Zoombinis pro tip: The game allows you to create up to two zoombinis of each hair/eye/nose/transport configuration. You can make things way easier by making your party consist of 8 twinned zoombini pairs as opposed to the usual 16 distinct zoombinis. (For puzzles that depend on zoombini features, which is pretty much all of them, the solution for a given zoombini and it's twin will be the same.)

I love how the game's wikipedia page has a fairly detailed explanation of every puzzle...