The Knight’s Tour problem is a classic algorithmic problem that asks you to find a sequence of moves for a knight on a chessboard such that the knight visits every square exactly once. Here is an example of how to solve this problem in Python using a backtracking algorithm:

```
def knights_tour(n):
board = [[-1] * n for _ in range(n)]
moves = [(2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2), (1, -2), (2, -1)]
def backtrack(row, col, num_moves):
if num_moves == n**2:
return True
for move in moves:
new_row = row + move[0]
new_col = col + move[1]
if 0 <= new_row < n and 0 <= new_col < n and board[new_row][new_col] == -1:
board[new_row][new_col] = num_moves
if backtrack(new_row, new_col, num_moves+1):
return True
board[new_row][new_col] = -1
return False
# start
```

In this solution, we use a nested function `backtrack`

to recursively generate all possible solutions to the Knight’s Tour problem. The function takes three input values: `row`

, `col`

, and `num_moves`

.

`row`

and `col`

represent the current row and column on the chessboard, and `num_moves`

represents the number of moves the knight has made so far.

In the main function, we first initialize a 2D list `board`

of size `n`

by `n`

with all values set to -1. We also define a list `moves`

of all possible knight moves.

Then, we call `backtrack`

with initial values of 0, 0, and 1 to start the knight’s tour from the top-left corner of the board.

Inside the `backtrack`

function, we first check if the knight has visited every square on the board (`num_moves == n**2`

). If this is the case, we return `True`

to indicate that a solution has been found.

Otherwise, we iterate through each possible knight move from the current square. If the move is valid (i.e., it does not go off the board and does not visit a square that has already been visited), we update the `board`

with the new move and recursively call `backtrack`

with the updated values of `row`

, `col`

, and `num_moves`

.

If the recursive call returns `True`

, we return `True`

to indicate that a solution has been found. Otherwise, we undo the last move by resetting the `board`

at the new square to -1.

Finally, in the main function, we return the `board`

if a solution has been found, and `None`

otherwise.

To use this function, simply call `knights_tour(n)`

with the appropriate integer value of `n`

. The function will return a 2D list representing a valid knight’s tour on an `n`

by `n`

chessboard, or `None`

if no valid tour exists.

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