He has a magic sword that can, in one stroke, chop off either one head, two heads, one tail, or two tails.

This dragon is of a type related to the hydra; if one head is chopped off, a new head grows. In place of one tail, two new tails grow; in place of two tails, one new head grows; if two heads are chopped off, nothing grows.

What is the smallest number of strokes required to chop off all the dragon's heads and tails, thus killing it?

Oh nate, I think Larry was kidding when he said the prince was going to jail. (But thanks for endorsing my 6-stroke solution as the "correct" answer. That makes one of us who does.)

By the way, dragons do exist on the island of Sumatra. They are called "komodo dragons".