PowerUp in easy mode can be solved in under a minute once you're good at it. Hard mode (with wrap on) takes about 5 minutes. So you can squeeze in a game pretty much anywhere.
PowerUp generates a fresh puzzle randomly every time you tap on the play button, so that you have an infinite supply of new puzzles.
Puzzles are generated by first creating a random solution and then messing up the tiles. So yes, every single puzzle you are faced with does have a solution... so keep trying.
FOUR LEVELS OF DIFFICULTY
Start with the learn mode (3x3 tiles) to get the hang of the puzzle. Graduate to easy (5x5), then medium (8x8) and finally hard (10x10).
ADD WRAPPING FOR EXTRA HARDNESS
Turn on wrap mode and now power flows off one edge and back to the corresponding tile on the other side. This makes the puzzle about twice as difficult to solve.