Ten Earthlings are abducted by aliens and lined up in single-file.
Each Earthling is given either a purple or green hat.
No one can see their own hat - they can only see the hats of the Earthlings in front of them.
Starting with the Earthling at the back of the line, each Earthling has to state correctly the color of his/her own hat, otherwise will be blasted by the aliens.
The Earthlings can only say “purple” or “green” (no intonations or saying it loudly or whatever).
The Earthlings are given ten Earth minutes to discuss a strategy.
How can at least nine Earthlings be saved?
The 10 Earthlings are P1 to P10 with P1 being at the back.
Each Earthling can hear:
1. The others say their color.
2. The blast event - no blast means the correct color was said for survival. This is significant for P3 to P10.
P1 looks ahead at the 9 Earthlings in front of her and says purple/green to convey an even/odd number of greens in P2 to P10.
P2 says purple/green to make an even/odd number of greens in P2 to P10 as conveyed by P1.
P3 says purple/green to make an even/odd number of greens in P3 to P10 as conveyed by P2.
And so on.
P1 may or may not survive but conveys an even/odd number of green hats in P2 to P10. P1 risks her life for the group.
P2 knows there are an even/odd number of green hats in P2 to P10 as conveyed by P1. P2 looks ahead at P3 to P10 to determine the hat color of self. The even/odd number of green hats beyond P2 (from P3 to P10) which P2 sees is known to others when P2 correctly declares its own color. If P2 says green, it means P2 sees the opposite of the P1 conveyed even/odd; if P2 says purple, it means P2 sees the same even/odd as conveyed by P1.
P3 knows the hat color of P2 as correctly declared (no blast, P2 survived). P3 knows the even/odd number of green hats from P3 to P10 (as explained in previous paragraph). P3 looks ahead at P4 to P10 to determine the hat color of self.
P4 through to P10 repeat the same method as P3 - relying on the hat color of the person immediately behind and the even/odd number of green hats from self to P10 (as explained above).