Logan pleads his case to Rory and asks her to come home with him; Luke tells Lorelai that April has asked him to chaperone her math team's trip to Philadelphia for a national contest; Zack asks Mrs Kim's permission to marry Lane, but she has a demand he must meet first; Rory shops at Anna's store to see what she's like; and Lorelai hears some disturbing news about a big step her parents are planning.