The Arkenstone
(Published on 11. November 2022, 16:00 by Blobz)
Bilbo Bobbins is on a quest to, uh, "procure" the Arkenstone (R5C5) that sits in Dragon Snyder's Lair (a 2x2 region in box 5) under Logic Mountain.
R9C1 marks the entrance to the Whispering Tunnels: an orthogonally connected region leading to the lair. Adjacent digits along the tunnels (and deadends) differ by at least 5. The path from start to lair (ignoring deadends) is 26 cells.
With Arkenstone acquired, Bilbo must escape through the Modular Passage, that begins on the opposite side of the lair and leads to a secret door exiting the mountain (R5C9). Every set of three digits along this passage (which does not branch) must contain one each from the sets {1,4,7}, {2,5,8}, and {3,6,9}. The total sum of digits along this "Secret" passage is 45.
Normal sudoku rules apply.
Shade some cells ("walls") and leave others unshaded ("tunnels", "lair", "passage") such that no 2x2 region (except the lair) is fully shaded or unshaded. Also, there are no "checkerboard" patterns of shaded/unshaded cells, i.e. the unshaded region does not touch itself diagonally. All wall cells must be in orthogonally connected groups with at least one cell at the grid's edge.
All caged cells are either tunnel or passage. The digit in the cage, plus its modifier, indicates how many unshaded cells (including itself) can be seen orthogonally from that position (walls block sight). E.g., if a cage contains a 7 and has a "-2" modifier, then that cell can "see" 5 unshaded cells total (including itself).
Have fun, leave a comment if you enjoy the puzzle!
Solution code: Row 3 followed by Row 7
Comments
on 30. March 2024, 00:00 by Ratfinkz
Lovely puzzle!
on 29. January 2024, 12:16 by rich_27
My god this puzzle tripped me up so many times. I must have tried 10+ times to solve it and ran into the same pitfall each time; it wasn't until I read the rules for the 5th? 6th? time that I realised I'd been calculating sight wrong. Lovely solve once I caught that mistake!
on 19. November 2022, 17:22 by timotab
Fun theme. Nice interactions, but read the rules carefully.
on 11. November 2022, 20:22 by gfoot
Fun to solve! The rules are complex, and it's challenging at the start, but gets easier later on, and there are nice interactions between overlapping rules.
I wasn't sure if you intended "opposite side of the lair" to be a little vague in its meaning - being more precise about that could make that stage of the puzzle somewhat easier, if that's what you'd intended.
-- The fact that you solved it makes me happy! I think the slight vagueness of where the passage starts is acceptable. Thanks for playing :)
