Разгадка, в которую невозможно поверить: задача о 100 заключённых [Veritasium]

Vert Dider・2 minutes read

A strategy involving a specific sequence of opening boxes increases the overall success rate of prisoners finding their numbers to 31%, ensuring that all prisoners in the same cycle have an equal chance of success or failure. This interconnected probability scenario guarantees that either all prisoners succeed or all fail, with the success rate remaining above 30% regardless of the number of prisoners involved.

Insights

  • The strategy introduced in the scenario significantly increases the chances of success for all prisoners, reaching a 31% success rate by following a specific sequence of opening boxes based on numbers found.
  • The success of the strategy hinges on closed chains of boxes, where the length of the chain determines the outcome, with a calculated 69% probability of failure and 31% probability of success due to cycle limitations.

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Recent questions

  • How do prisoners increase their chances of survival?

    By following a specific sequence of opening boxes.

  • What is the success rate of the introduced strategy?

    31%

  • What determines the success or failure of the strategy?

    The length of the closed chains of boxes.

  • How does the strategy ensure equal chances for all prisoners?

    By connecting individual success chances based on box layout.

  • What is the probability of failure in the scenario?

    69%

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Summary

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"Prisoner Box Strategy Ensures Collective Success"

  • The scenario involves hundreds of prisoners entering a room one by one to find a box with their number hidden among randomly placed boxes.
  • If all prisoners find their numbers within 50 attempts, they are released; otherwise, all are executed.
  • The initial probability of success for each prisoner finding their number is extremely low, akin to finding the same grain of sand on all beaches.
  • A strategy is introduced where prisoners follow a specific sequence of opening boxes based on the numbers found, increasing the overall success rate to 31%.
  • The success of this strategy relies on the concept of closed chains of boxes, with the length of the chain determining success or failure.
  • The probability of failure is calculated to be 69%, while the probability of success is 31% due to the limitation of cycles longer than 50 boxes.
  • The strategy ensures that all prisoners in the same cycle have an equal chance of success, either all succeeding or all failing.
  • The probability of success remains above 30% regardless of the number of prisoners involved, even reaching close to 31% with a billion prisoners.
  • The strategy connects the individual chances of success for each prisoner, ensuring a collective success or failure based on the layout of the boxes.
  • Ultimately, the strategy guarantees that either all prisoners succeed or all fail, creating a unique and interconnected probability scenario.
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