away.
Users have yet another dimension opened to them in being able to play by only pressing buttons that are already on. Although all puzzles that can be solved normally can also be solved by only pressing on buttons, it makes for a much more difficult challenge because the way that most learn to solve the 5x5 board requires pressing off buttons.
Mathematical Optimization
I already mentioned how any 5x5 board can be solved in at most 15 button presses. Puzzle enthusiasts and recreational mathematicians like Jaap Scherphuis proved this to be the case. Jaap in particular uses a method of treating solving the board as a linear algebra problem that is described by mathematician Marlow Anderson and Todd Feil in their 1998 paper Turning Lights Out with Linear Algebra.
I implemented Anderson and Feil's method of row reducing matrices modulo 2 to determine the minimum number of clicks needed to solve any given board. This way users can know how their solve is compared to the absolute best they could do.
Although this value is only one number on a screen, I think it provides valuable information to users about a given puzzle's difficulty and their own solving abilities that no other app has.
The app is currently available for free download on the Google Play Store. If you have an iOS device or would like to play on a PC, you can play an online version that doesn't have the minimum clicks implemented that I created using JavaScript. The Android Studio project, which includes the Java source code is available on GitHub.