Trianglia is a jacked-up island where no road has a dead end, and all the crossroads are "Y" shaped.
The young prince of Trianglia mounts his horse, and is about to go on a quest to explore the land of Trianglia. He gets to the road by his palace, when the mother queen comes out and shouts:
"But Charles, how will you find your way back?".
"Don't worry Elizabeth", the prince replies, "I will turn right in every second crossroad to which I arrive, and left otherwise. Thus I shall surely return to the palace sooner or later."
Is the prince right?
(In reply to re: Solution
[LeviK] I wonder if the same logic applies in the case where he would only be making left (or right) turns all the time. Or any kind of a deterministic turning behavior.
The key is that the state transition function be reversible. Examples of reversible functions include always left (or right), alternation, left iff the angle between any 2 of the 3 roads is less than 90 degrees, etc.
Non-reversible functions include: take the northerly-most route that I didn't come in on, take the first 10 lefts then all rights, etc.
Posted by Jim Lyon
on 2002-09-12 05:48:23