Dual Slitherlink
(Published on 8. May 2020, 11:09 by Phistomefel)
Between the dots, two closed paths shall be drawn. The numbers in the cells indicate how many of the edges of a cell belong to the slitherlinks. None of the slitherlinks may cross or touch itself. There is an outer and an inner slitherlink, which neither touch nor cross each other.
In addition, there are exactly n cells in each column and each row, which lie between the outer and the inner slitherlink. The number n must first be determined. Here an example of such a puzzle:
In the upper example the number n=4. The cells lying between the two slitherlinks are colored in green, the rest of them in red.
The puzzle is also available online via Penpa Plus. Have fun solving!
Solution code: The sizes of all regions outside of the outer slitherlink in clockwise direction, starting at the bottom left corner. In the case of more-digit numbers please include all digits. In the example the solution code would be 3 4.
Comments
on 6. August 2024, 22:01 by filuta
loved it!!
on 29. May 2024, 01:09 by Piatato
Very nice!
on 2. December 2021, 23:01 by Phistomefel
@polar: Wow, solving all of my puzzles is quite an achievement. Thank you so much for this!
on 2. December 2021, 22:20 by polar
This had stood for quite a while as the last puzzle of yours I hadn't completed, since I lack far more experience in slitherlink puzzles.. I feel very chuffed to have finally logically completed it! Thank you :)
on 2. September 2021, 13:18 by dissonance
Interesting puzzle, definitely challenging.
Thanks for sharing.
on 21. August 2021, 18:50 by Phistomefel
Added tag "Online solving tool".
on 6. November 2020, 12:59 by Phistomefel
Added Penpa link.
on 17. July 2020, 07:54 by Phistomefel
@Alphish: Thanks a lot for your nice comment! I'm glad you enjoyed it.
If you are interested in more slitherlink puzzles with this n-cells constraint, you can try bernis's magic slitherlink which has this constraint without an inner loop. Here the link:
https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=00003K
on 16. July 2020, 19:41 by Alphish
That's a pretty curious take on Slitherlink.
Typical Slitherlink has a pretty localised logic, focusing on a small subset of clues at a time; the only exception is making sure the loop as a whole doesn't have loose ends or inner loops.
From that perspective, I really appreciate the n-cells constraint (i.e. each row and column must have the same number of cells between loop), as it introduces a more global logic. Adding the inner loop also works well together with this constraint. Well done. ^^
on 16. May 2020, 11:33 by Phistomefel
@Realshaggy: So it is possible! Thanks for sharing the puzzle. :)
on 15. May 2020, 20:40 by Realshaggy
You mean something like that?
https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=00003K
on 15. May 2020, 19:07 by Phistomefel
@ahaupt: It might be quite as interesting to include only one slitherlink with this constraint and this was in fact my starting point. Unfortunately, I did not manage to construct a slitherlink with that constraint. I tried it on smaller grids and failed, but maybe it was an oversight of mine or it is possible for larger grids.
on 15. May 2020, 18:28 by ahaupt
Very nice puzzle! I find it very interesting how one cannot apply uniqueness, like one can usually do in Slitherlinks when there are lone 2s in corners. The n per row/column rule adds more global constraints to the puzzle.
Maybe this variant would also be interesting without the second Slitherlink - just the n per row constraint.
on 9. May 2020, 07:20 by Phistomefel
Changed difficulty rating from average to hard.
