Task: Knight's tour
C#: using System;
using System.Collections.Generic;

namespace prog
{
	class MainClass
	{	
		const int N = 8;
		
		readonly static int[,] moves = { {+1,-2},{+2,-1},{+2,+1},{+1,+2},
			                         {-1,+2},{-2,+1},{-2,-1},{-1,-2} };
		struct ListMoves
		{
			public int x, y;			
			public ListMoves( int _x, int _y ) { x = _x; y = _y; }
		}		
		
		public static void Main (string[] args)
		{
			int[,] board = new int[N,N];
			board.Initialize();
			
			int x = 0,						
			    y = 0;
			
			List<ListMoves> list = new List<ListMoves>(N*N);
			list.Add( new ListMoves(x,y) );
						
			do
			{								
				if ( Move_Possible( board, x, y ) )
				{										
					int move = board[x,y];					
					board[x,y]++;
					x += moves[move,0];
					y += moves[move,1];			
					list.Add( new ListMoves(x,y) );							
				}
				else
				{					
					if ( board[x,y] >= 8 )
					{						
						board[x,y] = 0;																
						list.RemoveAt(list.Count-1);						
						if ( list.Count == 0 )
						{
							Console.WriteLine( "No solution found." );
							return;
						}		
						x = list[list.Count-1].x;
						y = list[list.Count-1].y;						
					}
					board[x,y]++;
				}				
			}
			while( list.Count < N*N );
			
			int last_x = list[0].x,
			    last_y = list[0].y;
			string letters = "ABCDEFGH";
			for( int i=1; i<list.Count; i++ )
			{				
				Console.WriteLine( string.Format("{0,2}:  ", i) + letters[last_x] + (last_y+1) + " - " + letters[list[i].x] + (list[i].y+1) );
				
				last_x = list[i].x;
				last_y = list[i].y;
			}
		}
		
		static bool Move_Possible( int[,] board, int cur_x, int cur_y )
		{			
			if ( board[cur_x,cur_y] >= 8 ) 
				return false;
			
			int new_x = cur_x + moves[board[cur_x,cur_y],0],
			    new_y = cur_y + moves[board[cur_x,cur_y],1];
			
			if ( new_x >= 0 && new_x < N && new_y >= 0 && new_y < N && board[new_x,new_y] == 0 )
				return true;
			
			return false;
		}
	}
}

Python: import copy

boardsize=6
_kmoves = ((2,1), (1,2), (-1,2), (-2,1), (-2,-1), (-1,-2), (1,-2), (2,-1)) 


def chess2index(chess, boardsize=boardsize):
    'Convert Algebraic chess notation to internal index format'
    chess = chess.strip().lower()
    x = ord(chess[0]) - ord('a')
    y = boardsize - int(chess[1:])
    return (x, y)
    
def boardstring(board, boardsize=boardsize):
    r = range(boardsize)
    lines = ''
    for y in r:
        lines += '\n' + ','.join('%2i' % board[(x,y)] if board[(x,y)] else '  '
                                 for x in r)
    return lines
    
def knightmoves(board, P, boardsize=boardsize):
    Px, Py = P
    kmoves = set((Px+x, Py+y) for x,y in _kmoves)
    kmoves = set( (x,y)
                  for x,y in kmoves
                  if 0 <= x < boardsize
                     and 0 <= y < boardsize
                     and not board[(x,y)] )
    return kmoves

def accessibility(board, P, boardsize=boardsize):
    access = []
    brd = copy.deepcopy(board)
    for pos in knightmoves(board, P, boardsize=boardsize):
        brd[pos] = -1
        access.append( (len(knightmoves(brd, pos, boardsize=boardsize)), pos) )
        brd[pos] = 0
    return access
    
def knights_tour(start, boardsize=boardsize, _debug=False):
    board = {(x,y):0 for x in range(boardsize) for y in range(boardsize)}
    move = 1
    P = chess2index(start, boardsize)
    board[P] = move
    move += 1
    if _debug:
        print(boardstring(board, boardsize=boardsize))
    while move <= len(board):
        P = min(accessibility(board, P, boardsize))[1]
        board[P] = move
        move += 1
        if _debug:
            print(boardstring(board, boardsize=boardsize))
            input('\n%2i next: ' % move)
    return board

if __name__ == '__main__':
    while 1:
        boardsize = int(input('\nboardsize: '))
        if boardsize < 5:
            continue
        start = input('Start position: ')
        board = knights_tour(start, boardsize)
        print(boardstring(board, boardsize=boardsize))