Partitioning Puzzles

• The goal of these puzzles is to divide the grid in a certain way to satisfy certain constraints.

Anraikumazaiku §

• Goal: Divide the grid into rectangular regions.
• Constraint: Each region contains one circle.
• Constraint: Black cells do not belong to any region.
• Constraint: Regions of the same size do not share an edge.

Araf §

• Goal: Divide the grid into regions
• Constraint: Each region contains exactly two numbers.
• Constraint: The area of each region must be between the two numbers inside it.

Area Division §

• Goal: Divide the grid into regions.
• Constraint: Regions have letters in the given range.
• Constraint: Regions contain each letter exactly once.
• Constraint: Each letter is part of exactly one region.

Bodaburokku §

• Goal: Divide the grid into regions.
• Constraint: Cells with the same number belong to the same region.
• Constraint: All points where three or four lines meet are given (indicated by dots).
• Constraint: Every region contains at least one cell with a number.

Deddoanguru §

• Goal: Divide the grid into regions.
• Constraint: Regions contain one black circle.
• Constraint: The black circle is an eye that looks at all orthogonal directions until it hits a region border. The number in the eye represents how many cells in the region the eye doesn’t see.

Dominosa §

• Goal: Place borders to form dominoes within the grid.
• Constraint: The domino numbers are shown on the grid.
• Constraint: No domino may repeat.

Double Choco §

• Goal: Divide the grid into regions.
• Constraint: Each region contains one contiguous area of white and one contiguous area of black cells.
• Constraint: A pair of areas must be of the same shape and size (subject to rotation or mirroring)
• Constraint: Numbers indicate the number of same colored cells in the region.
• Constraint: Regions can contain more than one number.

Doueieru §

• Goal: Divide the grid into L shaped regions. The legs of these regions are one cell wide
• Constraint: A circle represent a cell in which an “L” must bend. All circles are given.
• Constraint: If a cell contains a double circle, the two legs of the region must have the same length.
• Constraint: If a cell contains a black circle, the two legs must be different.
• Constraint: If a cell contains a white circle, the ratio of the lengths of the two legs is unknown.

FIllomino §

• Goal: Divide the grid into polyominoes by filling in the boundaries of the cells (i.e., the edges)
• Constraint: Each clue given is part of a polyomino of size .
• Constraint: No polyominoes of matching size are adjacent to each other (i.e., share a side).
  • It is possible for two givens with matching numbers to be part of the same polyomino
  • It is possible for a polyomino to have no given at all.
• Variant: No Rectangles - no rectangular regions allowed.
• Variant: Only Rectangles - only rectangles.
• Variant: No 2x2 - no 2x2 cell area can contain the same numbers.
• Variant: Non-Consecutive - any two adjacent regions must differ in size by at least two.
• Variant: Consecutive - any region of size must be orthogonally adjacent to at least one other region of size or .
• Variant: Deadomino - in each row and each column all cells with the same number must belong to the same region.
• Variant: All Odds - all region sizes must be odd.
• Variant: All Evens - all region sizes must be even

Firumatto §

• Goal: Divide the grid into rectangular regions.
• Constraint: Regions are one cell wide.
• Constraint: Regions are o length 1-4 cells.
• Constraint: Numbered cells indicate the size of the region. Not all numbers are given
• Constraint: Regions of the same size must not be orthogonally adjacent.
• Constraint: Grid dots are not shared by the corners of four regions.

Fosenzuru §

• Goal: Divide the grid into regions.
• Constraint: The regions must contain exactly four cells.
• Constraint: A number in a cell represents how many of its four sides are segment of a region’s borders (including the grid’s borders).

Furisuri §

• Goal: Locate some regions on the grid
• Constraint: Regions are of size .
• Constraint: Each block contains one circle.
• Constraint: It must be possible to move each block by one cell in at least one orthogonally direction.

Galaxies / Tentai Show §

• Goal: Draw lines along the edges of the grid to divide the grid into regions representing galaxies
• Constraints: All galaxies must have rotational symmetry.
• Constraint: All galaxies contain exactly one dot at its center. The dot, therefore acts as the center of the symmetry

Heki §

• Goal: Divide the grid into regions of exactly six sells
• Constraint: Each region contains exactly two numbers.
• Constraint: Numbers indicate how many cells of the same region are orthogonally adjacent to the cell with the number.

