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?
What if he turned right on every third crossroad (repeating two lefts and a right, two lefts and a right)? Then, isn't it possible that he could enter a loop on the first left turn, which came back to that crossroad on the second left turn, and get him stuck in a loop?
I know it's not in the problem, but I saw this 'old' problem in the Bonus section, and I wondered if it is true for any fixed pattern of moves..
Posted by Aaron
on 2004-03-07 00:01:58