solutions.py

import copy

solution_count = 0

def dfs(start, path = []):
    if start in path:
        return

    path.append(start)
    if len(path) == 9:
        print path
        global solution_count
        solution_count += 1
        return

    for i in adj_list[start]:
        dfs(i, copy.deepcopy(path))

row = [0, 1, 1, 1, 2, 2, 2, 3, 3, 3]
col = [0, 1, 2, 3, 1, 2, 3, 1, 2, 3]

grid = [[0, 0, 0, 0],
        [0, 1, 2, 3],
        [0, 4, 5, 6],
        [0, 7, 8, 9]]

adj_list = list()
for i in xrange(10):
    adj_list.append(list())

valid_movement = [[1, 1], [1, -1], [-1, 1], [-1, -1], [1, 2], [1,-2], [-1, 2], [-1,-2], [2, 1], [2, -1], [-2, 1], [-2, -1]]
rm = 0
cm = 1

for i in xrange(1, 10):
    for move in valid_movement:
        r = row[i] + move[rm]
        c = col[i] + move[cm]
        if 1 <= r <= 3 and 1 <= c <= 3:
            adj_list[i].append(grid[r][c])

for i in adj_list:
    i.sort()

for x in xrange(1,10):
    dfs(x, [])
print solution_count, 'solutions'