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The knight's tour problem is the mathematical problem of finding a knight's tour. Creating a program to find a knight's tour is a common problem given to computer science students. [ 3 ] Variations of the knight's tour problem involve chessboards of different sizes than the usual 8 × 8 , as well as irregular (non-rectangular) boards.
Koltanowski's most sensational chess entertainment was the ancient exercise known as the Knight's tour, in which a lone knight traverses an otherwise empty board visiting each square once only. Of the countless patterns for achieving this feat, there are trillions of sequences for performing the more restricted version known as the re-entrant ...
Chess puzzles can also be regular positions from actual games, usually meant as tactical training positions. They can range from a simple "Mate in one" combination to a complex attack on the enemy king. Solving tactical chess puzzles is a very common chess teaching technique. They are helpful in pattern recognition.
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A mathematical chess problem is a mathematical problem which is formulated using a chessboard and chess pieces. These problems belong to recreational mathematics.The most well-known problems of this kind are the eight queens puzzle and the knight's tour problem, which have connection to graph theory and combinatorics.
A Hamiltonian cycle on the knight's graph is a (closed) knight's tour. [1] A chessboard with an odd number of squares has no tour, because the knight's graph is a bipartite graph (each color of squares can be used as one of two independent sets , and knight moves always change square color) and only bipartite graphs with an even number of ...
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Even earlier, Hamiltonian cycles and paths in the knight's graph of the chessboard, the knight's tour, had been studied in the 9th century in Indian mathematics by Rudrata, and around the same time in Islamic mathematics by al-Adli ar-Rumi. In 18th century Europe, knight's tours were published by Abraham de Moivre and Leonhard Euler. [2]