04:15 Yes, as you know, if the time shows 3:45 and it's 15 minutes slow, we would add those 15 minutes to 3:45, which would be 4:00. However, if the actual time is "a quarter past the hour" after 4:00, then the correct time must be 4:15. "A quarter past" means 15 minutes past the hour. Therefore, the correct time based on that cryptic birthday riddle clue would be 04:15.