From the Super Mario Wiki
Battle Trunks are a type of clothing in Paper Mario: The Thousand-Year Door. After Mario takes on Jolene's trouble, he discovers that twenty of these smelly shorts litter the storage room in the Glitz Pit. As such, Mario has to pick them up, then deliver them to Goomfrey, the Goomba outside of Professor Frankly's house in Rogueport that Goombella said is the kind of person who can make problems disappear, and then return to Jolene to complete the trouble and get a 30 coin reward.
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