Negative Caving
(Published on 11. December 2020, 10:00 by Mark Sweep)
Cells have to be shaded to create cave walls, such that these walls are orthogonally connected to the edges of the grid. At the same time, the unshaded cells (the cave) need to be orthogonally connected to each other. The clues indicate the amount of cave cells (unshaded) that is seen from that cell, including itself.
In addition, all possible 2 and 3 clues have been given. This acts as a negative constraint: if in the final grid, all unshaded cells were converted to clues, there wouldn’t be any other 2s and 3s than given.
Solve on PuzzLink. If you would first like to try a smaller, easier version to get familiar with the concept, try this 10 by 10.
Solution code: The number of shaded cells in each row, from top to bottom.
Comments
on 28. July 2021, 17:48 by Mark Sweep
Updated tags
on 6. January 2021, 12:13 by PixelPlucker
Negative caving was a positive experience!
--- Haha, nice one! Glad you felt this way!
on 17. December 2020, 16:06 by bob
I didn't think I would be able to solve this at first, but by the end I almost intuitively knew how the cave walls had to bend because of the negative constraint. Thanks for the originall puzzle.
--- I'm glad you found your way through and got familiar with the logic!
on 14. December 2020, 21:41 by marcmees
What a cave! great puzzle. thanks
--- Thank you for your nice comment!
on 13. December 2020, 17:50 by Phistomefel
Wow, quite the mental workout - at least for me. Lovely puzzle with elegant logic to discover - thank you for constructing it!
--- No problem! I am glad to hear you enjoyed it. Thanks for your comment!
