Summation U-Bahn Aquarium
(Published on 22. July 2025, 23:21 by Nell Gwyn)
- Summation U-Bahn: Draw a single connected loop network along the edges of some cells, which may branch or turn or cross itself, but cannot have any dead ends.
- For each vertex that is visited by the loop network, assign its line shape (regardless of rotation) a digit from 1 to 4 as follows: corner = 1, straight line = 2, branch = 3, crossing = 4. Clues outside the grid indicate the sum of "digits" in each contiguous sequence of vertices visited by the loop network, in order.
- Adjacent sums must be separated by at least one vertex that is not visited by the loop network.
- A question mark may represent any digit from 0 to 9. A two-digit sum cannot start with a 0.
- For each row and column, either all clues or no clues are given, with the caveat that a "..." stands for any number of missing clues (including no clues at all).
- Aquarium: Shade some cells gray to represent water. Clues on the bottom and right of the grid show the number of water cells in the indicated row or column.
- The loop network divides the grid into regions. Within each region, cells in the same row are either all water or all unshaded ("air"), and water cells cannot appear above air cells in the same region.
- Some regions do not have borders along the outer edge of the grid (and some regions may only be partially bordered along those outer edges). These regions can still have water cells in them; however, a water cell cannot appear along any outer edge of the grid without a region border to contain it.
- Some Aquarium clues are given as inequalities.
Solution code: For each row from top to bottom, the number of vertical lines along that row (in the 6x6 example puzzle, this would be 254664).
Solved by MadHypnofrog, Agent, Jesper, ns08, Paletron
Comments
on 25. July 2025, 16:30 by Jesper
Great puzzle, thanks!
on 25. July 2025, 03:22 by Agent
Awesome puzzle, good to see another Summation U-Bahn! Cool ruleset and very fun solve.
