U-Bahn Inception
(Published on 28. February 2026, 09:00 by Agent)
Rules
- In both grids, draw a loop network through the centers of some cells, which may branch or turn, but may not have any dead ends. Assign each line shape (irrespective of rotation) a digit from 1 to 4 as follows: corner = 1, straight line = 2, branch = 3, cross = 4.
- Summation U-Bahn: In the left side grid, clues to the left and top of the grid indicate the sum 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 cell not visited by the loop network. For a given row or column, either all clues or no clues are given. A question mark may represent any digit from 0 to 9, but for double digit numbers, the first digit may not be 0.
- Standard U-Bahn: In the right side grid, clues to the left and top of the grid indicate how many times the corresponding line shape (i.e. a cross, branch, straight line, or turn) appears in the corresponding row or column, irrespective of the line shape's rotation.
- Interaction: The "digits" in the Standard U-Bahn grid represent the amount of distinct line shapes (irrespective of rotation) in the corresponding 2x2 area of the Summation U-Bahn. Empty cells in the Standard U-Bahn represent a value of 0, meaning that the corresponding 2x2 area of the Summation U-Bahn must be completely empty.
Example Puzzle (4x4, 8x8)
Main Puzzle (6x6, 12x12)
Solution code: For each row of the Summation U-Bahn except the last, from top to bottom, the number of lines leading down from that row.
Comments
on 22. July 2026, 00:05 by Christounet
Great!! Such an engaging solve for me. I was always overlooking options for some of the sums, which Led to a couple dead ends. But it was all worth the satisfaction in the end. Another beauty in the summation U-Bahn série. Thanks :)
on 3. July 2026, 23:50 by Silverstep
Took me much longer than I expected! Forgot some crucial theories about Summation U-Bahn... re-discovered them along the way...
on 17. March 2026, 09:05 by Piatato
Awesome puzzle!
on 13. March 2026, 08:45 by AnnaTh
What a fascinating, challenging puzzle. I couldn't let go. The interaction is more important than I first thought.
Thank you so much for setting!
on 10. March 2026, 18:03 by Alex
Amazing puzzle!
on 10. March 2026, 12:26 by Playmaker6174
Dayum, what an engrossing puzzle from start to finish!
The opening was especially cool but the whole puzzle never gave up till the very end, and despite being terribly slow in the middle, I still enjoyed how everything came together later on.
[Also I recommend trying out the example puzzle too, it's just as neat if not better x) ]
on 10. March 2026, 10:07 by MagnusJosefsson
Fantastic! Very consistently challenging and interesting.
on 4. March 2026, 16:50 by akodi
Brilliant
on 2. March 2026, 08:56 by ddx02
Lovely!
on 1. March 2026, 14:16 by Jesper
Very cool!
on 1. March 2026, 01:01 by ibag
Einfach grandios!
on 1. March 2026, 00:13 by cyddrdrd
Superb and crazy puzzle! The interaction is perfect.
