Cross+A can solve many kinds of puzzles.
Kakuro (also known as "Cross Sums") is a logic puzzle, a mathematical equivalent of crosswords.
A kakuro consists of a playing area of filled and empty cells similar to a crossword puzzle. Some black cells contain a diagonal slash from top left to bottom right with numbers in them, called "the clues". A number in the top right corner relates to an "across" clue and one in the bottom left a "down" clue.
The object of a kakuro is to insert digits from 1 to 9 into the white cells to total the clue associated with it. However no digit can be duplicated in an entry. For example the total 6 you could have 1 and 5, 2 and 4 but not 3 and 3.
Hitori (from Japanese "Hitori ni shite kure"; literally "let me alone") is played on a grid of squares. At the beginning, each cell contains a number. The goal is to paint out some cells so that there are no duplicate numbers in any row or column, similar to the solved state of a Sudoku puzzle (except with black squares added to the grid).
Orthogonal connections are important as well; painted-out (black) cells cannot be connected orthogonally, and the other cells must be connected orthogonally in a single group (i.e. no two black squares can be adjacent to each other, and all un-painted squares must be connected, horizontally or vertically, to create a single shape).
Slitherlink (also known as "Fences", "Loop the Loop", "Dotty Dilemma", "Sli-Lin", "Great Wall of China") is a logic puzzle. It was invented by Nikoli Puzzles in Japan.
Slitherlink is played on a rectangular lattice of dots. Some of the squares formed by the dots have numbers inside them. The objective is to connect horizontally and vertically adjacent dots so that the lines form a single loop with no loose ends. In addition, the number inside a square represents how many of its four sides are segments in the loop.
Link-a-Pix (also known as "Paint by pairs") consists of a grid, with numbers filling some squares; pairs of numbers must be located correctly and connected with a line filling a total of squares equal to that number. Squares containing '1' represent paths that are 1-square long. Paths may follow any horizontal or vertical direction. Paths are not allowed to cross other paths.
There is only one unique way to link all the squares in a properly-constructed puzzle. When completed, the squares that have lines are filled; the contrast with the blank squares reveals the picture.
Fill-a-Pix (also known as "Mosaik", "Japanese Mosaic", "Nurie Puzzle", "Nampre Puzzle") consists of a grid with number clues scattered in various places. Each number shows how many of the nine squares - the one with the number plus the eight around it - should be filled in.
It is necessary to determine which squares are filled in and which should remain empty until the hidden picture is completely exposed.
Battleship (also known as "Solitaire Battleships", "Battleship Solitaire") is a logic puzzle based on the Battleship guessing game. In a square grid of 10 x 10 small squares, an armada of battleships is located. There is one battleship of 4 squares, two cruisers of 3 squares, three destroyers of 2 squares, and four submarines of 1 square. Each ship occupies a number of contiguous squares on the grid, arranged either horizontally or vertically. The boats are placed so that no boat touches any other boat, not even diagonally.
The numbers on the bottom and on the right of the grid show how many squares in the corresponding rows and columns are occupied by ships. Occasionally some squares may contain given ship or water segments as hints to help start the puzzle. The object is to discover where all ships are located.
Hashiwokakero (from Japanese "Hashi o kakero"; literally "build bridges"; also known as "Hashi", "Bridges", "Chopsticks", or "Ai-Ki-Ai") is a type of logic puzzle. It is played on a rectangular grid with no standard size, although the grid itself is not usually drawn. Some cells start out with (usually encircled) numbers from 1 to 8 inclusive; these are the islands. The rest of the cells are empty.
The goal is to connect all of the islands into a single connected group by drawing a series of bridges between the islands. The bridges must follow certain criteria:
- They must begin and end at distinct islands, travelling a straight line in between.
- They must not cross any other bridges or islands.
- They may only run orthogonally.
- At most two bridges connect a pair of islands.
- The number of bridges connected to each island must match the number on that island.
