The Last Hat Signal

Ten prisoners are placed in a single-file line. Each is given either a black hat or a white hat. Everyone can see the hats worn by the people ahead, but nobody can see their own hat or any hat behind them. Starting with the prisoner at the very back, they must each say either “black” or “white.” Every answer is heard by the others. A correct answer means survival; a wrong answer means death. Before the hats are placed, the group may agree on a strategy, but once lined up they may communicate only through their required answers. What is the greatest number of prisoners they can guarantee will survive, regardless of how the hats are arranged?