Guess a moon and see the placement of the correct answer relative to it, and then go from there.
List of possible answers, in order of size: Ganymede Callisto Io Europa Amalthea Himalia Thebe Elara Pasiphae Carme Metis Lysithea Sinope Changelog 1.1: Added Carme, fixed Lysithea's spelling. 2: Added glow, and an indicator for the moons you have guessed so far. 2.1: List is ingame now.