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Pros
Pro Teaches logic in an approachable fashion
Each puzzle is a logic exercise, most utilizes the difference in appearances of the zoombinis (in a "guess who" fashion). Others are more varied, like process of elimination (guess what the gatekeepers want on their pizza), state machines (get the zoombinis through the active maze), etc. Most puzzles are very intuitive, yet all require a logic based approach to succeed.
Pro Various logic puzzles
Pro Great for teaching logic to young children
Although parental guidance is better than kids just "punching their way out of a paper bag", the puzzles are fun and engaging, and simple to explain. This creates a perfect environment to teach children deductive reasoning.
Cons
Con Might become too difficult for very young children
Although the puzzles have simple solutions at the beginning, each round/playthrough, the difficulty increases. The difficulty increases the farther you progress. Becomes quite challenging after a while, so younger children may struggle.