Logic Masters Deutschland e.V.

This puzzle is my response to Kolot's challenge which I quote here: "I leave it as a challenge for everyone to construct a 9x9 Chaos Construction sudoku with an empty grid and only question mark clues outside the grid where exactly the same rule applies to all question mark clues in their respective row/column ".

I apologize in advance for the excessively long rule set. The bottom line is that setting a chaos puzzle with no clues in the grid and only '?' on the outside is not easy. The solution path to the puzzle is tricky at a couple of points, but it can be solved without bifurcation.

RULES

Chaos Construction: Divide the grid into nine orthogonally connected 9-cell large non-overlapping regions. Place the digits 1-9 once each in every row, column, and region.

Question Marks: Question marks ‘?’ represent unknown positive numbers to be determined by the solver.

Region Gaps: A region is defined to contain a gap in a row/column if it contains at least two separate region segments within that row/column. The cells sandwiched between those segments form the gap and do not have to all belong to a single region.

Gap-X-Sums: Clues outside the grid indicate that the first region seen (from that side) in the row/column contains a region gap in that row/column. The size of the gap is X where X is the first cell seen in the row/column. The clue itself is equal to the sum of the digits in the gap. Furthermore, the clue and the digit X must have opposite parity. That is, if one of them is even, the other one must be odd and vice-verse.

Modular Lines: Also, the digits in the region gaps described above form modular lines. Any three digits in sequence along a modular line must yield three different remainders after a division by three. In other words, they are not congruent (mod 3). If the gap has only two digits, then those digits must yield different remainders after a division by three. If the gap has only one digit, then this rule doesn’t do anything.

Reverse Skyscrapers: Clues outside the grid also indicate that the first cell seen in the row/column X is a valid Skyscraper clue for that row/column as seen from the opposite end of the row/column. For instance, if the clue is on the left side of the grid, then X is the leftmost cell of the row and is a valid Skyscraper clue for that row as seen from the right side of the grid. Skyscraper clues give the number of cells seen in a row/column from that point of view, given that large digits obscure the view of smaller ones.

I've included an example row below to help illustrate the rules.

We see that there is a '?' in row 2. The first cell seen in that row is X therefore X=3. We then see that the first region seen in that row from that side – the blue region – contains the cells R2C1 and R2C2 which is followed by "the gap" which consists of X=3 cells: R2C3, R2C4, and R2C5. These cells add to the given clue ? = 1 + 6 + 5 = 12. X is odd while ? Is even. That's opposite parity as required. Furthermore, the digits 1, 6, and 5 do indeed form a modular line (They yield different remainders after dividing by 3). Finally, X=3 is a valid Skyscraper clue for the row as seen from the opposite side. The digits 4, 7, and 9 are the only three visible digits from the right side.

I appreciate solves, comments, and suggestions

Solve the puzzle at Penpa+ with answer check. To trigger the answer check you must fill all the digits and delineate the region borders using green edges.