Logic Masters Deutschland e.V.

As a certified U-Bahn engineer, you were selected for a once-in-a-lifetime opportunity: you'll be leading the construction of a new underground project in downtown Tokyo. Upon arriving at the construction site, your supervisor handed you the network plan provided by the Japanese architect in charge of this project.

"It must be a mistake," you said upon seeing the plan, "this doesn't look like a U-Bahn diagram at all!" "I can assure you there's no mistake", answered your supervisor, "the Japanese architect is a trained professional." Besides, the architect left some notes attached with the network plan:

"While I was designing the plan for my beloved U-Bahn, it occurred to me that the rail manufacturer provides four different rail parts: corners, straight lines, branches, and crosses. I have numbered these rail parts, in accordance with our standard practice, such that corners are 1s, straight lines are 2s, branches are 3s, and, last but not least, crosses are 4s. Now if you consider the numbers outside the U-Bahn canvas, in a given row or column, they represent the sum of each group of adjacent rail parts in that row or column. It is important that all such rail part groups must be separated by at least one unused cell. As a Japanese native this is second nature to me!"

"Oh, I should also inform you we've had a... er... minor incident with the network plan. I accidentally spilled coffee over some hints outside the canvas. I replaced each of the missing digits with a question mark, but two-digit numbers cannot start with a leading zero. I trust that an accomplished U-Bahn engineer such as yourself will have no issues making sense of these incomplete markings. That's about all. Good luck!"

Puzzle links

Example Puzzle (SudokuPad)
Example Puzzle (Penpa+ solving link)
Example Puzzle (Penpa+ finished solution)
Main Puzzle (SudokuPad)
Main Puzzle (Penpa+)