June 13th, 2006

quadrum

Puzzle 33: Ariadne's Lament


You've probably seen one of these before in a toy store:



They're universally called "Labyrinth", and they are a game of skill: rotating the knobs on the sides tilt the playfield, the task being to maneuver the marble from "Start" to "Finish" in only that manner and without the marble falling into any of the myriad of holes along the way. They're manufactured in many sizes and difficulty levels by a number of different companies. Microsoft Windows XP Plus! comes with an excellent computerized version.

Anyway, Nikoli has this clever and very entertaining puzzle (my absolute favorite among their offerings!) named Yajilin - "arrow link", or Arrow Ring for those who "attended" last year's United States Puzzle Championship - whose solutions look so much like one of these to me that I decided to break the ring and put in a "start" and "finish" to get the logic-puzzle version of the classic game. Throw in a title that alludes to 'labyrinth', and the metamorphosis is complete - without further ado, I bring you Ariadne's Lament:



Unsolved sample on left, unique solution on right.

Condensed instructions would, like The One Ring, not be terribly condensed, so I'll skip straight to the list:

1) The objective is twofold:
- 1a) determine for each dot if it is a "pit" or if it's "open" (I suggest shading in pits and marking open dots with a smaller dot);
- 1b) to create a linear path of "edges", each edge connecting two orthogonally adjacent open dots, that travels from the 'S' (start) to the 'F' (finish) and uses ALL open dots EXACTLY ONCE and NEVER uses a pit. I call this path the "thread", and it's essentially the way out of the maze - like the black path on the labyrinth game, it connects start to finish without encountering any holes.
2) The dots marked 'S' and 'F' are open (natch).
3) The thread may not touch or cross itself at any point. This means the 'S' and 'F' dots will have exactly one edge incident on them, and all other open cells will have exactly two edges.
4) All the edges must be unit-length (so you can't draw an edge through spots where dots are "missing" from the otherwise evenly-spaced grid).
5) Number/arrow pairs - "signs" - appear where dots are missing. Each number is the quantity of pits pointed at by, and directly aligned with, its arrow. These signs, not unlike the arrows in Stargazers, "see" right through each other, straight on through to the edge of the grid.
6) No two pits may be orthogonally adjacent to each other (that is, one edge-length apart).

The sample serves the job of introduction rather nicely; if you're finding it a bit tricky, I'll show you what to look for:

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This is my first attempt at creating one of these - I actually made this before the sample - and I must say, I really like how it came out. It's fairly challenging. I ran into a few snafus putting it together, but it was educational. I'm glad I can pull these off. Any questions or comments about the rules or design can be posted here; email me your solution and whether or not you own a working NES and I'll check your solution and maybe offer a prize. Maybe. - ZM