Lord_Enki said: never understood how she got the first set of colors though.
In the doujin (hosted here on the site) called Passion For Your Sake, Alice claims to have mastered the seven elemental disciplines practiced by magicians -- the same ones that Patchouli mastered. Sun, Moon, Fire, Air, Earth, Water, Wood. In that doujin, Marisa had only mastered Fire and Sun, which matches the canon that her magic is almost entirely about producing heat, light, and extremely offensive attacks.
Patchouli took her mastery of all seven elements so far that she could combine each of the elements with any of the other six, and produce the Philosopher's Stone by mixing five of them. Since each element is associated with a day of the week (Sunday, Mo(o)nday, Fireday), this all-encompassing mastery earned her the title "One-Week Magician".
Alice didn't go that far, and instead devoted herself to puppetmastery. She's the "Seven-Colored Puppeteer" because she's an amazing puppeteer-magician who has mastered all seven elements.
"Nine Colored Puppeteer"I've come to destroy THAT.