The Riddle That Seems Impossible Even If You Know The Answer
Veritasium・14 minutes read
A mathematical strategy involving loops increases the chance of success for 100 prisoners finding their numbers in boxes to nearly one in three, with a 31% success rate. The strategy ensures that all prisoners have an equal chance of success, highlighting the importance of linking everyone's outcomes together in the process.
Insights
- Following a loop strategy significantly increases the chance of success in the prisoner number finding scenario to around 31%, far better than random guessing.
- The loop strategy in the prisoner number finding scenario ensures equal chances for all prisoners, emphasizing the interconnectedness of their outcomes and the importance of a systematic approach over random guessing.
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Recent questions
How do prisoners increase chances of success?
By following loops to find their numbers.
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Summary
00:00
"Prisoner Loop Strategy Boosts Success Odds"
- A riddle involves 100 prisoners searching for their numbers in boxes to avoid execution.
- If each prisoner searches randomly, the chance of success is extremely low at 0.00000000 30 zeros and an eight.
- A mathematical strategy involving following loops increases the chance of success to nearly one in three.
- The strategy entails prisoners following loops to find their numbers, with a 31% chance of success.
- The length of the loop determines success, with a 69% chance of failure if the loop is longer than 50.
- The probability of success is calculated based on unique loop arrangements, resulting in a 31% success rate.
- The loop strategy ensures that all prisoners are more likely to find their numbers than by random guessing.
- The strategy relies on the guarantee that starting with a box containing a prisoner's number will lead to success.
- A sympathetic guard can ensure success by swapping contents of two boxes, breaking longer loops.
- Increasing the number of prisoners does not significantly impact the probability of success, with a limit around 30-31%.
14:41
Prisoner Number Finding Strategies: Calculations and Outcomes
- The probability of success in the prisoner number finding strategy is calculated using the integral of one over X from n to 2n, resulting in a probability of success of one minus the natural log of two, approximately 30.7%.
- The loop strategy in the prisoner number finding scenario ensures that all prisoners have an equal chance of success, with the outcome being either 100% success or complete failure, emphasizing the importance of linking everyone's outcomes together in the process.
