Script that solves the wooden snake cube puzzle.

snake_cube.py

#!/usr/bin/env python3

directions = [
    (1, 0, 0), (0, 1, 0), (0, 0, 1),
    (-1, 0, 0), (0, -1, 0), (0, 0, -1),
]


def new_position(position, direction, length):
    length -= 1
    new_pos = [pos + dir*length for pos, dir in zip(position, direction)]
    for coord in new_pos:
        if not 0 <= coord < 3:
            return None
    return new_pos


def clone_state(state):
    new_state = []
    for x in state:
        new_row = []
        new_state.append(new_row)
        for y in x:
            new_col = []
            new_row.append(new_col)
            for z in y:
                new_col.append(z)
    return new_state


def modify_state(state, pos, direction, length):
    """Return a new state, if valid, othrewise return None."""
    new_pos = new_position(pos, direction, length)
    if not new_pos:
        return None

    state = clone_state(state)
    # Don't count the first one, which will already
    # be set to 1.
    length -= 1
    while length:
        x = pos[0] + direction[0] * length
        y = pos[1] + direction[1] * length
        z = pos[2] + direction[2] * length

        if state[x][y][z] == 1:
            return None
        state[x][y][z] = 1
        length -= 1
    return state, new_pos


def crack(state, position, lens):
    global directions

    if len(lens) == 0:
        return []

    for direction in directions:
        state_pos = modify_state(state, position, direction, lens[0])
        if not state_pos:
            continue

        new_state, new_pos = state_pos
        dirs = crack(new_state, new_pos, lens[1:])
        if dirs is not None:
            dirs.insert(0, direction)
            return dirs

    return None


if __name__ == "__main__":
    lengths = [3, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3]
    state = [
        [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
        [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
        [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
    ]

    # Try all posible initial states
    for x in range(3):
        for y in range(3):
            for z in range(3):
                state[x][y][z] = 1
                res = crack(state, (x, y, z), lengths)
                if res:
                    print(state)
                    print(res)
                    print()
                state[x][y][z] = 0