You don’t. The trick is to take advantage of the fact that you, the author, exist outside the time constraints of the story.

Have your smarty-pants solve in one day a problem that took you all month. Have them learn in two months what took you two years. Have them know things offhand that you had to look up. Have them fire off snappy comebacks that took you a week to think of.

No need to pretend to knowledge you don’t have or give them nonsense Moffat brain magic.

All the logic is there. It’s just more impressive.