Can you solve the prisoner hat riddle? - Alex Gendler

Summary

In a hypothetical scenario, ten individuals are captured by aliens who plan to eat them unless they can demonstrate logical cooperation. The aliens test them by placing them in a line with either black or white hats and requiring them to guess their own hat color without communication. The solution involves the first person to use 'black' or 'white' to indicate the parity of black hats seen, enabling the others to deduce their colors. This strategy, despite a 50% chance of the first person guessing wrong, ensures the survival of the group by logical deduction based on parity.

Takeaways

• 👽 Aliens have captured 10 individuals and are considering eating them, but have a rule against eating highly logical and cooperative beings.
• 🧢 The captives are lined up in a single file with hats of either black or white color, without knowing their own hat color.
• 🚫 The captives are not allowed to look behind or communicate in any way other than guessing the color of their hat.
• 🔢 The aliens will spare the captives if at least nine of them guess the color of their hats correctly.
• ⏱ The captives have five minutes to devise a strategy to maximize their chances of survival.
• 📣 The first person in line can see all the other hats and will use the color 'black' or 'white' to communicate coded information.
• 🔑 The coded information is the parity (odd or even) of the number of black hats, which is the only piece of information needed for the strategy.
• 🤔 The strategy involves each person deducing their own hat color based on the parity information and the number of black hats they see in front of them.
• 🎩 The first person has a 50% chance of guessing wrong about their own hat but provides crucial information for the others to guess correctly.
• 🔄 Each subsequent person in line adjusts their expected parity based on the information given by the previous person and what they observe.
• 🏁 The strategy ensures that, except for the first person, everyone else can determine their hat color with certainty, thus saving the group.

Q & A

What is the situation presented in the video script?

In the script, ten individuals have been captured by super intelligent aliens who are considering eating them but need to determine if they are logical and cooperative enough to be spared.

Why does the alien civilization forbid eating highly logical and cooperative beings?

The script does not provide a specific reason, but it implies that the aliens have a moral or cultural code that respects the intelligence and cooperation of certain beings.

What is the test the aliens have decided to give the captured humans?

The test involves the humans standing in a line, each wearing a randomly assigned black or white hat, and guessing the color of their own hat based on the colors visible in front of them without any communication other than a single word.

Why is communication limited to only the words 'black' or 'white'?

Any other form of communication, including signals through intonation or volume, would result in the immediate execution of all humans, as per the rules set by the aliens.

What is the goal of the humans in this test?

The goal is for at least nine of the humans to guess the color of their hats correctly to ensure that all of them are spared from being eaten by the aliens.

What strategy is suggested by the script to solve the problem?

The strategy involves the person at the back of the line using the words 'black' or 'white' to communicate the parity (odd or even) of the number of black hats they see, which allows the others to deduce their own hat colors.

Why is the parity of the number of black hats a key element in the strategy?

Parity has only two possible values (odd or even), which fits the limitation of using only two words to communicate, and it provides enough information for the others to deduce their own hat colors.

What is the role of the first person in the line regarding the strategy?

The first person in the line is expected to communicate the parity of the black hats they see, which sets the expectation for the rest of the line to deduce their own hat colors.

How does the strategy ensure that all but one person can determine their hat color correctly?

By using the parity information and the expectation of odd or even counts, each person can determine their hat color with certainty unless their count doesn't match the expected parity, indicating that their hat is the color that makes the count match.

What is the expected outcome if the strategy is executed correctly?

The expected outcome is that nine people will guess their hat colors correctly, and one person (the first in line) may guess incorrectly, still meeting the requirement to be spared by the aliens.

What does the script imply about the aliens' perception of logic and cooperation?

The script implies that the aliens value logic and cooperation to such an extent that they are willing to spare beings who demonstrate these qualities, even if it means going hungry.