Aliens capture ten humans and imprison them on their spaceship. They will all be killed the following day unless they complete a task successfully. The task is explained to them and they have until the following morning to devise a strategy to complete it successfully.
The task is this.
They ten people will be lined up in height order, with he tallest at the back and the shortest at the front. The person at the back can see the other nine people and the person at the front can see no one. The aliens will then place a black hat or a white hat randomly on the heads of the ten people.
Starting with the person at the back, each person must call out the colour of their hat. They can say nothing except the word Black or White.
To complete the task successfully, at least nine of the ten people must get their hat colour correct - two failures and they will all die!
Can you devise a strategy to ensure that the humans survive?
The person at the back can see nine hats, and so there will be either an odd number of black hats or an odd number of white hats. This person calls out the colour of the hats of which there are an odd number. This has a 50% chance of being correct for that person's hat.
However, the second person can deduce their hat colour from the number of that colour hats that they can see. And by keeping track of the successive guesses everyone can deduce their hat colour.