Logic Masters Deutschland e.V.

Hi everyone, I'm back after a two-year break from puzzling, with yet another 6x6 !
Huge thanks to sanabas for testing this puzzle, as well as for a very detailed explanation of the thought process that went into solving it !

This puzzle should be very challenging for a 6x6, with a lot of deductions arising from the maximum rule, so I recommend examining very accurately its implications, as it's easy to miss an option ! It's why I put it at 5 stars...

Without further ado, here it is !



Rules :
Chaos Construction : Divide the grid into regions, each consisting of six orthogonally connected cells. Each row, column and region must contain the digits 1 to 6 once each.

Japanese sums : Clues outside the grid are japanese sums : they give the sum of all the digits in a contiguous stretch of cells that are in the same region (ending either at the edge of the grid or a different region).
These are ordered in the same way the stretches of regions are disposed along the row/column.
→ Here the '12' is the closest clue to the grid, thus indicating that the [region containing r4c6]'s contiguous stretch on that row has a sum of 12, same goes for the '?' and r6c6's region. Moreover, the '?' represents here any odd integer.

Additionaly, when the grid is completed, and all japanese sum clues (including the given twelve and the ?) are written outside the puzzle (one for each stretch in a region), this particular solution contains the maximal number of two-digit japanese sums among all possible 6x6 irregular grids (whether it is with or without the clues here).
In this puzzle however, there are no 2x3 (or 3x2) regions .

Region Sum Line : region borders divide the blue line into segments that each have the same sum; if the line exits a region and reenters it elsewhere, these segments are to be counted separately.

You can play it on the CtC app here !

Interestingly enough, the puzzle is unique even without the '?' clue, but there was one deduction that was very difficult to spot, and could be bypassed by some bifurcation. If you're looking for a challenge, you can try removing it...
And finally, I wondered whether there existed other grids (excluding rotations and symmetries of this one) that satisfied the maximum rule and the anti-rectangle one as I couldn't find any by hand, so if anyone has results, they are very welcome ! Deducing the maximum value should be pretty straightforward, but there's a slight roadblock in the way : (highlight the following hidden text to reveal it)You should be able to find an upper bound rather easily. To prove that it can actually be reached, don't forget that regions with rectangular regions are included in all possible 6x6 irregular grids !

As usual, comments and ratings are very much appreciated, and I hope you enjoy this puzzle !