Logic Masters Deutschland e.V.

This puzzle is a hybrid of Sudoku and Fillomino. The 159 tag is used as there is not one for other indexing variants such as numbered rooms.

• Sudoku:
  Draw a regular 9×9 Sudoku in the grid, consisting of nine 3×3 square regions of nine cells each. Place a digit from 1-9 into each cell of the Sudoku such that no digit repeats in a row, column or region. Divide the remaining cells into Fillomino regions, such that the Sudoku is entirely surrounded by Fillomino regions.
• Fillomino:
  Divide the rest of the grid into regions of orthogonally connected cells and place a number into each cell, indicating the size of its region. Numbers may not be the same either side of region borders, except along the border between the Fillomino and the Sudoku.
• Unique Ordered Sums:
  In cages, numbers must not repeat and sum to a total. All totals are ranked in ascending order and these rankings are displayed in the top left corner of each cage. Each cage total is unique. Question marks may be replaced by any number and inequalities must be satisfied.
• Numbered Rooms:
  Every Fillomino number adjacent to the edge of the Sudoku acts as a numbered rooms clue. A digit X in a numbered rooms clue is placed Y cells along the respective row/column in the Sudoku, where Y is the number adjacent to the clue in the Sudoku.

Löse SudokuPad

Löse Penpa

Answer check on Penpa requires all numbers to be correctly filled and green edges to be drawn between regions, while SudokuPad just requires numbers, but those greater than 9 must be replaced with letters using A = 10, B = 11, C = 12 etc.

This puzzle was constructed for tesseralis in the 2024 Secret Satan puzzle exchange. Having looked at tesseralis' puzzle page, I decided that a Sudoku surrounded by a Fillomino would be an ideal gift.

Having not set a Fillomino hybrid before, I was unsure how to begin and spent a lot of time thinking about how I could get the two genres to interact in an interesting and unusual way. Most Fillomino/Sudoku hybrids that I have solved tend to have a crossover where the rows and columns on the edge of the Sudoku are also part of Fillomino regions, but I didn't want to do this. In the end I decided to use the numbered rooms constraint, which would allow interesting interactions along the permaculture border. While setting I found that far more interactions were forced than I anticipated, causing the puzzle to break multiple times, but eventually I found a working grid while preserving the discoveries that I wanted to share. The use of unique ordered sums, colloquially called ranked cages, allowed the solve path to be kept reasonably narrow.