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