Logic Masters Deutschland e.V.

Good help is hard to find...

One of the boxes was opened, we despairingly yelled NO! across the first 3 rows, we put the renban cage back together in region 3, but too late. The cat escaped, it messed up a few clues. Luckily, it is still solvable...

This puzzle is a partner to Really, don't open the box

You can attempt this puzzle at this sudokupad link

Good Luck!

Questions, comments, feedback are always welcome.



Normal Schrodinger Sudoku rules apply: Fill the grid with the digits 0-9 such that no digit repeats in a row, column, or box.

S-cells: In each row, column, and box there is exactly one S-cell, S-cells contain two digits instead of one, and their value for the purpose of other clues is the sum of those digits.

Schrodinger boxes: Every S-cell is a box, and every box is an S-cell.
These boxes are supposed to remain closed, but somebody opened one.
The eight boxes that are still closed simultaneously satisfy two different rules. Opening the box resolved the choice, so the single opened box only satisfies one of the two rules. It's up to the solver to work out which box was opened. The two rules are:
Rule 1: Counting boxes: Every digit N appearing in a counting box appears N times in counting boxes.
Rule 2: Even boxes: The box has an even value
I've added additional explanation and hints at the bottom of the page for this

Austrian Whispers: Adjacent cells on a red line are either equal, or they differ by at least 10.

Killer cages: Digits do not repeat in cages (though values may repeat) and values sum to the total in the top left corner of each cage.

Renbans: Each purple line contains a set of consecutive values with no repeats.

Nabners: No two values on a gold line can be consecutive or equal. e.g. If one cell on a gold line has the value 5, then no other cell on that line can have the values 4, 5 or 6.

Kropki: Values in cells separated by a white dot are consecutive. Values in cells separated by a black dot have a 2:1 ratio. Not all dots are necessarily given.

My three most recent puzzles:
Don't open the box
Austrian Whispers
Schrodingerenban


Clarification of the opened box rule:
There are two options: First, the 9th s-cell obeys the counting box rule but not the even rule. So there are 9 counting boxes, 8 have an even value, 1 has an odd value.
Second, the 9th s-cell obeys the even rule, but not the counting box rule. So there are 8 counting boxes, and the final s-cell is irrelevant for the counting boxes, can simply be any even value.

I am no programmer, my attempts to use basic html and get spoiler text aren't working, sorry. So you'll need to copy and paste these if you want a hint. A hint:

9 counting boxes means 18 digits. 8 even values + 1 odd value can't equal 18. So it is the other option, 8 counting boxes (meaning 16 digits), and the final s-cell is simply any even value.

Another hint:

How to make 16? We can't use 9, as there are only eight boxes. So possible digit combos in the counting boxes are 8,6,2 or 7,5,3,1

One last hint to get started:

If the digits are 7,5,3,1, what does r9 look like? What's the smallest possible value for the cage?
After working that out, r6 is a good place to look...