Jemini §

• Goal: Divide the grid into regions
• Constraint: Each region contains one letter.
• Constraint: In regions of the same size, shape and orientation, the same letter must be at the same position.

Kapetto §

• Goal: Divide the grid into rectangular blocks.
• Constraint: Each block contains exactly one number.
• Constraint: The numbered clues represent the amount of cells in the block.
• Constraint: Cells do not have to belong to a block.

Knossos §

• Goal: Divide the grid into rooms.
• Constraint: Each region contains exactly one number.
• Constraint: The number represents the border’s length of the region (sides of the board incident to the region count to the border length)

Makaro §

• Goal: Divide the grid into regions.
• Constraint: Each region must be filled with the numbers where is the size of the region.
• Constraint: Arrows on cells point to the greatest number among the four cells adjacent to it.
• Constraint: Arrows are not part of a region.
• Constraint: When two numbers are orthogonally adjacent across a region boundary, the numbers must be different.
• Variant: Masakuchi - Arrows now have numbers. Numbers indicate the difference between the highest and second highest orthogonal neighbors around the black cells (excluding itself)

Meadows §

• Goal: Divide the grid into square blocks.
• Constraint: Each block contains exactly one circle.

Mubunanba §

• Goal: Separate the grid into regions.
• Constraint: Regions have exactly three cells in size.
• Constraint: Not all cells have to be part of a region.
• Constraint: Each region contains exactly one digit.
• Constraint: Digits indicate the number of possible directions the block can move. Movement is orthogonal.
• Variant: Mubunanba+ - allows for question marks as clues
  • Regions include exactly one digit or question mark, which represents an unknown digit.
  • All cells that are not part of any block must be connected orthogonally

Nawabari §

• Goal: Divide the grid into rectangular regions.
• Constraint: Each region contains exactly one digits.
• Constraint: Digits in the cell represent how many sides of the cell belongs to the border of the region. Edges of the grid are included.

Neibadomino §

• Goal: Locate the dominoes on the grid and fill these blocks with numbers.
• Constraint: Not all cells belong to a domino
• Constraint: Numbers in the grid should be part of a domino.
• Constraint: Numbers indicate the number of orthogonally adjacent dominoes.
• Constraint: Dominoes with the same numbers must not be orthogonally adjacent.
• Constraint: No area can be covered by only dominoes.

Neighbors §

• Goal: Divide the grid into regions.
• Constraint: Region sizes must be the same.
• Constraint: Regions contain exactly one number (or question mark).
• Constraint: Regions have as many neighbors as their number indicates. Regions are neighbors when they share a part of their border.

Raneko §

• Goal: Divide the grid into regions
• Constraint: Each region contains one circle (the cat)
• Constraint: Numbered circles indicate the size of the region.
• Constraint: The grid may contain black cells. Numbers in black cells indicate how many regions share an edge with that cell.

Rekuto §

• Goal: Divide the grid into rectangular pieces.
• Constraint: Each piece contains exactly one number
• Constraint: The number in each piece represents the the sum of the width and height of the rectangle

Renkatsu §

• Goal: Divide the grid into regions.
• Constraint: Each region contains digits , where is the number of cells in the region.

Sashigane §

• Goal: Divide the grid into L shaped regions.
• Constraint: The two legs of the region must be exactly one cell wide.
• Constraint: A circle represents which cell in an L must bend. Not all regions have circles
• Constraint: An arrow marks the end of the region’s leg, pointing to the cell in which the L bends.

Sashikaku §

• Goal: Divide the grid into rectangular regions.
• Constraint: Each region contains exactly one number.
• Constraint; The number represents the difference between the width and length of the region.

Sashikazune §

• Goal: Divide the grid into L shaped regions.
• Constraint: The two legs of the region must be exactly one cell wide.
• Constraint: Each region contains no more than three cells with numbers Some regions may not have numbers
• Constraint: Numbers indicate the amount of cells up to a place where the L will bend (including the cell with the number)
• Constraint 1’s indicate where the L bends.

Scrin §

• Goal: Divide the grid into rectangular regions.
• Constraint: Regions contain at most one circle.
• Constraint: Regions must have the same number of cells as the number in the circle.
• Constraint: Regions do not share edges.
• Constraint: Regions form a single non-branching loop where all of them touch each other by the corners.

Seethrough §

• Goal: Every cell denotes a room. Close some doors by placing edges.
• Constraint: Open doors allow looking into other rooms.
• Constraint: The number in the cell indicates the total number of rooms visible orthogonally (excluding the room itself)
• Constraint: All rooms must be connected (going through doors).

