Logic Masters Deutschland e.V.

Inspiration for this puzzle came from various places, including MathPesto’s LITSomino, MicroStudy’s Quintessence, Dumediat’s Réaltraí, and Zetamath’s setting/solving stream. Thanks again to Christounet and Agent for their testing, feedback, and mentorship.

Rules:

• Fillomino (Except 4): Divide the grid into polyominoes and fill each cell with a number equal to the size of its polyomino. Polyominoes of the same size may not share an edge, EXCEPT FOR TETROMINOES (size four; see below for further explanation).

• Nurikabe: Shade some cells (representing water) such that all shaded cells are orthogonally connected, without creating a fully-shaded 2x2 area. Unshaded cells form connected groups representing islands. Different islands may not share an edge but may share a corner.

• Interaction: All Fillomino tetrominoes are island (unshaded), while all other polyomino sizes are water (shaded). An island may contain multiple connected tetrominoes, but an island may not contain two tetrominoes of the same shape (regardless of rotation and reflection). For clarity, there are 5 possible tetromino shapes (L, I, T, S, O).

• Arrows: Numbers on cells with an arrow indicate the number of polyominoes seen in the direction of the arrow (consider multiple arrows within the same cell individually, not summed). Arrows do not count their own cell, but may count their polyomino if a cell within its polyomino is visible in the direction of the arrow.

• Another Special Property of Tetrominoes: Tetrominoes (i.e. island polyominoes) count as 1.5 (one and a half) polyominos for arrow clues.

Main Puzzle: THE SWAMP

Links to Solve The Swamp:
Penpa+
SudokuPad

Playable Example Puzzle: THE MARSH