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?

Chopping off one head does nothing. That shouldn't be considered in the solution of this problem. The problem needs to end with chopping off two heads. Just the same, since removing one head is irrelevant, we can concentrate solely on tails until we have no tails and an even number of heads.

The most direct way (I can see) is to chop off one tail three times, followed by two tails three times, followed by two heads three times. My guess would be that these three things can be done in a bunch of different ways.

Edited on December 10, 2004, 4:52 pm

Posted by Eric on 2004-12-10 15:01:10