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The Fifteen puzzle can be solved in 80 single-tile moves [6] or 43 multi-tile moves [7] in the worst case. For its generalization the n -puzzle, the problem of finding an optimal solution is NP-hard , [ 8 ] so it is not known whether there is a practical God's algorithm.
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a ...
Named after the number of tiles in the frame, the 15 puzzle may also be called a "16 puzzle", alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle, which has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modeling algorithms involving heuristics.
Solving the puzzle requires a combination of logical techniques. [2] Numbers in each row and column restrict the number of possible values for each position, as do the inequalities. Once the table of possibilities has been determined, a crucial tactic to solve the puzzle involves "AB elimination", in which subsets are identified within a row ...
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape , consisting of multiple layers of pieces along each axis which can rotate independently of each ...
A minimal puzzle is a proper puzzle from which no clue can be removed without introducing additional solutions. Solving Sudokus from the viewpoint of a player has been explored in Denis Berthier's book "The Hidden Logic of Sudoku" (2007) [ 7 ] which considers strategies such as "hidden xy-chains".
"Light chasing" is a method similar to Gaussian elimination which always solves the puzzle (if a solution exists), although with the possibility of many redundant steps. [2] [6] [8] In this approach, rows are manipulated one at a time starting with the top row. All the lights are disabled in the row by toggling the adjacent lights in the row ...
The remaining rules differentiate Heyawake from other "dynasty" puzzles: Rule 5 is the defining rule of the puzzle; black cells must be placed to prevent any (orthogonal) lines of white cells that cross two room borders ("spanners"). Numbered rooms typically provide solvers a starting place, among other deductions.