Logic Masters Deutschland e.V.

Welcome, victim, to another round of torture hosted by yours truly. (For a peek at last year's round, click here!) This year's victim was the iconic setter zzw. I decided I needed to make them suffer, along with all of you poor souls. So, I think I broke the difficulty meter with this one. If you enjoy it, please leave a comment!

I had many inspirations for this puzzle, most notably zzw's own Order Out Of Chaos, Niverio's Liar Japanese Sum series (most specifically number 7), and Agent's Marco Polo and Summation U-Bahn. Thank you to all these incredible setters for inspiring me!

Many thanks to the (extremely perseverant) testers, who were chameleon and MathGuy12, for their extensive feedback and suggestions, including the title of the puzzle!

Here are the rules of the beast.

R U L E S

Place N islands in the grid, one of each size from 1 to N. An island of size k consists of k cells numbered 1 through k. Starting from 1, each consecutive number must be placed orthogonally adjacent to the previous one. Islands may not touch orthogonally, although they may touch diagonally. Numbers may not repeat within a row or column.

Place into all remaining cells an orthogonally connected network of lines, which may branch but may not contain any dead ends. Each line shape (irrespective of rotation) has a value: corner = 1, straight = 2, branch = 3, cross = 4.

Each clue outside the grid either gives the sum in that row or column of all consecutive cells in a stretch of an island, or the sum in that row or column of all consecutive cells in a stretch of the path network. All outside clues are given....

However, the clues for each row and column have been sorted in ascending order by total within that particular row or column.

In addition, the interior rows and columns (all except the first and last row and column) themselves have also been sorted (but all row clues are to the left of a row, and all column clues are above a column). This means that for every row of clues, there is exactly one row of the grid (not necessarily the grid row next to those clues) that has the given sums in its region stretches (which can be in any order within that row). Likewise every column of clues corresponds to exactly one column in the grid.

Because I'm so nice, I'm giving you a playable, toy example of the sorting mayhem to follow. Click to play, scroll to read about the different images!

In the left image, the clues are completely unsorted: they are in their place within their rows and columns, and they are directly in line with the rows and columns that they reference.
In the middle image, the clues are sorted from low to high within their columns and rows, but they stay put in their places.
Finally, in the right image, the grey clues are fixed in the correct column and row, but all other clues are placed in order by size of the first clue (1, then 2, then 3; and 1, then 2, then 11). Note that if two first clues are tied, the second clue is a tiebreaker; and so on.

But enough being nice; it's time to suffer. Click the image to play the monstrosity......

Good luck, and I hope you don't have..... Thalassophobia.

"Happy" solving! Please leave a comment if you enjoyed this one! It took a lot of brainpower and near breakdowns to bring to this state, so it is much appreciated. :)