Logic Masters Deutschland e.V.

After I made my first U-Bahn hybrid, I wanted to explore further with some other hybrid. This puzzle is vaguely inspired by 2 puzzles from Nell Gwyn, who experimented a nurikabe / bridges hybrid. It seemed very natural to connect all the bridges with a U-Bahn network. I modified the usual bridge rule a bit, allowing bridges to cross, to create a new layer of logic. Testing feedback estimated a solid 4* difficulty, maybe 5*. I hope you enjoy !

The puzzle :

Play on Penpa (answer check with grey shading for the water, and green lines for U-Bahn)

Rules :

- Standard U-Bahn : Draw a loop network through the centers of some cells, which may branch or turn, but may not have any dead ends. Clues to the left and above the grid indicates 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.

- Nurikabe : Shade some cells in the grid so that all shaded cells (water) are orthogonally connected, and no 2x2 area may be entirely shaded. Unshaded cells form groups of orthogonally connected cells (islands).

- Bridges : Some islands are connected to other islands by bridges. A bridge must go straight from a cell on one island to a cell on another island. Bridges cannot turn or branch, but they may cross one another. They cannot start or end on the same cell as another bridge. All bridges are part of the U-Bahn network. In water cells, there cannot be any U-Bahn cell that is not part of a bridge.

- Clues : All clued cells in the grid are part of islands. A clue can either be the size of that island or the number of bridges connecting that island to other islands. If a cell contains 2 clues, one of them is the island size, the other one a number of bridges. Each island has at least 1 clue indicating its size, and at most 2 clues (indicating its size and number of bridges). A ”?” represents any digit from 1-9.

Example puzzle :

Play on Penpa (answer check)

Here are examples of forbidden patterns of U-Bahn network in the water cells :