The Riddle That Seems Impossible Even If You Know The Answer

TL;DR

The 100 prisoners riddle presents a seemingly impossible probability problem, but a mathematical strategy involving loops increases their chances of success to nearly one in three.

Transcript

There is a riddle that is so counterintuitive, it still seems wrong even if you know the answer. - You'd think it's an almost impossible number. - I feel like you probably hit me with some truth bomb. - I mean, if you're trying to create controversy and you're trying to confuse people, you're gonna succeed. (both laughs) - There are a bunch of YouT... Read More

Key Insights

• 😘 The probability of success for the 100 prisoners is extremely low (0.0000000038%) if they search randomly.
• 🍱 The loop strategy increases their chances to 31% by following the numbers in the boxes.
• 🔁 The length of the loop determines whether a prisoner finds their number or not.
• 💋 Renumbering the boxes redistributes the slips and brings the probability back to 31% if a malicious guard arranges a long loop.
• #️⃣ As the number of prisoners increases, the probability of success remains around 30.7%.
• 🍻 The loop strategy links everyone's outcomes, resulting in either complete success or failure.

Questions & Answers

Q: What is the best strategy for the 100 prisoners to find their numbers?

The best strategy is for each prisoner, when entering the room, to open the box with their number and continue following the numbers in the boxes until they find their slip. This increases their chances of success to 31%.

Q: How does the length of the loop affect the prisoners' chances of finding their numbers?

If the loop is shorter than 50, the prisoners will find their number. But if it's longer, they won't have enough boxes to search and will fail to find their numbers.

Q: How does renumbering the boxes affect the prisoners' chances of success?

Renumbering the boxes essentially redistributes the slips, resulting in a random arrangement of loops. This brings the prisoners back to their 31% chance of survival.

Q: What happens if there is a sympathetic guard or a malicious guard in the room?

A sympathetic guard can guarantee success by swapping the contents of two boxes, breaking any loop longer than 50. A malicious guard who arranges the numbers to form a loop longer than 50 can be counteracted by arbitrarily renumbering the boxes, returning the probability of success to 31%.

Summary & Key Takeaways

• The riddle involves 100 prisoners searching for their own numbers in 100 boxes. If even one prisoner fails, they will all be executed. Randomly searching gives them a 0.0000000038% chance of success.

• However, by using a loop strategy, where prisoners follow the numbers in the boxes, their chances of success increase to 31%.

• The length of the loop determines whether prisoners find their numbers or not. If the loop is shorter than 50, they will find it, but if it's longer, they won't have enough boxes to search.

• The probability of finding a loop longer than 50 is 69%, meaning there is a 31% chance of success using the loop strategy.