Can you solve the prisoner hat riddle?

information

tags: Collaboration, Creativity, Memory
length: 4:24

Summary

You and nine other individuals have been captured by aliens. They think humans look quite tasty, but they forbids eating highly logical and cooperative beings.
So, they want test everyone is qualified. This exam is that everyone sorted by size order, and watch shorter person's head, execpt end. Each of you will have either black or white hat randomly. the each hat's count don't notice, and you can tell only black or white. When atleast 9 people guess correct, alien will not eat you. How can you guess your hat?

Answer is that tallest person can not notice everyone how many black hat is exist, but he can notice binary information that black hat's count is odd or even? When He said to that information, person front of him can know self hat color because, can see front persons hat and can know black is odd or not. If is not equal his information, can guess "my hat is black", vice versa.

Review

When i watch that i can understand first person can notice binary information. But, I cannot find answer that information is what have.
And, When I see answer of this problem, directly understand this problem's solution process.
It's funny. :)

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Reference

Can you solve the prisoner hat riddle?, https://www.ted.com/talks/alex_gendler_can_you_solve_the_prisoner_hat_riddle, Alex Gendler