Spatial Scaling (Double U-Bahn Cave Latin Square)
(Published on 17. September 2026, 02:00 by SennyK)
Today I am very happy to share a puzzle I am very proud of :-)
For the Scojo's Impostor prompt, I had to learn U-Bahn in less than a week and set a puzzle trying to impersonate the wonderful setter Agent.
If you know his setting style, you can judge how I did, and if you don't, I really recommend trying his puzzles, they are the real work of art! :-)
I hope you will enjoy and I would be really grateful for all the comments and ratings.
In the top left side grid:
Latin Square: Place the digits 1 to 6 once each in every row and every column.
Cave: Shade some cells so that all unshaded cells are orthogonally connected, and all shaded cells are orthogonally connected by other shaded cells to an edge of the grid. Given digits cannot be shaded, and represent the total number of unshaded cells that can be seen in a straight line vertically or horizontally, including itself.
U-Bahn: Draw a loop network through the centers of all unclued unshaded cells (given digits may or may not be on the loop network), which may branch or turn, but may not have any dead ends. Assign each digit from 1 to 6 a line shape (irrespective of rotation) as follows: 1, 5, 6 = corner, 2 = straight line, 3 = branch, 4 = cross. Each cell on the loop network must contain a line shape matching its digit.
In the bottom right side grid:
Summation U-Bahn: 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. 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.
Interaction: The digits in the Latin Square grid represent the amount of cells visited by the loop network in the corresponding 2x3 area of the Summation U-Bahn.
Solution code: For each row except the last of the Summation U-Bahn grid, from top to bottom, the number of lines leading down from that row.
Comments
on 7. October 2026, 13:37 by AnnaTh
Amazing puzzle. Great fun. But easy to make mistakes. Thanks for setting.
on 25. September 2026, 04:15 by ViKingPrime
Is everything okay at home? I mean, I assume you neglected a lot of important people in your life as well as your own well-being to produce this... I'm just saying I'm here for you, you know, if you want to talk.
on 19. September 2026, 04:45 by Chefofdeath
Very nice puzzle!
on 17. September 2026, 17:42 by Jesper
Enjoyed it a lot!
on 17. September 2026, 11:40 by cyddrdrd
Very cool!
on 17. September 2026, 11:12 by Myxo
Incredible work!
on 17. September 2026, 10:30 by Fusce
Can the network in the latin square go through shaded cells ?
SK: Thanks for asking! The network cannot go through the shaded cells. It visits all unclued unshaded cells, and also may or may not visit given digits :-)
on 17. September 2026, 07:58 by Laake
You need to be locked up
on 17. September 2026, 07:27 by aqjhs
easy DUBCLS
on 17. September 2026, 06:21 by Christounet
Well done AgentK! That was a great puzzle and an impressive work from someone who had very little experience of U-Bahn prior to setting this. Looking forward to more! Thanks :)
on 17. September 2026, 04:02 by Agent
Wonderful puzzle, fun combination of rules and a good variety of logic!
on 17. September 2026, 02:10 by MaizeGator
This puzzle was such a wonderful rising to a very tall task. I especially appreciated the interesting ramp-up in difficulty and the variety of logic
