Unendliches Höhlenrätsel (Infinity Cave)
(Published on 3. April 2023, 20:00 by Phistomefel)
Almost normal cave rules apply, but due to the infinite size and the grid structure, some clarifications are needed.
- The grid is divided into nested rings. The rings are identical in structure and clues and extend inward and outward to infinity.
- Shade some cells so that no contiguous set of shaded cells is completely enclosed by unshaded cells. I.e. a contiguous set of shaded cells continues to infinity in at least one direction.
- All unshaded cells form a contiguous set. I.e. between any two unshade cells there must be an orthogonally connected path over finitely many unshaded cells.
- A cell with a number is unshaded. The number indicates the number of unshaded cells visible from the cell with the number in a straight line to the east, south, north and west. The cell with the number itself is counted once and shaded cells obstruct the view.
Here is a small diagram on the topic of visibility on this grid. Cells that are seen from the cell with the 8 are marked with a +, cells which are not seen from there with a -.
Here you find an example for an infinity cave:
As you can see, this puzzle does not satisfy the conditions of a normal cave puzzle. E.g. the cell in the lower left corner is isolated, the 5 in the innermost ring is not fulfilled and a shaded cell in the innermost ring is isolated. These seeming contradictions are resolved by including the next ring in each case.
If you want to try this puzzle, you find the link here.
The actual puzzle is also available online in Penpa Plus. Have fun solving!
Solution code: Select one of the rings with the most shaded cells in the last two columns as the starting ring. Write down the length of each shaded block in the last two columns. Then go one ring out and write down the length of each shaded block in the last two columns of that ring. Repeat this process until the cave pattern repeats. The first repetition is no longer part of the solution code.
The information that the rings have different numbers of shaded cells in the last two columns is not necessary for solving the puzzle.
In the example, we can choose the second innermost ring with 8 shaded cells in the last two columns as the starting ring (vs. 6 in the innermost ring) and the solution code is 1114111121.
Comments
on 15. June 2024, 03:37 by Uuuiiiooop
Wow, what a unique puzzle! I had never tried something with this "infinity" concept. Once I wrapped my head around how it all works, it wasn't too difficult! Thanks for the puzzle.
on 17. August 2023, 04:18 by sugardude
I loved this unique experience that big portion of difficulty comes from ruleset. Studying the ruleset and examining the example itself is already enjoyable. And the mind bending nature of infinity made the solve rough but rewarding. I felt like I'm a researcher in the pencil puzzle facility!
on 10. June 2023, 13:55 by wazdra
Hello ! Small question concerning rule 2: when you say "continues to infinity in at least one direction", do you mean "either inward or outward", or "both at the same time along some axis" ?
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The idea is really borrowed from regular cave puzzles where the walls have to touch the edge of the grid. Another way to phrase it is that walls may not be surrounded by green cells. Now this was all just for regular cave puzzles. For an infinity grid you can also use the wording that gray cells may not be completely enclosed by green cells or equivalently that the gray cells have to extend inward or outward or in both direction to infinity.
on 11. April 2023, 21:59 by wand
oof my head hurts, and that took several hours over several days, but they were fun hours, and my head hurts. a fascinating puzzle!
on 8. April 2023, 02:59 by wooferzfg
Thanks for the puzzle! Very mind bending for sure
on 6. April 2023, 22:43 by Gliperal
One of those fascinating puzzles that took me almost two times longer to understand than to solve. Do you allow people to make solution videos of your puzzles?
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Thanks for the nice comment, Gliperal! To asnwer your question: everyone is free to make a solution video of my puzzles.
on 3. April 2023, 23:20 by RJBlarmo
Very cool puzzle. Despite the daunting nature of an infinite puzzle, this one seemed more on the approachable side.
on 3. April 2023, 22:58 by Phistomefel
Updated difficulty.
on 3. April 2023, 22:51 by KNT
Well, that was something quite different. Interesting puzzle.
