Captives are presented with a logic test by aliens who cannot eat highly logical beings.

• Ten individuals are captured by aliens who find humans tasty but cannot consume logical beings.
• The aliens are uncertain about humans' logical abilities and offer a test to prove their capacity for logic and cooperation.

The aliens explain the rules of the test that will determine the captives' fate.

• The captives will be lined up in size order, unable to see behind them or leave the line.
• They will each have a randomly assigned black or white hat and must guess its color when prompted, without using signals or words other than 'black' or 'white'.
• If at least nine captives guess correctly, they will be spared; otherwise, they will be eaten.

The captives must devise a strategy that uses limited communication to save themselves.

• The captives have five minutes to discuss a plan using the limited communication allowed by the aliens.
• The key to the strategy lies in the first person's ability to see all other hats and communicate coded information.

The solution centers on using the parity of visible black hats to inform the others.

• The solution is to use the first person's statement to indicate the parity of the number of black hats he sees.
• By saying 'black' or 'white', the first person conveys whether the number of black hats ahead is odd or even, allowing others to deduce their hat color.

The captives apply the agreed-upon strategy to determine their hat colors.

• The tallest captive starts by indicating the parity he observes, sacrificing his chance to guess correctly.
• Each captive uses the parity information and the previous guesses to deduce the color of their own hat.

The strategy ensures the captives' survival, demonstrating their logical prowess.

• The strategy proves successful as it allows each captive, except the first, to guess their hat color with certainty.
• The parity rule ensures that the aliens cannot eat the captives due to their logical and cooperative behavior.