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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 ...
To solve the puzzle, the numbers must be rearranged into numerical order from left to right, top to bottom. The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and more) is a sliding puzzle. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with one ...
Lebbeus Edward A Hordern, known as Edward Hordern, (21 March 1941 [1] - 2 May 2000 [2]) was the world's leading authority on sliding block puzzles, and was renowned for his puzzle solving abilities. Hordern had an extensive mechanical puzzle collection and was an author on the topic of mechanical puzzles.
Pocket cube with one layer partially turned. The group theory of the 3×3×3 cube can be transferred to the 2×2×2 cube. [3] The elements of the group are typically the moves of that can be executed on the cube (both individual rotations of layers and composite moves from several rotations) and the group operator is a concatenation of the moves.
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 ...
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These puzzles do indeed have efficient solutions. It doesn't work for more general sliding-block puzzles. The fact that general sliding-block puzzles are PSPACE-complete to solve means that effectively, you can build computers out of sliding-block puzzles. Here is another paper, more accessible than the above references, which shows this: Hearn ...