Logic Masters Deutschland e.V.

For those who have been checking out my weekly puzzles, let us take a break from Destruction and try a Fillomino+Sudoku hybrid. If you would like an approachable example of this genre, try out eap314's Ominoku 5x5. I believe these constraints are flexible and mesh well enough that some very interesting puzzles can be made out of them.

The rules are as follows:

• Place the digits 1-9 once in every row and column.
• Ominoku: Divide the grid into orthogonally connected regions such that no two regions of the same size are orthogonally adjacent and no digits repeat within a region. The value of a cell is equal to the size of the region it belongs to. Given digits are the value of their cell, but any digits deduced by the solver are not necessarily the value of their cell.
• Cages: Within a cage, the sum of the digits is equal to the sum of the values, which may repeat.
• Thermometers: Both digits and values along a thermometer increase without repeating when read from the bulb end (independent of each other). Additionally, along the red two-cell thermometer in the top left, the difference between the digits must equal the difference between the values.

The puzzle is available on SudokuPad (checks digits only) and Penpa (checks digits and regions with the edge tool). If you would like to keep track of Fillomino values and Sudoku digits on separate grids side-by-side: Penpa (checks only digits, but on both grids). Have fun solving!