Berlin
(Published on 13. March 2023, 04:08 by zetamath)
Draw a network of lines through the centers of some cells in the 12x12 grid below. The lines must not leave the 12x12 grid. Cells which do not contain lines contain digits from 1-9.
The Network: The network of lines you draw may freely branch, but the line network must be connected. Additionally, the network has the following properties:
-) Every 2x2 square in the grid contains at least one cell of the line network.
-) If a cell in the network does not orthogonally border a digit, that cell must be a four way intersection.
-) The network contains no loops of any size.
-) Clues on the left and top grid indicate how many cells in that row or column have that many line segments entering/exiting them. For example, the 2 clue indicates how many of the cells have exactly two lines emanating from them.
-) Cells with only one entrance/exit are called dead ends. Each dead end within the network has the property that the sum of all digits in the grid which are orthogonally adjacent to it is 10. Digits may not repeat within one of these sums.
Unvisited cells: Each cell not containing a line contains a digit from 1-9. These digits do not repeat within rows and columns. Additionally, cells containing digits act like the walls in a cave puzzle. That is to say, they are orthogonally connected to the edges of the grid by other cells containing digits.
J-Sums clues: Clues to the right and bottom are standard cryptic Japanese sums clues with values 0-9. Same letters stand for same digits, different letters for different digits. As standard, ? stands for any digit 0-9, and no clue may have a leading zero. (Point of clarification: Digits placed in the grid are 1-9). The ...'s within clues indicate any number of omitted clues including zero.
Below is an example puzzle which uses the digits 1-6 within the grid and the digits 0-6 for the cipher. This puzzle is solvable, and probably 3-4 stars. You can solve the example in penpa here. Links to the full puzzle can be found at the bottom of the page.
Have fun, leave a comment if you enjoy the puzzle!
PS: I stream solving sudoku like puzzles three days a week. You can check out the channel, as well as some videos I have made about setting puzzles, at my YouTube channel here.
Solution code: The digits from row 7. Skip cells which contain track.
Comments
on 20. January 2024, 12:17 by Silverstep
It was generous (?) to have all the letters resolve in alphabetical order, but it wasn't satisfying to solve that way.
on 15. July 2023, 04:12 by wand
wow, that was just awesome. definitely got stuck a few times forgetting a relevant rule, but absolutely worth it the way everything comes together
on 3. April 2023, 07:03 by wooferzfg
Very fun puzzle, thanks!
on 31. March 2023, 00:42 by Christounet
A real masterpiece that would deserve a much higher rating than it got so far. I loved discovering the properties and side effects of the ruleset along the way, even if it cost me breaking it a couple times at the start. For future solvers, you should definitely consider reading the rules again very carefully if you ever get stuck !
on 22. March 2023, 19:06 by Statistica
Es gibt keine Stelle während des Lösens, an der es "einfach" weiter geht. Superklasse, ein Meisterwerk.
on 21. March 2023, 20:13 by chalk235
I was totally stuck and ready to give up with this one - but then I remembered and reread the network 4-way intersection rule and could then make some more progress albeit at a snails pace. Amazing puzzle - thanks!
on 16. March 2023, 14:58 by Niverio
I have solved 1000 puzzles and I have never seen a singular cell's shading being known be this impactful to the solve path. Stunning.
on 14. March 2023, 22:35 by JayForty
Hard and well-balanced puzzle, I really enjoyed it! Thanks :)
on 13. March 2023, 22:29 by Jesper
Great puzzle, sustained high difficulty level but progress is always possible, enjoyed it!
on 13. March 2023, 16:31 by polar
As someone who loves u-bahn I admit to being a bit hesitant reading the rules for this puzzle, but you won me over with the example puzzle and ever moreso on the main one. A very enjoyable solve with some awesome and intricate logic. Thanks Zeta :)
on 13. March 2023, 07:00 by ddx01
Thank you for the puzzle.
It was a good challenge! But the puzzle constantly rewards you for being on the right track, where even the difficult steps are elegant and feel intended.
Loved it!
