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The rectangular grid sizes can vary greatly. Since the objective is to have equal number of both symbols in each row and column, the number of rows and columns is normally even. Though not required, grids are often square. Common sizes range from 4x4 to 20x20. [10] [11] Larger puzzles are also made, including ones that use a 30x40 grid. [12]
A 1×3 room containing a '2' must have the two end cells painted, as a painted centre cell would force a breach of rule 1. More generally, a 1×(2n−1) room containing an n must have every other cell within it painted. A 3×3 room containing a '5' must have a checkered pattern, with painted cells in all corners and the center.
When numbers 1, 2 or 3 get its connections, one can fill remaining cells The other way around applies: numbers 1, 2 or 3 with that amount unfilled cells and other cells avoiding the number specify the remaining cells points to the number. Edge 1 make that cells to have common value (marked "A"), although to be specified.
As in Sudoku, the goal of each puzzle is to fill a grid with digits –– 1 through 4 for a 4×4 grid, 1 through 5 for a 5×5, 1 through 6 for a 6×6, etc. –– so that no digit appears more than once in any row or any column (a Latin square). Grids range in size from 3×3 to 9×9.
⌈ x/3 ⌉ = ⌈ x′/3 ⌉ and ⌈ y/3 ⌉ = ⌈ y′/3 ⌉ (same 3×3 cell) The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them. A Sudoku solution grid is also a Latin square. [9]
Example grid for a cross-figure puzzle with some answers filled in. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells.
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The name stemmed from a Nipponised form of the English words "sum number place." Killer sudokus were introduced to most of the English-speaking world by The Times in 2005. Traditionally, as with regular sudoku puzzles, the grid layout is symmetrical around a diagonal, horizontal or vertical axis, or a quarter or half turn about the centre.