The Riddle That Seems Impossible Even If You Know The Answer

Veritasium2 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.
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