Logic Masters Deutschland e.V.

A while ago, I published another hybrid with U-Bahn and Chaos Sudoku. Here is one using the summation U-Bahn I discovered in Agent's excellent serie. I have started making a bigger version, with a 9x9 sudoku grid and a slightly different ruleset, but it could be a while before I find a grid I like. Meanwhile, do have a go at this one ! Estimated difficulty around 4. Enjoy :)

The puzzle :

Play on Penpa (answer check with green lines for the U-Bahn).

Rules :

Chaos construction sudoku : Divide the 6x6 grid into regions, each consisting of 6 orthogonally connected cells. Each row, column and region must contain the digits 1 to 6 once each.

Clues (sudoku grid) : Digits in cells with arrows indicate the number of cells seen in the indicated directions combined, including itself. Cells that belong to different regions block the view.

U-Bahn : Draw a loop network through the centers of some cells, which may branch or turn, but may not have any dead ends. A clue outside 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.

Values : Assign each line shape (irrespective of rotation) a digit from 1 to 4 as follows: corner = 1, straight line = 2, branch = 3, cross = 4.

Interaction : The digit in each sudoku cell must equal the sum of the values of the line shapes in the corresponding 2x2 box of the U-Bahn grid. However, in each row and column (not necessarily each region) of the sudoku grid, one digit equals that sum off-by-one.

Example for the summation rule :

Note : the corner pencil marks are not needed for the solve or answer check. They are a way of notating that I use while solving this kind of puzzle, and it is useful here to keep track of the sums.