From the Super Mario Wiki
Mechakoopa is a character in Mario Party Advance. According to his description, he works at the Mushroom Library and often gets lost in thought. He is found at the library, engrossed in a book. When approached, he introduces himself as a mathematician, and boasts that he discovered Mechakoopa's Theorem. He then sets up a quiz of sorts: if the player correctly answers his three questions (all of which relate to math), they receive a Gaddget. If all three of the questions are answered correctly, he ecstatically praises the character as a genius before giving them the Castle Night Gaddget. He states that this Gaddget, among many others, recently fell out of the sky, and he hopes that the player can help clean up this mess. The ending credits state that he spends all of his time trying to write a new mathematical theorem.
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