County Map
(Published on 22. January 2023, 20:23 by bodemeister)
Rules:
- Place the digits 1-9 into each row, column and region. Each region is a set of 9 orthogonally-connected cells, and each cell is part of one region. No 2x2 square can be contained in a single region.
- Cells containing 9's in the grid represent cities, and there is a road passing through each city that forms a loop through orthogonally-connected cells in the grid. The road cannot encounter the same cell more than once.
- Two cities are neighboring if there is a road segment between the cities that doesn't contain a third city. Digits on the road between any neighboring cities sum to 10, and each road segment connecting neighboring cities has only two possibilities: moving horizontally in the row of one city and then vertically in the column of the other city or vice versa.
- Orthogonally-adjacent cells outside of cities but along the road must be in different regions.
- Numbers outside the grid are sandwich sums, giving the sum of the digits between 1 and 9 in the corresponding row or column. All sandwich clues bigger than 10 are either given or masked by a question mark.
- Digits in circled cells give the number of borders between regions that can be seen vertically and horizontally from that cell. Not all circles are given.
Below is the 9x9 puzzle. It is also available here at CtC. Enjoy!
Solution code: Row 4, Row 7
Comments
on 3. March 2024, 15:14 by wullemuus
Another jewel because of the unusual ruleset and the unexpected interactions between all the moving parts. Fortunately, I found the breakin very fast. The colouring of the regions took a lifetime (therefore I appreciate another coaching ;)). After that the digits could be placed like on a string of pearls- really wonderful!
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Nice job on the break-in! For me coloring took place up until the very end, but as the positions of all the 9's and 1's can be found early along with a decent portion of road that provide region borders, most of the 9's and 1's can be color-paired and the 2x2 rule helps a lot. But yeah it's hard. There are reasons this puzzle has the fewest solves of all my puzzles :)
Thanks again for yet another solve of one of my puzzles!
on 1. January 2024, 12:03 by Lavender Gooms
Lovely. It's quite a daunting ruleset, but incredibly satisfying.
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Wow I didn't think I'd ever get any more solves for this beast. Thanks for solving and glad you found it enjoyable!
on 24. January 2023, 19:54 by bodemeister
@henry yes the loop can occupy a 2x2 shape.
on 24. January 2023, 18:39 by henrypijames
You still haven't asnwered if the loop is allowed to occupied a 2×2 like R3C1-R1C1-R2C1-R2C2, which the example doesn't do. The rules only say that a region cannot occupy 2×2.
on 24. January 2023, 18:33 by bodemeister
Edited the rules for clarity.
on 24. January 2023, 18:09 by bodemeister
@henry, no cell can be part of the road twice, as that would make multiple loops in the grid. The sum of the digits adding to 10 doesn't count the cities, but the road segment not turning more than once does include the cities, meaning that from one city to a neighboring city, there are only two possible roads: one traveling vertically and then horizontally, and the other horizontally and then vertically. I will update the rules to make these points more clear. Thank you for your questions and interest in the puzzle!
on 24. January 2023, 17:01 by henrypijames
Is the loop allowed to touch and/or cross itself? The one in the example doesn't, but the rules don't mention this.
on 24. January 2023, 16:15 by henrypijames
I also (still) don't understand the meaning of "including the cities at the endpoints". How could the rules be interpreted differently if this phrase were left out?
EDIT: I think I understand it now: It rules out R3C3 and R6C6 from being connected via R3C3-R3C2-R7C2-R7C6-R6C6.
on 24. January 2023, 00:18 by bodemeister
@kjholt, thanks for your question and checking out my puzzle! It means if two neighboring cities are at R2C2 and R4C5, the road segment connecting them must be horizontal on row 2 and then vertical on column 5, or it must be vertical on column 2 and then horizontal on row 4. Any other route would require the road segment to have at least two corners. For any two neighboring cities, there are only two ways to draw a road connecting them.
on 23. January 2023, 21:26 by dennischen
I think it means "changes direction once" (alternatively, "turns exactly once"). That would probably be clearer verbiage, assuming I am correct.
on 23. January 2023, 21:17 by kjholt
I'm not following this part of rule 2: "each road segment connecting neighboring cities (including the cities at the endpoints) has only one corner." What does "including the cities at the endpoints" mean?
