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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.
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 ...
A standard pentomino puzzle is to tile a rectangular box with the pentominoes, i.e. cover it without overlap and without gaps. Each of the 12 pentominoes has an area of 5 unit squares, so the box must have an area of 60 units.
The corners can be placed just as they are in any previous order of cube puzzle, and the centers are manipulated with an algorithm similar to the one used in the 4×4×4 cube. [11] A less frequently used strategy is to solve one side and one layer first, then the 2nd, 3rd and 4th layer, and finally the last side and layer.
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Like other sliding-block puzzles, several different-sized block pieces are placed inside a box, which is normally 4×5 in size. Among the blocks, there is a special one (usually the largest) which must be moved to a special area designated by the game board.
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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.