Shikaku §

• Goal: Divide the grid into rectangular pieces.
• Constraint: Each piece contains exactly one number, and that number represents the area of the rectangle.

Slash Pack §

• Goal: Divide the grid into regions by placing diagonal lines into empty cells.
• Constraint: Each region must contain the numbers exactly once.
• Constraint: Two diagonals cannot cross in one cell.
• Constraint: No loose ends. Diagonals must to the edge of the grid.

Snake Pit §

• Goal: Divide the grid into regions called snakes.

• Constraint: A snake is a one-cell-wide path at least two cells long.
• Constraint: A snake cannot touch itself, not even diagonally.
• Constraint: A cell with a circle must be at one of the ends of a snake.
• Constraint: A snake may contain one circled cell, two circled cells, or no circled cells at all.
• Constraint: A cell with a number must be part of a snake with a length of exactly that number of cells.
• Constraint: A snake may contain any amount of numbered cells.
• Constraint: Two snakes of the same length must not be orthogonally adjacent.
• Constraint: A cell with a cross cannot be the end of a snake.

Sukima §

• Goal: Locate some regions on the grid.
• Constraint: Each region has three cells.
• Constraint: Regions contain one circle.
• Constraint: Each area has at least one cell that does not belong to any one region.
• Constraint: Unshaded cells do not belong to any region.

Tatamibari §

• Goal: Divide the grid into rectangular regions.
• Constraint: Regions must contain only one symbol.
• Constraint: Crosses indicate that the region must be square.
• Constraint: Vertical bars indicate the region’s height is greater than its width.
• Constraint: Horizontal bars indicate the region’s width is greater than its height.
• Constraint: Grid dots are not shared by he corners of four regions

Tetoron §

• Goal: Divide the grid into regions of exactly four cells.
• Constraint: Each region contains exactly two different symbols.
• Constraint: Regions of the same shape must contain the same symbols.
• Constraint: Tetrominoes can be rotated or mirrored. These count as having the same symbols.

Tetroid §

• Goal: Divide the grid into regions of exactly four cells, forming tetrominoes
• Constraint: Tetrominoes can be mirrored or rotated.
• Constraint: Black cells are not part of any tetromino.
• Constraint: When two tetrominoes in adjacent regions share an edge, they must not be of the same type.

Trinudo §

• Goal: Divide the grid into blocks.
• Constraint: Blocks may be either of one, two or three cells.
• Constraint: Blocks of the same size are not orthogonally adjacent.
• Constraint: Each given number represents the size of the block to which it belongs.

Turf §

• Goal: Shade some cells in the grid to divide the grid into regions
• Constraint: Regions must contain at least one number
• Constraint: Numbers in the region indicate the size of the region.
• Constraint: Additional numbers in the region indicate how many surrounding cells are white (counting itself, orthogonal, and diagonal neighbors)

Usotatami §

• Goal: Divide the grid into rectangular regions.
• Constraint: Regions contain exactly one number.
• Constraint: Every region is exactly one cell wide.
• Constraint: The number of cells in the region is not equal to the number in the region.
• Constraint: Grid dots are not shared by the corners of four regions.

Yagit §

• Goal: Divide the grid into regions
• Constraint: Each region must be non-empty
• Constraint: Each region separates circles (goats) and squares (wolves). Thus, a region must either contain all circles or all squares.
• Constraint: Border lines start and end at edges of the grid.
• Constraint: Lines can turn but only at the black dots on the grid.
• Constraint: Lines can cross each other, except at black dots.
• Constraint: Not all black dots need to be used.

Yokibunkatsu §

• Goal: Divide the grid into regions of exactly five cells.
• Constraint: Regions contain a star.
• Constraint: The cells of a region must be foldable to a cube with the star at the bottom and without the top side.
• Constraint: Some region borders are given.
• Constraint; Not all cells have to be part of a region.

Yonmasu §

• Goal: Divide the grid into regions
• Constraint: Regions contain exactly four cells.
• Constraint: Each region contains one circle.
• Constraint: Black cells are not part of any region.

Yunikumaka §

• Goal: Divide the grid into regions of tetrominoes
• Constraint: Each region contains exactly one dot either in the center of a cell or a border between the cells.
• Constraint: Dots on the border between regions are ignored.