This week a puzzle that we remember from our childhood, but if you have not heard it you might ponder it for a while. Nothing wrong with a good, old puzzle.
A man is living on an island covered in dry woods and grassland, and the island is a very close approximation to a circle. One day, with the wind blowing from the west a fire starts at the extreme west end of the island (shall we say it was caused by lightning) and soon a raging inferno is moving eastwards across the island. There is nothing to stop the fire spreading across the whole island.
The man has no means of extinguishing the blaze, can't jump into the sea (either very high cliffs with rocks at the bottom or sharks, depending on who is recalling this puzzle), has no boat, and no place like a cave to shelter.
How does he survive the fire?
Leaving aside the questions relating to how he is living on the island under these circumstances, he does have a means of escape.
He makes a firebrand from a piece of dry wood and grasses, ignites it from the leading edge of the flames, walks quickly to within 100 metres of the east end of the island, and starts another fire. As this second fire burns towards the end of the island he takes refuge there from the original fire.