Without further ado, here are the rules:
RULES:
Modulo 4: All clues in this puzzle are given modulo 4; i.e. all clues are the remainder when dividing the true values of each clue by 4. All clues' true values are nonzero.
Cave: Shade some cells such that all unshaded cells are orthogonally connected and all shaded cells are connected to the edge of the grid. Digits inside the grid give the number of unshaded cells seen in all directions from the clue, including itself, modulo 4. Shaded cells block vision.
Summation U-Bahn: Draw a loop network through the centers of all unshaded cells, which may branch or turn, but may not have any dead ends. The network may not travel on shaded cells. Assign each line shape (irrespective of rotation) a digit from 1 to 4 as follows: corner = 1, straight line = 2, branch = 3, cross = 4. Clues to the top and left of the grid indicate the sum modulo 4 of "digits" in each contiguous sequence of cells visited by the loop network, in the correct order. Consecutive sequences must be separated by at least one shaded cell. For each row or column, either all clues or no clues are given. '?' may replace any number. '...' replaces 0 or more clues in the position given.
Clone: The marked 3x3 areas are exact clones of each other with respect to both the U-bahn network and the cave shading.
Click the image of the puzzle to play in Penpa!
Happy solving! Please check out some more summation u-bahns if you are so inclined, and leave a comment if you enjoyed this one!
Lösungscode: For each row except the last, the number of lines leading down from that row.
am 7. Oktober 2025, 00:17 Uhr von Piatato
Very nice!
am 27. September 2025, 02:07 Uhr von cyddrdrd
Clean and smooth!
am 25. September 2025, 10:01 Uhr von Silverbyte
Very clean puzzle and surprisingly not that hard for how difficult the ruleset seems to be
am 24. September 2025, 18:24 Uhr von damasosos92
Beautiful logic in this one.
am 24. September 2025, 16:51 Uhr von Agent
Great Summation U-Bahn variant, very approachable and fun!
am 24. September 2025, 16:11 Uhr von Christounet
The mod 4 is a surprisingly restrictive rule here. A very nice take on the summation U-Bahn ruleset. Enjoyed it! Thanks :)
| Schwierigkeit: | ![]() |
| Bewertung: | 98 % |
| Gelöst: | 18 mal |
| Beobachtet: | 1 mal |
| ID: | 000PC1 |