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 Trianglia (Posted on 2002-09-11)
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?

 See The Solution Submitted by levik Rating: 4.0000 (5 votes)

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 re(2): Solution | Comment 7 of 9 |
(In reply to re: Solution by levik)

I'd been stuck on the possibility of a loop that did not include the first leg of the journey, myself.

Once Jim pointed out the reversibility of the journey, it all fell into place: If I am taveling south on Road A from Junctin M to Junction N, and I intend to turn right at Junction N, then I must have turned left at Junction M therfore coming from Road Z going west, etc. In order to be on a loop with a tail, some condition must have allowed me to make a right turn onto Road A from Road B at Junction M, and still be planning a right turn at Junction N

It becomes obvious that if I am on a loop, I have always been on that loop. If I am not on a loop, I'll never find myself on one. Since there are only a finite number of roads, R (and as Jim pointed out, the total state description only needs two other either-or factors for a total of R' = 4R states, you must loop at some point, so you begin on the loop and will eventually arrive back at your starting point.
 Posted by TomM on 2002-09-12 08:21:08

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