snakepath.py

def snakepath(path, size):
    x = path[-1]%size
    y = path[-1]//size
    possible = []

    if 0 <= y-1 and path[-1]-size not in path: #up
        possible.append(path[-1]-size)
    if 0 <= x-1 and path[-1]-1 not in path: #left
        possible.append(path[-1]-1)
    if x+1 < size and path[-1]+1 not in path: #right
        possible.append(path[-1]+1)
    if y+1 < size and path[-1]+size not in path: #down
        possible.append(path[-1]+size)

    for direction in possible:
        new = path+(direction,)
        yield new
        for p in snakepath(new, size):
            yield p

size = 6
start = 0, 1

for path in snakepath(start, size):
    if len(path) == size**2 and path[-1] == size:
        print(*path, sep='-')