Logic Masters Deutschland e.V.

This is the fifth puzzle in the Black Hole series. I'd love to hear your thoughts about the puzzle.

Thanks to Darth Paradox, joshjohnson, and Scojo for testing and feedback.

Black Hole Series

1. Tachyons and Black Holes (Ransk Solve)
2. Quasar Accretion Disc (Ransk Solve)
3. Corotating Photon Sphere (Ransk Solve)
4. Information Paradox
5. Manifold Paths
6. The Colour out of Space

WARNING: I highly recommend solving Information Paradox (#4) before attempting this puzzle. The branching path in that puzzle is useful for understanding how the infinitely-branching paths in this puzzle work.

Completing this puzzle involves: shading some cells, and doing killer cage, little killer, and hole sandwich sum logic with double-value, zero-value, and multi-digit cells.

The addition of S-cells increases the complexity. Choose your notation carefully to track special cells.

Rules:

Normal S-cell rules apply. Place the digits 0-9 once each in every row, column, and box. Place one "S-cell" with two digits in each row, column, and box. An S-cell's value is the sum of its digits.

Place nine "black holes" and nine "white holes" in the grid, such that there is one hole of each type in every row, column, and box. Black and white holes cannot occupy the same cell (a cell can have an S-cell and a hole). Digits cannot repeat within holes of the same type. Black holes have a value of zero. White holes have a value equal to double their digit(s).

Values in a cage sum to the clue in the top left corner of the cage (if given). Digits cannot repeat in a cage (though values can). A cage must contain an equal number of black and white holes (number may be zero).

Teleporting little killers. Clues outside the grid with arrows are the sum of the values along the pointed diagonals. A little killer will teleport *from* any black hole it visits *to* the white hole with the same digit (not the other way), where it continues in the pointed direction. The sum includes the value of all holes on the path. A black hole with two digits creates two paths on *every* visit - sum each path separately. An "x" in a clue means it has infinitely-many values: one for each positive integer "x". A path must visit an equal number of black and white holes (number may be zero).

Hole sandwiches. Clues outside the grid without arrows are the sum of values between holes in the row or column.

Comments are always welcome. Have fun!

Streamers have permission to use this puzzle. Recommended betting cell for streaming is r9c8.

Play in SudokuPad