Build Your Own Nuri-Maze #3: Crossing Slitherlink
(Published on 22. February 2024, 14:43 by Myxo)
Another entry in my Nuri-Maze hybrid series. This one is potentially my toughest puzzle yet, because the ruleset has a couple of unusual implications. However, if the right way of thinking is found, the puzzle can be solved without bifurcation or heavy look-ahead. Enjoy!
Rules:
Crossing Slitherlink: Draw a single closed loop along the edges of the grid. The loop may cross itself, but not overlap itself in other ways. Numbers inside the grid indicate the number of adjacent edges that are used by the loop.
Nuri-Maze: Shade some cells to form a maze. Circles, triangles, S and G cannot be shaded. There can not be a 2x2 square of all shaded or all unshaded cells. For each pair of unshaded cells, there is exactly one path of edge-adjacent unshaded cells connecting them, i.e. all unshaded cells form an orthogonally contiguous area without any loops. There is exactly one path between S and G that doesn't require backtracking. Circles must be part of this path, while triangles must not.
Interaction: The loop divides the grid into regions. A region is either completely shaded or unshaded. Regions that touch the edge of the grid must be unshaded if they are inside the loop, and shaded if they are outside the loop.
Example for Build Your Own Nuri-Maze #3:
Build Your Own Nuri-Maze #3 (main puzzle):
Solution code: the number of vertical loop segments in each row from top to bottom
Comments
on 20. June 2024, 03:31 by Agent
Some really peculiar implications indeed!
on 15. March 2024, 11:29 by Silverstep
Incredibly rich genre, would love to see more. Did you take inspiration from an existing "Crossing Slitherlink", or is this an original invention?
on 28. February 2024, 07:26 by wisty
Another truly incredible deep dive from you! This was certainly one of my longest solves, but it is always fair and clean if one fully understands how crossing slitherlink affects slitherlink shading techniques. I struggled with the slitherlink scanning a lot more than the nuri-maze scanning, if that makes sense, but what looks like a minimal grid is in retrospect a maximal exploration of guiding the solver to the full implications of the ruleset and then putting their understanding to the test, without holding anything back! :)
on 26. February 2024, 14:34 by Myxo
added example puzzle
on 26. February 2024, 14:12 by Myxo
deutsche Regeln korrigiert
on 26. February 2024, 13:44 by Dandelo
Bezieht sich "Hinweise dürfen nicht geschwärzt werden." nur auf die Nuri-Maze-Hinweise oder auch auf die Zahlen?
Myxo: Das bezieht sich nur auf die Nuri-Maze-Hinweise, mir ist bei der Übersetzung ein Fehler unterlaufen. Die Regeln sind jetzt korrigiert.
on 22. February 2024, 20:00 by zzw
Amazing puzzle! After you work out the little bits of theory used here, everything fits together very well (the ending in particular made me smile). It's wild how few clues are needed too!
on 22. February 2024, 15:23 by filuta
quite unique and mostly fun puzzle even when you totally miss the intended way to approach in. great challenge in any case.
