# Knight's Tour

A **knight's tour** is a sequence of moves of a knight on a chessboard 
such that the knight visits every square only once. If the knight 
ends on a square that is one knight's move from the beginning 
square (so that it could tour the board again immediately, 
following the same path), the tour is **closed**, otherwise it 
is **open**.

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.
Variations of the knight's tour problem involve chessboards of 
different sizes than the usual `8×8`, as well as irregular 
(non-rectangular) boards.

The knight's tour problem is an instance of the more 
general **Hamiltonian path problem** in graph theory. The problem of finding 
a closed knight's tour is similarly an instance of the Hamiltonian 
cycle problem.

![Knight's Tour](https://upload.wikimedia.org/wikipedia/commons/d/da/Knight%27s_tour_anim_2.gif)

An open knight's tour of a chessboard.

![Knight's Tour](https://upload.wikimedia.org/wikipedia/commons/c/ca/Knights-Tour-Animation.gif)

An animation of an open knight's tour on a 5 by 5 board.

## References

- [Wikipedia](https://en.wikipedia.org/wiki/Knight%27s_tour)
- [GeeksForGeeks](https://www.geeksforgeeks.org/backtracking-set-1-the-knights-tour-problem/)