How to Play
Click on a square. It will change color, as will its neighbors. Keep clicking until all the squares are white.
The 'easy' level is quite easy and is really just to teach the rules. The harder levels have more squares and more colors.
All the games are winnable.
You can undo a move by repeating it until it returns to its original color.
How to Win
There are countless ways to win each game. You don't have to find the 'right' set of moves, just one that works. For example, if you have a sequence of moves that clears the puzzle, you make those moves in any order and it will still work.
The general strategy is to simplify the grid until you get to one of a few simple patterns that you know how to clear. You will not always get to the same simple pattern, you will have to learn to clear a few different ones.
I don't have any trouble with the 'hard' puzzles, but I can't win the 'abandon hope' level.
There is a hidden, for-your-eyes-only method to win by brute force. Click here if you know how to keep a secret.