How do prisoners increase chances of success?

Name: The Riddle That Seems Impossible Even If You Know The Answer
Uploaded: 2024-05-14T18:39:12.772Z
Description: 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.

By following loops to find their numbers.

The Riddle That Seems Impossible Even If You Know The Answer

Veritasium・2 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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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.