Logic Masters Deutschland e.V.

WARNING: You normal sudoku intuition may lead to errors with this ruleset. DO NOT place hidden singles in cells that could possibly be Schrödinger cells. The definition of a hidden single is when a pencil mark is the only one of its kind in an entire row, column, or block. See example image below.

Edit: Because this puzzle had only been solved 6 times, I took a second look to analyze it carefully. As a result I made a few changes. Compared to the first published version, half of clues have been changed, removed or replaced. The solution is still mostly the same, but now it should be slightly easier to solve. Even more importantly it's much more likely that you will find the intended way through, and not solve it in the wrong order.

Rules

10-in-9 variant

Every row, column and 3x3 box contains digits 0-9. There's one Schrödinger cell (S-cell) in each row, column and box, containing two different digits.

Hidden Killer Cages

Digits in a cage cannot repeat and must sum to the total given in the top left corner. The cages must be determined by the solver and cannot overlap. The clue cell must be the leftmost cell of the topmost row of the cage, can't be an S-cell, and contains a digit equal to the cage size. If S-Cell is in a cage, both digits contribute as separate numbers towards cage total. E.g. 19 sum cage might contain 2 in the clue cell and 8/9 in the adjacent S-cell right or down from the clue. See cage examples below.

Thermometers

Along a thermometer, digits increase from the bulb end. If S-cell in on a thermometer, both digits must satisfy constraint independently.

Solution

The correct solution is not unique. All the digits are uniquely placed, but exactly one of the cages has two possible shapes, as quantum effects make it impossible to determine whether the revolver is cocked or not. Gun's state might be quantum entangled to cat's fate.

Link

Play on the CtC web app.

Example of Correct Cages and Thermometers

Red color is used to mark Schrödinger cells. 36 cage starting at R5C2 has two possible shapes. Brown shape shows "cat is alive", while in the gray shape "cat is dead".

Counter Examples of Invalid Cages

• 9 cage has wrong size, it only contains 3 cell, but 4 in the clue
• 10 cage has two digits in the clue cell
• thermometer is not strictly increasing, because digit 3 is repeated
• 15 cage has digit 0 repeated twice
• 11 cage has wrong sum
• 21 cage the clue is not in the top left corner position
• also there's two S-cells in column 4 and no S-cells in column 5

Example on 10-in-9 Variant Notation

Image below shows an example of notation I use when solving 10-in-9 variant sudokus. You may find some other notation more useful. Red cells show known Schrödinger cell locations, grey cells possible locations, and unshaded cells are normal cells with a single digit. Corner marks show all possible options for a digit in a 3x3 box.