Logic Masters Deutschland e.V.

This is my response to Scojo's setting prompt from a couple of weeks ago, for which the wheel spun German Whispers and Counting Circles. I was already exploring the absurd combination of Doppelgänger and Schrödinger cells, and these constraints seemed to complement the genre perfectly. Many thanks to aqjhs for testing another of these crazy Doppelgänger puzzles!

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I've actually been sitting on this puzzle for a couple of weeks because it is unique and solvable without the X clue, and it goes against all my instincts as a minimalist to add it in! I will concede though that it does help to make the solving experience a little smoother and better signposted. For an explanation of how to solve the puzzle without the X, please highlight the black block below (and appreciate me for resisting the urge to publish this without the X)!

At one stage, you must consider which two digits share an S-cell in box 3. The two cases that are hardest (but in my opinion most interesting!) to disprove are:
a) 3 and 4: If this went in column 1, then the 0 in column 3 would be missing the same digit in its box as its column, and vice versa if the S-cell went in column 3;
b) 6 and anything: Wherever this S-cell goes, it would share a column with a cell that must be either 6 or an S-cell, and this would break both options.

The X clue quickly reduces the options such that the only moderately difficult case to disprove is 3 and 5. It also makes the rule requiring each to be missing different digits in its row, column and box redundant across the whole puzzle, which is a shame, but may be for the best!

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SCHRÖDINGER DOPPELGÄNGER
• Fill each cell of the main grid with one or two digits such that every row, column and box contains a 0 and six different digits from 1-7;
• No two rows, no two columns and no two boxes may be missing the same digit;
• For each 0 in the grid, the digits missing in its row, column and box must be three different digits.

LOCAL CONSTRAINTS
• Adjacent values on a green German Whisper line differ by at least 5, where a cell's value is the sum of its digits;
• A digit (not value), N, in a circle counts the number of circles containing that digit;
• Cells joined by an X contain digits summing to 10.

(Cells outside the main 6x6 grid can be used to record missing digits and do not affect solution check)