Masyu (also known as "Shiroshinju Kuroshinju", "White pearls and black pearls") is a type of logic puzzle. It is played on a rectangular grid of squares, some of which contain circles; each circle is either "white" (empty) or "black" (filled). The goal is to draw a single continuous non-intersecting loop that properly passes through all circled cells. The loop must "enter" each cell it passes through from the center of one of its four sides and "exit" from a different side; all turns are therefore 90 degrees.
The two varieties of circle have differing requirements for how the loop must pass through them:
- White circles must be traveled straight through, but the loop must turn in the previous and/or next cell in its path.
- Black circles must be turned upon, but the loop must travel straight through the next and previous cells in its path.
Light Up (also known as "Akari", "Bijutsukan") is a logical puzzle. It is played on a rectangular grid of white and black cells. The player places light bulbs in white cells such that no two bulbs shine on each other, until the entire grid is lit up. A bulb sends rays of light horizontally and vertically, illuminating its entire row and column unless its light is blocked by a black cell. A black cell may have a number on it from 0 to 4, indicating how many bulbs must be placed adjacent to its four sides; for example, a cell with a 4 must have four bulbs around it, one on each side, and a cell with a 0 cannot have a bulb next to any of its sides. An unnumbered black cell may have any number of light bulbs adjacent to it, or none. Bulbs placed diagonally adjacent to a numbered cell do not contribute to the bulb count.
Fillomino is a type of logic puzzle. It is played on a rectangular grid of squares. Some cells of the grid start containing numbers, referred to as "givens". The goal is to divide the grid into blocks. The block must contain the number of cells indicated by the number in the cells of the block. The block cannot touch a similarly sized block, horizontally or vertically. Cells without numbers may form blocks necessary to complete the puzzle.
Futoshiki (from Japanese, literally "not equal"; also known as "Hutoshiki", "Unequal") is a logic puzzle. The puzzle is played on a square grid, such as 9 x 9. The objective is to place the numbers 1 to 9 (or whatever the dimensions are) in each row, ensuring that each column also only contains the digits 1 to 9. Some digits may be given at the start. In addition, inequality constraints are also initially specifed between some of the squares, such that one must be higher or lower than its neighbour. These constraints must be honoured as the grid is filled out.
Kuromasu (from Japanese "kuromasu wa doko da", literally "Where is black cells?") is played on a rectangular grid. Some of these cells have numbers in them. Each cell may be either black or white. The object is to determine what type each cell is.
The following rules determine which cells are which:
- Each number on the board represents the number of white cells that can be seen from that cell, including itself. A cell can be seen from another cell if they are in the same row or column, and there are no black cells between them in that row or column.
- Numbered cells may not be black.
- No two black cells may be horizontally or vertically adjacent.
- All the white cells must be connected horizontally or vertically.
Nurikabe is a logic puzzle ("nurikabe" in Japanese folklore is an invisible wall that blocks roads and upon which delays in foot travel are blamed; other names for the puzzle: "Cell Structure", "Islands in the Stream"). The puzzle is played on a grid, typically rectangular with no standard size. Some cells of the grid start containing numbers.
The goal is to determine whether each of the cells of the grid is "black" or "white" according to the following rules:
- All of the black cells must be connected.
- Each numbered cell must be part of a white island of connected white cells.
- Each island must have the same number of white cells as the number it contains (including the numbered cell).
- Two islands may not be connected.
- There cannot be any 2 x 2 blocks of black cells.
Tents ("Tents and Trees") is played on a grid of squares, some of which contain trees. The goal is to place tents in some of the remaining squares, in such a way that the following conditions are met:
- There are exactly as many tents as trees.
- The tents and trees can be matched up in such a way that each tent is directly adjacent (horizontally or vertically, but not diagonally) to its own tree. However, a tent may be adjacent to other trees as well as its own.
- No two tents are adjacent horizontally, vertically or diagonally.
- The number of tents in each row, and in each column, matches the numbers given round the sides of the grid.
