Ten frogs perch in a line along a fallen branch, all facing the same way. The heron sets a cap on each, green or brown at its whim, so that every frog can see the caps of all the frogs ahead of it, but never its own and never any behind it.
Starting from the very back, each frog in turn must croak a single word, green or brown, guessing the colour of its own cap. The heron eats any frog that guesses wrong, and every frog hears each croak as it is made.
The frogs may agree on a plan beforehand but may not signal in any other way. With the cleverest plan, how many of the ten frogs can be saved for certain?