The Punctuality Paradox

You've known each other for years, ever since childhood, as cousins who spent summers together. Despite this, you've never seen eye to eye with 'The Punctuality Paradox,' as your family nicknames him. This individual is someone who has consistently let you down, being late for every family gathering without fail, which has always irritated you to no end. Today, however, is different. During a heated argument over his chronic tardiness, you both were mysteriously whisked away and locked in this room, with a sign that reads: 'Resolve or remain forever!'