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Intelligence determines how well your character learns and reasons. This ability is important for archmages, assassins, and wizards because it affects how many spells they can cast, how hard their spells are to resist, and how powerful their spells can be. It’s also important for psions because it affects how many powers they can know, how hard their powers are to resist, and how powerful their powers can be. It’s also important for any character who wants to have a wide assortment of skills.
You apply your character’s Intelligence modifier to:

An assassin, archmage, or wizard gains bonus spells based on her Intelligence score. The minimum Intelligence score needed to cast an assassin or wizard spell is 10 + the spell’s level.
The minimum Intelligence score needed to know a psionic power is 10 + the power’s level.
An animal has an Intelligence score of 1 or 2. A creature of humanlike intelligence has a score of at least 3.
A character does not retroactively get additional skill points for previous levels if she increases her intelligence.