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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.
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.
John Harold Fleming obtained patent for a puzzle in 1934 in England, with almost identical configuration as described in this page. [5] The puzzle concerned has the same blocks and almost identical placement as forget-me-not, only that the unique horizontal 2×1 block is placed at the bottom instead of beneath the 2×2 block.
The Classics section also had the 2x2, 4x4, and 5x5 versions of the puzzle. Cover Up: On a grid of various sizes, a series of colored columns are stacked up, and the player's job is to lay all the tiles so they completely cover the grid. As the grids become larger the stacks also become larger and more difficult to figure out in which patterns ...
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 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.
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 ...