To disable a bomb, Detective John McClane must measure out exactly 4 gallons of water, and place the resulting weight on a scale. His tools are yours: a 3-gallon and a 5-­gallon jug—and a single fountain. https://www.popsci.com/solve-water-puzzle-die-hard-3/

buckets.py

from dataclasses import dataclass
from typing import Optional, Callable


def fill_b3(b3, b5):
    return 3, b5

def fill_b5(b3, b5):
    return b3, 5

def empty_b3(b3, b5):
    return 0, b5

def empty_b5(b3, b5):
    return b3, 0

def b3_into_b5(b3, b5):
    return max(0, b3 - (5 - b5)), min(5, b3+b5)

def b5_into_b3(b3, b5):
    return min(3, b3 + b5), max(0, b5 - (3-b3))


ACTIONS = [fill_b3, fill_b5, empty_b3, empty_b5, b3_into_b5, b5_into_b3]


ACTION_2_DESC = {
    fill_b3: "Fill bucket3 from the well. End state is: ",
    fill_b5: "Fill bucket5 from the well. End state is: ",
    empty_b3: "Empty bucket3. End state is: ",
    empty_b5: "Empty bucket5. End state is: ",
    b3_into_b5: "Move the contents of bucket3 into bucket5. End state is: ",
    b5_into_b3: "Move the contents of bucket5 into bucket3. End state is: ",
    None: ""
}


@dataclass()
class Node:
    state: tuple[int, int]
    parent: Optional["Node"] = None
    func: Optional[Callable] = None


def find_solution():
    seen_states = {(0, 0)}
    root = Node((0, 0))
    current_level = [root]
    while True:
        new_level = []
        for node in current_level:
            for action in ACTIONS:
                end_state = action(*node.state)
                if end_state not in seen_states:
                    seen_states.add(end_state)
                    new_node = Node(end_state, node, action)
                    new_level.append(new_node)
                    if sum(end_state) == 4:
                        return new_node
        current_level = new_level


def print_lineage(node):
    parent = node.parent
    lineage = []
    while True:
        if parent is None:
            break
        lineage.insert(0, node)
        node = node.parent
        parent = node.parent

    for node in lineage:
        print(ACTION_2_DESC[node.func], node.state)


if __name__ == "__main__":
    print_lineage(find_solution())

results.txt

Fill bucket3 from the well. End state is:  (3, 0)
Move the contents of bucket3 into bucket5. End state is:  (0, 3)
Fill bucket3 from the well. End state is:  (3, 3)
Move the contents of bucket3 into bucket5. End state is:  (1, 5)
Empty bucket5. End state is:  (1, 0)
Move the contents of bucket3 into bucket5. End state is:  (0, 1)
Fill bucket3 from the well. End state is:  (3, 1)