52 Factorial
4 hours ago
- The number of possible arrangements of a standard 52-card deck is 52! (factorial), a number so large it exceeds most common scales of magnitude.
- Calculating 52! manually or on standard calculators is impossible; even 12! exceeds typical calculator limits, illustrating the rapid growth of factorials.
- A random shuffling of a deck, with 52 choices for the first card, 51 for the second, and so on, results in 52! total permutations, approximately 8.0658e67.
- To grasp 52!'s enormity, a thought experiment involves walking the Earth's equator (40,075,017 meters) at one step per billion years, removing a drop from the Pacific Ocean (707.6 million km³) per circumnavigation, and repeating until the ocean is empty, then stacking paper to the Sun (149,597,870.691 km), repeating 1000 times, yet the countdown would barely progress.
- Further analogies include dealing poker hands (royal flush odds: 1 in 649,740) every billion years, winning lottery jackpots, and moving sand to fill the Grand Canyon, then removing rock from Mt. Everest (357 trillion pounds), repeating 255 times, still leaving billions of years—the timer would reach zero only during the 256th repetition.
- In reality, such time spans are impossible due to cosmic events: the Sun's red giant phase boils away the Pacific Ocean before the first steps are complete, and all stars eventually burn out, making the universe a dark, near-absolute-zero void.
- The author concludes the exercise is purely theoretical, as physical limitations (like stellar evolution and heat death) preclude any actual implementation of these analogies.