Prince Valiant went to fight a 3-headed, 3-tailed dragon.

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?

I agree that 9 is the "correct" answer, but consider this:

In 3 cuts, you can render the beast headless, and with only one tail (cut 2 tails, then cut 2 heads, then cut 2 heads).   Clearly we have at this point not yet satisfied the sentence: "What is the smallest number of strokes required to chop off all the dragon's heads and tails, thus killing it?"

But how could an animal live without any heads?  I couldn't eat, so would it not eventually die?  Further, since this is an endangered species, wouldn't Prince Valiant face serious prison time?

Posted by Larry on 2004-12-10 16:03:43