The Counterintuitive 100 Prisoners Riddle: A Mathematical Breakthrough

You've likely encountered brain teasers that twist your mind in knots, but this riddle is a real head-scratcher. It's a scenario so counterintuitive that even when you know the answer, it still feels wrong. Imagine a challenge where the odds are seemingly insurmountable, yet a clever strategy flips the game on its head. Are you ready to dive into the world of probability and mathematics where a twist of logic can change everything?