4_sat_mysterious_manor.py

# The Mysterious Manor

'''
In a secluded and eerie manor nestled deep in the misty woods, there lies a collection of enchanted artifacts. Each artifact possesses its own unique dark power. The eccentric owner of the manor, Count Mortimer, has set specific rules for arranging the artifacts in his collection:

    Rule 1: Each artifact must be placed in a different location within the manor.
    Rule 2: Certain pairs of artifacts have conflicting energies and should not be placed together.

Your task is to determine if it is possible to arrange Count Mortimer's artifacts in the manor while satisfying these rules. We can encode this problem as a SAT problem.

Let's assume Count Mortimer has five artifacts in his collection, labeled from 1 to 5. We can use variables x1, x2, x3, x4, and x5 to represent the locations of the artifacts within the manor.

To encode the rules, we can define the following clauses:

    Rule 1: Each artifact must be placed in a different location within the manor:
        Clause 1: (-x1 v -x2) AND (-x1 v -x3) AND (-x1 v -x4) AND (-x1 v -x5)
        Clause 2: (-x2 v -x3) AND (-x2 v -x4) AND (-x2 v -x5)
        Clause 3: (-x3 v -x4) AND (-x3 v -x5)
        Clause 4: (-x4 v -x5)

    Rule 2: Certain pairs of artifacts have conflicting energies and should not be placed together:
        Clause 5: (-x1 v -x2)
        Clause 6: (-x2 v -x3)
        Clause 7: (-x4 v -x5)
'''

import pycosat

def arrange_artifacts():
    clauses = [
        [-1, -2], [-1, -3], [-1, -4], [-1, -5],       # Rule 1: Unique locations
        [-2, -3], [-2, -4], [-2, -5], # Rule 1: Unique locations
        [-3, -4], [-3, -5], # Rule 1: Unique locations
        [-4, -5], # Rule 1: Unique locations
        [-1, -2], # Rule 2: Conflicting artifacts
        [-2, -3], # Rule 2: Conflicting artifacts
        [-4, -5] # Rule 2: Conflicting artifacts
        ]

solution = pycosat.solve(clauses)
if solution != "UNSAT":
    arrangement = ""
    for i in range(5):
        artifact = abs(solution[i])
        location = i + 1
        arrangement += f"Artifact {artifact} at Location {location}\n"
    return arrangement
else:
    return "No valid arrangement exists."

artifact_arrangement = arrange_artifacts()
print("The valid arrangement of artifacts is:\n", artifact_arrangement)